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In Carius method of estimation of halogen. 0.45 g of an organic compound gave 0.36 g of AgBr. Find out...

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250 g solution of D-glucose in water contains 10.8% of carbon by weight. The molality of the solution is nearest...

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Which among the following represent reagent 'A'?

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Stability of $\alpha$ - Helix structure of proteins depends upon

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For $z \in \mathbb{Z}$ if the minimum value of $(|z-3 \sqrt{2}|+|z-p \sqrt{2} i|)$ is $5 \sqrt{2}$, then a value of...

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Let the area enclosed by the $x$-axis, and the tangent and normal drawn to the curve $...

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If the circles $x^2+y^2+6 x+8 y+16=0$ and $x^2+y^2+2^{(3-\sqrt{3})} x+2^{(4-\sqrt{6})} y=k+6 \sqrt{3}+8 \sqrt{6}, k>0$, touch internally at the point $\mathbf{P}(\alpha, \beta)$,...

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Let $a_n=\int_{-1}^n\left(1+\frac{x}{2}+\frac{x^2}{3}+\ldots . .+\frac{x^{n-1}}{n}\right) d x$ for every $n \in N$. Then the sum of all the elements of the...

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Let $f$ be a twice differentiable function on $R$. If $f^{\prime}(0)=4$ and $...

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The sum of the maximum and minimum values of the function $f(x)=|5 x-7|+\left[x^2+2 x\right]$ in the interval $\left[\frac{5}{4}, 2\right]$, where...

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Let $...

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Let $f(x)$ be a quadratic polynomial with leading coefficient 1 such that $f(0)=p, p \neq 0$, and $f(1)=\frac{1}{3}$. If the...

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Let $A=\{1,2,3,4,5,6,7\}$. Define $B=\{T \subseteq A$ : either $1 \notin T$ or $2 \in T\}$ and $C=\{T \subseteq A: T$...

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Consider the following statements : P : Ramu is intelligent. Q : Ramu is rich. R : Ramu is not...

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$2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\frac{7 \pi}{22}\right) \sin \left(\frac{9 \pi}{22}\right)$ is equal to :

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If the mean deviation about median for the number 3, 5, 7, 2k, 12, 16, 21, 24 arranged in the...

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The shortest distance between the lines $\frac{x+7}{-6}=\frac{y-6}{7}=z$ and $\frac{7-x}{2}=y-2=z-6$ is

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A plane $E$ is perpendicular to the two planes $2 x-2 y+z=0$ and $x-y+2 z=4$, and passes through the point...

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Let the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{7}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{\alpha}=\frac{1}{25}$ coincide. Then the length of the latus rectum of...

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The tangents at the points $A(1,3)$ and $B(1,-1)$ on the parabola $y^2-2 x-2 y=1$ meet at the point $P$. Then...

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If the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets the line $\frac{x}{7}+\frac{y}{2 \sqrt{6}}=1$ on the $x$-axis and the line $\frac{x}{7}-\frac{y}{2 \sqrt{6}}=1$ on the $y$-axis,...

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Let a smooth curve $y=f(x)$ be such that the slope of the tangent at any point ( $x, y$ )...

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Let the point $\mathrm{P}(\alpha, \beta)$ be at a unit distance from each of the two lines $\mathrm{L}_1: 3 \mathrm{x}-4 \mathrm{y}+12=0$,...

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Let $[t]$ denote the greatest integer less than or equal to $t$. Then the value of the integral $$ \int_{-3}^{101}\left([\sin...

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If $A$ and $B$ are two events such that $P(A)=\frac{1}{3}, P(B)=\frac{1}{5}$ and $P(A \cup B)=\frac{1}{2}$, then $...

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$\lim _{n \rightarrow \infty} \frac{1}{2^n}\left(\frac{1}{\sqrt{1-\frac{1}{2^n}}}+\frac{1}{\sqrt{1-\frac{2}{2^n}}}+\frac{1}{\sqrt{1-\frac{3}{2^n}}}+\ldots \ldots+\frac{1}{\sqrt{1-\frac{2^n-1}{2^n}}}\right)$ is equal to

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$$ \lim _{x \rightarrow \frac{\pi}{4}} \frac{8 \sqrt{2}-(\cos x+\sin x)^7}{\sqrt{2}-\sqrt{2} \sin 2 x} $$ is equal to

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Production of iron in blast furnace follows the following equation $\mathrm{Fe}_3 \mathrm{O}_4(\mathrm{~s})+4 \mathrm{CO}(\mathrm{g}) \rightarrow 3 \mathrm{Fe}(\mathrm{l})+4 \mathrm{CO}_2(\mathrm{~g})$ when 4.640 kg...

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Let $\ell$ be a line which is normal to the curve $y=2 x^2+x+2$ at a point $P$ on the curve....

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The number of real solutions of $x^7+5 x^3+3 x+1=0$ is equal to $\_\_\_\_$ .

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Two inclined planes are placed as shown in figure. A block is projected from the Point A of inclined plane...

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A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the...

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A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If...

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A wire of length 30 cm, stretched between rigid supports, has it’s $\mathrm{n}^{\text {th }}$ and $(n+1)^{t h}$ harmonics at...

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A parallel plate capacitor with width 4 cm, length 8 cm and separation between the plates of 4 mm is...

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As show in the figure, in steady state, the charge stored in the capacitor is ………… $\times 10^{-6} \mathrm{C}$.

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A conducting circular loop is placed in X – Y plane in presence of magnetic field $...

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A thin prism of angle 6º and refractive index for yellow light $\left(n_Y\right)$ 1.5 is combined with another prism of...

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In the given figure of meter bridge experiment, the balancing length AC corresponding to null deflection of the galvanometer is...

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In an experiment to determine the Young’s modulus, steel wires of five different lengths (1,2,3, 4 and 5 m) but...

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A square wave of the modulating signal is shown in the figure. The carrier wave is given by C(t) =...

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For a constant collector-emitter voltage of 8V, the collector current of a transistor reached to the value of 6 mA...

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The activity of a radioactive material is $6.4 \times 10^{-4}$ curie. Its half life is 5 days. The activity will...

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With reference to the observations in photo-electric effect, identify the correct statements from below: A. The square of maximum velocity...

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Two coherent sources of light interfere. The intensity ratio of two sources is 1 : 4. For this interference pattern...

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Identify the correct statements from the following descriptions of various properties of electromagnetic waves. A. In a plane electromagnetic wave...

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A series LCR circuit has L = 0.01 H, R = 10 $\Omega$ and C = 1 $\mu \mathrm{F}$ and...

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A cyclotron in used to accelerate protons. If the operating magnetic field is 1.0 T and the radius of the...

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A compass needle of oscillation magnetometer oscillates 20 times per minute at a place P of dip $30^{\circ}$ The number...

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A. The drift velocity of electrons decreases with the increase in the temperature of conductor. B. The drift velocity is...

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A charge of $4 \mu \mathrm{C}$ is to be divided into two. The distance between the two divided charges is...

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Let Q and R be two points on the line $\frac{x+1}{2}=\frac{y+2}{3}=\frac{z-1}{2}$ at a distance $\sqrt{26}$ from the point $P(4,2,7)$. Then...

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Let the function $f(x)=2 x^2-$ logex, $x>0$, be decreasing in (0, a) and increasing in (a, 4). A tangent to...

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The equations of the sides $A B, B C$ and $C A$ of a triangle $A B C$ are $...

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Let a curve $y=y(x)$ pass through the point $(3,3)$ and the area of the region under this curve, above the...

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If $n(2 n+1) \int_0^1\left(1-x^n\right)^{2 n} d x=1177 \int_0^1\left(1-x^n\right)^{2 n+1} d x, n \in N$ is equal to $\_\_\_\_$

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1`$x$ and $x^2$ in the expansion of $(1+x)^p(1-x)^q, p, q \leq 15$, are -3 and -5 respectively, then the coefficient...

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The number of distinct real roots of the equation $x^5\left(x^3-x^2-x+1\right)+x\left(3 x^3-4 x^2-2 x+4\right)-1=0$ is

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The series of positive multiples of 3 is divided into sets : {3}, {6, 9,12}, {15, 18, 21, 24, 27},......

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The number of 5-digit natural numbers, such that the product of their digits is 36, is

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If for some p, q, r in R, not all have same sign, one of the roots of the equation...

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The statement $(\sim(p \Leftrightarrow \sim q)) \wedge q$ is:

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$\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)$ is equal to:

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Let $S=\left\{\theta \in[0,2 \pi]: 8^{2 \sin ^2 \theta}+8^{20 \cos ^2 \theta}=16\right\}$. Then $n(S)+\sum_{\theta \in S}\left(\sec \left(\frac{\pi}{4}+2 \theta\right) \operatorname{cosec}\left(\frac{\pi}{4}+2 \theta\right)\right)$ is...

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For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which...

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Match List I with List II

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The metal complex that is diamagnetic is (Atomic number : Fe, 26; Cu, 29)

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R....

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R....

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The products obtained from a reaction of hydrogen peroxide and acidified potassium permanganate are

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The metal that is not extracted from its sulphide ore is :

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The metal that has very low melting point and its periodic position is closer to a metalloid is :

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R....

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At $30^{\circ} \mathrm{C}$, the half life for the decomposition of $\mathrm{AB}_2$ is 200 s and is independent of the initial...

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Class XII students were asked to prepare one litre of buffer solution of pH 8.26 by their chemistry teacher. The...

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If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions of $\lambda$, where $\frac{C}{V}=\lambda$ ?

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Let $E_1, E_2, E_3$ be three mutually exclusive events such that $P\left(E_1\right)=\frac{2+3 p}{6}, P\left(E_2\right)=\frac{2-p}{8}$ and $P\left(E_3\right)=\frac{1-p}{2}$. If the maximum and...

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The mean and variance of a binomial distribution are $\alpha$ and $\frac{\alpha}{3}$ respectively. If $P(X=1)=\frac{4}{243}$, then $P(X=4$ or 5) is...

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The total number of monobromo derivatives formed by the alkanes with molecular formula $\mathrm{C}_5 \mathrm{H}_{12}$ is (excluding stereo isomers).

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Let $\vec{a}=\alpha \hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=2 \hat{i}+\hat{j}-\alpha \hat{k}, \alpha>0$. If the projection of $\vec{a} \times \vec{b}$ on the vector $...

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The length of the perpendicular from the point (1, –2, 5) on the line passing through (1, 2, 4) and...

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Let the tangent drawn to the parabola $\mathrm{y}^2=24 \mathrm{x}$ at the point $(\alpha, \beta)$ is perpendicular to the line $...

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Optical activity of an enantiomeric mixture is +12.6° and the specific rotation of (+) isomer is +30°. The optical purity...

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A point P moves so that the sum of squares of its distances from the points (1, 2) and (–2,...

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If $\frac{d y}{d x}+2 y \tan x=\sin x, 0

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In the titration of $\mathrm{KMnO}_4$ and oxalic acid in acidic medium, the change in oxidation number of carbon at the...

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The separation of two coloured substances was done by paper chromatography. The distances travelled by solvent front, substance A and...

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The conductivity of a solution of complex with formula $\mathrm{CoCl}_3\left(\mathrm{NH}_3\right)_4$ corresponds to $1: 1$ electrolyte, then the primary valency of...

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If $a=\lim _{n \rightarrow \infty} \sum_{k=1}^n \frac{2 n}{n^2+k^2}$ and $f(x)=\sqrt{\frac{1-\cos x}{1+\cos x}}, x \in(0,1)$, then :

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At 310 K , the solubility of $\mathrm{CaF}_2$ in water is $2.34 \times 10^{-3} \mathrm{~g} / 100 \mathrm{~mL}$. The solubility...

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The line of shortest distance between the lines $\frac{x-2}{0}=\frac{y-1}{1}=\frac{z}{1}$ and $\frac{x-3}{2}=\frac{y-5}{2}=\frac{z-1}{1}$ makes an angle of $\cos ^{-1}\left(\sqrt{\frac{2}{27}}\right)$ with the plane...

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Let $f(x)=\left\{\begin{array}{ll}x^3-x^2+10 x-7 & , x \leq 1 \\ -2 x+\log _2\left(b^2-4\right) & , x>1\end{array}\right.$. Then the set of all...

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According to MO theory, number of species/ions from the following having identical bond order is _____:$\mathrm{CN}^{-}, \mathrm{NO}^{+}, \mathrm{O}_2, \mathrm{O}_2^{+}, \mathrm{O}_2^{2+}$

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The sum of diameters of the circles that touch (i) the parabola $75 x^2=64(5 y-3)$ at the point $\left(\frac{8}{5}, \frac{6}{5}\right)$...

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The number of chlorine atoms in bithionol is ____.

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If $f(x)=\left\{\begin{array}{cc}x+a, & x \leq 0 \\ |x-4|, & x>0\end{array}\right.$ and $g(x)=\left\{\begin{array}{cc}x+1, & x

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The molar heat capacity for an ideal gas at constant pressure is $20.785 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$. The change in internal...

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Let the equation of two diameters of a circle $x^2+y^2-2 x+2 f y+1=0$ be $2 p x-y=1$ and $...

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Amongst the following the number of oxide(s) which are paramagnetic in nature is $...

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If the function $f(x)=\left\{\frac{\log e\left(1-x+x^2\right)+\log e\left(1+x+x^2\right)}{\sec x-\cos x}, x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)-\{0\}\right.$ is continuous at $x=0$, then $k$ is equal to:...

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If $\lim _{n \rightarrow \infty} \frac{(n+1)^{k-1}}{n^{k+1}}[(n k+1)+(n k+2)+\ldots+(n k+n)]=33 . \lim _{n \rightarrow \infty} \frac{1}{n^{k+1}}\left[1^k+2^k+3^k+\ldots . .+n^k\right]$, then the integral...

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Consider two G.Ps. $2,2^2, 2^3$, ann and $4,4^2, 4^3$ of 60 and $n$ terms respectively. If the geometric mean of...

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Let $...

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Let $a_1=b_1=1, a_n=a_{n-1}+2$ and $b_n=a_n+b_{n-1}$ for every natural number $n \geq 2$. Then $\sum_{n=1}^{15} a_n \cdot b_n$ is equal to$\_\_\_\_$...

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20 mL of $0.02 \mathrm{M} \mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ solution is used for the titration of 10 mL of $\mathrm{Fe}^{2+}$ solution...

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The odd natural number $a$, such that the area of the region bounded by $y=1, y=3, x \mid=0, x=y^a$ is...

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Let $a, b$ be two non-zero real numbers. If $p$ and $r$ are the roots of the equation $...

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If the maximum value of the term independent of $t$ in the expansion of $\left(t^2 x^{\frac{1}{5}}+\frac{(1-x)^{\frac{1}{10}}}{t}\right)^{15}, x \geq 0$ is...

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Let A be a 2 × 2 matrix with det (A) = –1 and det ((A + I) (Adj (A)...

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The number of stereoisomers formed in a reaction of $( \pm) \mathrm{Ph}(\mathrm{C}=\mathrm{O}) \mathrm{C}(\mathrm{OH})(\mathrm{CN}) \mathrm{Ph}$ with HCN is $\_\_\_\_$ .

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A car covers $A B$ distance with first one-third at velocity $\mathrm{v}_1 \mathrm{~ms}^{-1}$, second one-third at $\mathrm{v}_2 \mathrm{~ms}^{-1}$ and last...

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The letters of the word ‘MANKIND’ are written in all possible orders and arranged in serial order as in an...

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If the system of linear equations. $$ \begin{aligned} & 8 x+y+4 z=-2 \\ & x+y+z=0 \\ & \lambda x-3 y=\mu...

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Let $A=\left[\begin{array}{ccc}2 & -1 & -1 \\ 1 & 0 & -1 \\ 1 & -1 & 0\end{array}\right]$ and $B=A-I$....

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A 1.84 mg sample of polyhydric alcoholic compound ' $X$ ' of molar mass $92.0 \mathrm{~g} / \mathrm{mol}$ gave 1.344...

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Which of the following statements is a tautology?

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Let $O$ be the origin and $A$ be the point $z 1=1+2 i$. If $B$ is the point $...

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A tower $P Q$ stands on a horizontal ground with base $Q$ on the ground. The point $R$ divides the...

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A sample of 4.5 mg of an unknown monohydric alcohol, $\mathrm{R}-\mathrm{OH}$ was added to methylmagnesium iodide. A gas is evolved...

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A sugar 'X' dehydrates very slowly under acidic condition to give furfural which on further reaction with resorcinol gives the...

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On complete combustion of 0.492 g of an organic compound containing $\mathrm{C}, \mathrm{H}$ and $\mathrm{O}, 0.7938 \mathrm{~g}$ of $\mathrm{CO}_2$ and...

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A uniform disc with mass $M=4 \mathrm{~kg}$ and radius $R=10 \mathrm{~cm}$ is mounted on a fixed horizontal axle as shown...

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The number of solutions of $|\cos x|=\sin x$, such that $-4 \pi \leq x \leq 4 \pi$ is in

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Match List I with List II Choose the correct answer from the options given below:

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Let $f: R \rightarrow R$ be a continuous function such that $f(3 x)-f(x)=x$. If $f(8)=7$, then $f(14)$ is equal to:

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Consider the following sulphure based oxoacids. $$ \mathrm{H}_2 \mathrm{SO}_3, \mathrm{H}_2 \mathrm{SO}_4, \mathrm{H}_2 \mathrm{~S}_2 \mathrm{O}_8 \text { and } \mathrm{H}_2 \mathrm{~S}_2...

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The spin-only magnetic moment value of $\mathrm{M}^{3+}$ ion (in gaseous state) from the pair $\mathrm{Cr}^{3+} / \mathrm{Cr}^{2+}, \mathrm{Mn}^{3+} / \mathrm{Mn}^2$,...

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If the numbers appeared on the two throws of a fair six faced die are $a$ and $b$, then the...

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If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then...

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The sum of number of lone pairs of electrons present on the central atoms of $\mathrm{XeO}_3, \mathrm{XeOF}_4$ and $\mathrm{XeF}_6$ is

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A liquid of density $750 \mathrm{kgm}^{-3}$ flows smoothly through a horizontal pipe that tapers in cross-sectional area from $...

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Let ABC be a triangle such that $\overrightarrow{\mathrm{BC}}=\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{CA}}=\overrightarrow{\mathrm{b}}, \overrightarrow{\mathrm{AB}}=\overrightarrow{\mathrm{c}},|\overrightarrow{\mathrm{a}}|=6 \sqrt{2},|\overrightarrow{\mathrm{~b}}|=2 \sqrt{3}$ and $\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}=12$ Consider the statements: $...

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Sum of oxidation state (magnitude) and coordination number of cobalt in $\mathrm{Na}\left[\mathrm{Co}(\mathrm{bpy}) \mathrm{Cl}_4\right]$ is $\_\_\_\_$ .

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Let P be the plane containing the straight line $\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{-5}$ and perpendicular to the plane containing the straight lines $\frac{x}{2}=\frac{y}{3}=\frac{z}{5}$...

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Total number of relatively more stable isomer(s) possible for octahedral complex $\left[\mathrm{Cu}(\mathrm{en})_2(\mathrm{SCN})_2\right]$ will be $\_\_\_\_$ .

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A tuning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm...

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Let the locus of the centre $(\alpha, \beta), \beta>0$, of the circle which touches the circle $x^2+(y-1)^2=1$ externally and also...

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The disproportionation of $\mathrm{MnO}_4^{2-}$ in acidic medium resulted in the formation of two manganese compounds A and B . If...

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A line, with the slope greater than one, passes through the point $A(4,3)$ and intersects the line $x-y-2=0$ at the...

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Assuming $1 \mu \mathrm{~g}$ of trace radioactive element X with a half life of 30 years is absorbed by a...

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The number of interhalogens from the following having square pyramidal structure is : $$ \mathrm{ClF}_3, \mathrm{IF}_7, \mathrm{BrF}_5, \mathrm{BrF}_3, \mathrm{I}_2 \mathrm{Cl}_6,...

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The general solution of the differential equation $\left(x-y^2\right) d x+y\left(5 x+y^2\right) d y=0$ is :

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For the given first order reaction $$ A \rightarrow B $$ the half life of the reaction is 0.3010 min...

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For the decomposition of azomethane. $\mathrm{CH}_3 \mathrm{~N}_2 \mathrm{CH}_3(\mathrm{~g}) \rightarrow \mathrm{CH}_3 \mathrm{CH}_3(\mathrm{~g})+\mathrm{N}_2(\mathrm{~g})$ a first order reaction, the variation in partial pressure...

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Match List I with List II Choose the correct answer from the options given below:

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The slope of the tangent to a curve $C: y=y(x)$ at any point $[x, y)$ on it is $...

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$\mathrm{K}_{\mathrm{a}}$ for butyric acid $\left(\mathrm{C}_3 \mathrm{H}_7 \mathrm{COOH}\right)$ is $2 \times 10^{-5}$. The pH of 0.2 M solution of butyric acid...

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For a cell, $\mathrm{Cu}(\mathrm{s}) \mid \mathrm{Cu}^{2+}\left(0.001 \mathrm{M}| | \mathrm{Ag}^{+}(0.01 \mathrm{M}) \mid \mathrm{Ag}(\mathrm{s})\right.$ the cell potential is found to be 0.43...

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150 g of acetic acid was contaminated with 10.2 g ascorbic acid $\left(\mathrm{C}_6 \mathrm{H}_8 \mathrm{O}_6\right)$ to lower down its freezing...

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For any real number $x$, let $[x]$ denote the largest integer less than equal to $x$. Let $f$ be a...

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The total number of $\mathrm{Mn}=\mathrm{O}$ bonds in $\mathrm{Mn}_2 \mathrm{O}_7$ is $\_\_\_\_$

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The number of paramagnetic species among the following is $\_\_\_\_$ . $\mathrm{B}_2, \mathrm{Li}_2, \mathrm{C}_2, \mathrm{C}_2^{-}, \mathrm{O}_2^{2-}, \mathrm{O}_2^{+} ;$and $\mathrm{He}_2^{+}$

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The area of the region given by $A=\left\{(x, y): x^2 \leq y \leq \min \{x+2,4-3 x\}\right\}$ is i.

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Given below are two statements: Statement I : Iron (III) catalyst, acidified $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ and neutral $\mathrm{KMnO}_4$ have the...

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1.80 g of solute A was dissolved in $62.5 \mathrm{~cm}^3$ of ethanol and freezing point of the solution was found...

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In the given circuit, the magnitude of $V_L$ and $V_C$ are twice that of $V_R$. Given that $f =50 \mathrm{~Hz}$,...

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An element M crystallises in a body centred cubic unit cell with a cell edge of 300 pm . The...

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A capacitor $\mathrm{C}_1$ of capacitance $5 \mu \mathrm{~F}$ is charged to a potential of 30 V using a battery. The...

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The curve $y(x)=a x^3+b x^2+c x+5$ touches the $x$-axis at the point $P(-2,0)$ and cuts the $y$-axis at the point...

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Which oxoacid of phosphorous has the highest number of oxygen atoms present in its chemical formula?

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In the given reaction, $$ \mathrm{X}+\mathrm{Y}+3 \mathrm{Z} \rightleftarrows \mathrm{XYZ}_3 $$ if one mole of each of $X$ and $Y$ with...

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If the absolute maximum value of the function $f(x)=\left(x^2-2 x+7\right) e^{\left(4 x^3-12 x^2-180 x+31\right)}$ in the interval $[-3,0]$ is $f(\alpha)$,...

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Consider, $\mathrm{PF}_5, \mathrm{BrF}_5, \mathrm{PCl}_3, \mathrm{SF}_6,\left[\mathrm{ICl}_4\right]^{-}, \mathrm{ClF}_3$ and $\mathrm{IF}_5$. Amongst the above molecule(s)/ion(s), the number of molecule(s)/ion(s) having $\mathrm{sp}^3 \mathrm{~d}^2$ hybridisation...

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Given below are two statements: Statement I : The chlorides of Be and Al have Cl-bridged structure. Both are soluble...

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" All resistances in figure are "1Omega" each. The value of current ' "l" ' is "(a)/(5)A". The value of...

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If $\lim _{n \rightarrow \infty}\left(\sqrt{n^2-n-1}+n \alpha+\beta\right)=0$ then $8(\alpha+\beta)$ is equal to :

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The number of $\theta \in(0,4 \pi)$ for which the system of linear equations $...

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Given below are two statements: Statement I : Hydrogen peroxide can act as an oxidizing agent in both acidic and...

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A 10 g mixture of hydrogen and helium is contained in a vessel of capacity $0.0125 \mathrm{~m}^3$ at 6 bar...

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While performing a thermodynamics experiment, a student made the following observations, $...

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For $\mathrm{n} \in \mathrm{N}$, let $\mathrm{S}_{\mathrm{n}}=\left\{\mathrm{z} \in \mathrm{C}:|\mathrm{z}-3+2 \mathrm{i}|=\frac{\mathrm{n}}{4}\right\}$ and $\mathrm{T}_{\mathrm{n}}=\left\{\mathrm{z} \in \mathrm{C}:|\mathrm{z}-2+3 \mathrm{i}|=\frac{1}{4}\right\}$. Then the number of elements in...

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For kinetic study of the reaction of iodide ion with $\mathrm{H}_2 \mathrm{O}_2$ at room temperature : (A) Always use freshly...

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' x ' g of molecular oxygen $\left(\mathrm{O}_2\right)$ is mixed with 200 g of neon $(\mathrm{Ne})$. The total pressure of...

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Which of the following methods are not used to refine any metal? (A) Liquation (B) Calcination (C) Electrolysis (D) Leaching...

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Consider an imaginary ion ${ }_{22}^{48} \mathrm{X}^{3-}$. The nucleus contains ' a ' $\%$ more neutrons than the number of...

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If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4+x^3+x^2+x+1=0$, then $\alpha^{2021}+\beta^{2021}+\gamma^{2021}+\delta^{2021}$ is equal to

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Statements about Enzyme Inhibitor Drugs are given below : (A) There are Competitive and Non–competitive inhibitor drugs. (B) These can...

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When the excited electron of a H atom from n = 5 drops to the ground state, the maximum number...

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The incorrect statement is

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The total number of functions, $f:\{1,2,3,4\} \cdot\{1,2,3,4,5,6\}$ such that $f(1)+f(2)=f(3)$, is equal to :

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For the below given cyclic hemiacetal (X), the correct pyranose structure is :

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A sealed flask with a capacity of $2 \mathrm{dm}^3$ contains 11 g of propane gas. The flask is so weak...

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56.0 L of nitrogen gas is mixed with excess of hydrogen gas and it is found that 20 L of...

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R....

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A compound ' X ' is a weak acid and it exhibits colour change at pH close to the equivalence...

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Boiling point of a 2% aqueous solution of a non¬volatile solute A is equal to the boiling point of 8%...

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In the given reaction (Where Et is $-\mathrm{C}_2 \mathrm{H}_5$ ) The number of chiral carbon/s in product A is

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$\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$ should be an inner orbital complex. Ignoring the pairing energy, the value of crystal field stabilization energy for this...

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Animal starch is the other name of :

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In base vs. Acid titration, at the end point methyl orange is present as

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In bromination of Propyne, with Bromine 1, 1, 2, 2-tetrabromopropane is obtained in 27\% yield. The amount of $1,1,2,2$ tetrabromopropane...

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Identify the correct statement for the below given transformation.

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Vulcanization of rubber is carried out by heating a mixture of :

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The number of $\mathrm{sp}^3$ hybridised carbons in an acyclic neutral compound with molecular formula $\mathrm{C}_4 \mathrm{H}_5 \mathrm{~N}$ is:

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In a linear tetrapeptide (Constituted with different amino acids), (number of amino acids) - (number of peptide bonds) is ______...

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Some drugs bind to a site other than, the active site of an enzyme. This site is known as

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Given below are two statements. One is labeled as Assertion A and the other is labeled as Reason R. Assertion...

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The correct sequential order of the reagents for the given reaction is :

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The reaction between X and Y is first order with respect to X and zero order with respect to Y....

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Given below are two statements. One is labeled as Assertion A and the other is labeled as Reason R. Assertion...

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Glycosidic linkage between $\mathrm{C}_1$ of $\alpha$-glucose and $\mathrm{C}_2$ of $\beta$-fructose is found in

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While estimating the nitrogen present in an organic compound by Kjeldahl's method, the ammonia evolved from 0.25 g of the...

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Identify the major product A and B for the below given reaction sequence.

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Given below are two statements. One is labeled as Assertion A and the other is labeled as Reason R. Assertion...

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Consider the above reaction and predict the major product.

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Among the following marked proton of which compound shows lowest $\mathrm{pK}_{\mathrm{a}}$ value ?

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Hydrolysis of which compound will give carbolic acid ?

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Among $\mathrm{Co}^{3+}, \mathrm{Ti}^{2+}, \mathrm{V}^{2+}$ and $\mathrm{Cr}^{2+}$ ions, one if used as a reagent cannot liberate $\mathrm{H}_2$ from dilute mineral acid...

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Given below are two statements. Statement I : $\mathrm{O}_{2, a, \mathrm{Cu}^{2+}}$ and $\mathrm{Fe}^{3+}$ are weakly attracted by magnetic field and...

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If $\mathrm{O}_2$ gas is bubbled through water at 303 K , the number of millimoles of $\mathrm{O}_2$ gas that dissolve...

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Which of the following is not an example of benzenoid compound ?

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Choose the correct option for the following reactions.

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Consider the following metal complexes : $$ \begin{aligned} & {\left[\mathrm{Co}\left(\mathrm{NH}_3\right)\right]^{3+}} \\ & {\left[\mathrm{CoCl}(\mathrm{NH} 3)_5\right]^{2-1}} \\ & {\left[\mathrm{Co}(\mathrm{CN})_6\right]^{3-}} \\ & {\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5\left(\mathrm{H}_2...

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When 600 mL of $0.2 \mathrm{M} \mathrm{HNO}_3$ is mixed with 400 mL of 0.1 M NaOH solution in a flask,...

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$ \mathrm{CH}_3-\mathrm{CH}_2-\mathrm{CN} \xrightarrow[\text { Efter }]{\mathrm{CH}_2 \mathrm{MgBr}} \mathrm{~A} \xrightarrow{\mathrm{H}_3 \mathrm{O}^{+}} \mathrm{B} \xrightarrow[\mathrm{HCl}]{\mathrm{Zn}-\mathrm{Hg}} \mathrm{C} $ The correct structure of C is

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Match List–I with List–II. Choose the correct answer from the options given below :

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The half life for the decomposition of gaseous compound A is 240 s when the gaseous pressure was 500 Torr...

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Arrange the following in decreasing acidic strength.

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Match List I with List II

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The minimum uncertainty in the speed of an electron in an one dimensional region of length $2 a_0$ (Where $\mathbf{a}_0=$...

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The cell potential for $\mathrm{Zn}\left|\mathrm{Zn}^{2+}(a q) \| \mathrm{Sn}^{\mathrm{X}+}\right| \mathrm{Sn}$ is 0.801 V at 298 K . The reaction quotient for...

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What is the major product of the following reaction?

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Ionic radii of cation $\mathrm{A}^{+}$and anion $\mathrm{B}^{\prime \prime}$ are 102 and 181 pm respectively. These ions are allowed to crystallize...

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The Hinsberg reagent is :

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Resistance of a conductivity cell (cell constant $129 \mathrm{~m}^{-1}$ ) filled with 74.5 ppm solution of KCl is $100 \Omega$...

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In the above reaction, 5 g of toluene is converted into benzaldehyde with $92 \%$ yield. The amount of benzaldehyde...

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A compound ' $X$ ' is acidic and it is soluble in NaOH solution, but insoluble in $\mathrm{NaHCO}_3$ solution. Compound...

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Major product of the following reaction is

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In a Youngs double slit experiment, an angular width of the fringe is $0.35^{\circ}$ on a screen placed at 2...

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The spin only magnetic moment of the complex present in Fehling's reagent is_______ B.M. (Nearest integer).

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Which of the following compounds is an example of hypnotic drug ?

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Given below are two statements : Statement I : In polluted water values of both dissolved oxygen and BOD are...

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The number of molecule(s) or ion(s) from the following having non-planar structure is_______.$...

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Consider the following reaction sequence : The product 'B' is :

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Match List I with List II. Choose the correct answer from the options given below:

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A Zener of breakdown voltage $\mathrm{V}_{\mathrm{Z}}=8 \mathrm{~V}$ and maximum zener current, $\mathrm{I}_{\mathrm{ZM}}=10 \mathrm{~mA}$ is subjected to an input voltage $...

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The oxidation state of manganese in the product obtained in a reaction of potassium permanganate and hydrogen peroxide in basic...

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Among the following ores Bauxite, Siderite, Cuprite, Calamine, Haematite, Kaolinite, Malachite, Magnetite, Sphalerite, Limonite, Cryolite, the number of principal ores...

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The correct order of energy of absorption for the following metal complexes is

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When enthanol is heated with conc. $\mathrm{H}_2 \mathrm{SO}_4$, a gas is produced. The compound formed, when this gas is treated...

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Consider the above reaction, the compound 'A' is :

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A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm , $...

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Consider the above reaction sequence, the Product 'C is :

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The total number of acidic oxides from the following list is: $...

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Which of the following has least tendency to liberate $\mathrm{H}_2$ from mineral acids?

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Given below are two statements.

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Considering the above reactions, the compound 'A' and compound 'B' respectively are :

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When a certain amount of solid A is dissolved in 100 g of water at 25 °C to make a...

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Amplitude modulated wave is represented by $V_{R M}=10\left[1+0.4 \cos \left(2 \pi \times 10^4 t\right)\right] \cos \left(2 \pi \times 10^7 t\right)$....

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The correct order of density is

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A gas (Molar mass $=280 \mathrm{~g} \mathrm{~mol}^{-1}$ ) was burnt in excess $\mathrm{O}_2$ in a constant volume calorimeter and during...

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Match List–I with List–II, match the gas evolved during each reaction. Choose the correct answer from the options given below...

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Which among the following pairs of the structures will give different products on ozonolysis? (Consider the double bonds in the...

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High purity (>99.95%) dihydrogen is obtained by

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Which among the following is the strongest Bronsted base ?

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For a real gas at $25^{\circ} \mathrm{C}$ temperature and high pressure ( 99 bar ) the value of compressibility factor...

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Given below are two statements. Statement I : Pig iron is obtained by heating cast iron with scrap iron. Statement...

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Which among the following pairs has only herbicides ?

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The normality of $\mathrm{H}_2 \mathrm{SO}_4$ in the solution obtained on mixing 100 mL of $0.1 \mathrm{M} \mathrm{H}_2 \mathrm{SO}_4$ with 50...

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In the given circuit the input voltage $\mathrm{V}_{\text {in }}$ is shown in figure. The cut-in voltage of $\mathrm{p}-\mathrm{n}$ junction...

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The metal complex that is diamagnetic is (Atomic number : Fe, 26; Cu, 29)

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The first ionization enthalpies of Be, B, N and O follow the order

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$\mathrm{Fe}^{3+}$ cation gives a prussian blue precipitate on addition of potassium ferrocyanide solution due to the formation of:

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R....

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For micelle formation, which of the following statements are correct? (A) Micelle formation is an exothermic process. (B) Micelle formation...

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Match List-I with List-II

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Compound A undergoes following sequence of reactions to give compound ' B '. The correct structure and chirality of compound...

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R....

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The molar conductivity of a conductivity cell filled with 10 moles of 20 mL NaCl solution is $\wedge_{\mathrm{m1}}$ and that...

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Following statements related to radioactivity are given below: (A) Radioactivity is a random and spontaneous process and is dependent on...

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Which of the following statement is incorrect ?

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The products obtained from a reaction of hydrogen peroxide and acidified potassium permanganate are

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Which of the following enhances the lathering property of soap?

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$\mathrm{Ka}_1, \mathrm{Ka}_2$ and $\mathrm{Ka}_3$ are the respective ionization constants for the following reactions (a) (b), and (c). (a) $...

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The metal salts formed during softening of hardwater using Clark's method are :

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Match List-I with List-IIChoose the correct answer from the options given below:

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Two solutions A and B are prepared by dissolving 1 g of non-volatile solutes X and Y. respectively in 1...

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An organic compound 'A' contains nitrogen and chlorine. It dissolves readily in water to give a solution that turns litmus...

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Match List I with List II : Choose the correct answer from the options given below

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Correct structure of $\gamma$-methylcyclohexane carbaldehyde is :

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The metal that is not extracted from its sulphide ore is :

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The metal that has very low melting point and its periodic position is closer to a metalloid is :

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Match List-I with List-II. Choose the correct answer from the option given below:

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Let $K_1$ and $K_2$ be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength $\lambda_1$ and...

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R....

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In the presence of sunlight, benzene reacts with $ \mathrm{Cl}_2 $ to give product, X. The number of hydrogens in...

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At $30^{\circ} \mathrm{C}$, the half life for the decomposition of $\mathrm{AB}_2$ is 200 s and is independent of the initial...

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Dinitrogen is a robust compound, but reacts at high altitude to form oxides. The oxide of nitrogen that can damage...

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The difference between spin only magnetic moment values of $\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_3\right]_{\mathrm{Cl}}$ and $\left[\mathrm{Cr}_2\left(\mathrm{H}_2 \mathrm{O}\right)_3\right]_{\mathrm{l}} \mathrm{Cl}_3$ is $\_\_\_\_$ .

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Class XII students were asked to prepare one litre of buffer solution of pH 8.26 by their chemistry teacher. The...

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In young's double slit experiment performed using a monochromatic light of wavelength $\lambda$, when a glass plate ( $\mu=1.5$ )...

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For a reaction $A \rightarrow 2 B+C$ the half lives are 100 s and 50 s when the concentration of...

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The amount of charge in F (Faraday) required to obtain one mole of iron from $\mathrm{Fe}_3 \mathrm{O}_4$ is $\_\_\_\_$ ....

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Arrange the following in increasing order of their covalent character. (A) $\mathrm{CaF}_2$ (B) $\mathrm{CaCl}_2$ (C) $\mathrm{CaBr}_2$ (D) $\mathrm{Cal}_2$

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At 298 K , the equilibrium constant is $2 \times 10^{15}$ for the reaction: $$ \mathrm{Cu}(\mathrm{~s})+2 \mathrm{Ag}^{+}(\mathrm{aq}) \rightleftharpoons \mathrm{Cu}^{2+}(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{~s})...

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An EM wave propagating in $x$-direction has a wavelength of 8 mm . The electric field vibrating $y$-direction has maximum...

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A coil is placed in a time varying magnetic field. If the number of turns in the coil were to...

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Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of xA in the same direction....

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The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to $...

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Hemoglobin contains 0.34% of iron by mass. The number of Fe atoms in 3.3 g of hemoglobin is : (Given...

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Match List-I with List-IIChoose the correct answer from the options given below:

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Major product 'B' of the following reaction sequence is:

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Among the following the number of state variable is ______. Internal energy (U) Volume (V) Heat (q) Enthalpy (H)

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Among the following the number of curves not in accordance with Freundlich adsorption isotherm is

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The structure of A in the given reaction is:

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For a reaction, given below is the graph of $\ln \mathrm{k}$ vs $\frac{1}{\mathrm{~T}}$. The activation energy for the reaction is...

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Resistance of the wire is measured as $2 \Omega$ and $3 \Omega$ at $10^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$ respectively. Temperature...

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On reaction with stronger oxidizing agent like $\mathrm{KIO}_4$, hydrogen peroxide oxidizes with the evolution of $\mathrm{O}_2$. The oxidation number of...

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Which of the reaction is suitable for concentrating ore by leaching process ?

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A sample of 0.125 g of an organic compound when analysed by Duma's method yields 22.78 mL of nitrogen gas...

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Given below are two statements: Statement I : The non bio-degradable fly ash and slag from steel industry can be...

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The reaction occurring as below comes to equilibrium under a total pressure of 1 atm. Analysis of the system shows...

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Low oxidation state of metals in their complexes are common when ligands:

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Two point charges $A$ and $B$ of magnitude $+8 \times 10^{-6} \mathrm{C}$ and $-8 \times 10^{-6} \mathrm{C}$ respectively are placed...

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In neutral or alkaline solution, $\mathrm{MnO}_4^{-}$ oxidises thiosulphate to:

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When 800 mL of 0.5 M nitric acid is heated in a beaker, its volume is reduced to half and...

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In which of the following pairs, electron gain enthalpies of constituent elements are nearly the same or identical ? (A)...

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A gaseous mixture of two substances A and B, under a total pressure of 0.8 atm is in equilibrium with...

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If the wavelength for an electron emitted from H -atom is $3.3 \times 10^{-10} \mathrm{~m}$, then energy absorbed by the...

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2.4 g coal is burnt in a bomb calorimeter in excess of oxygen at 298 K and 1 atm pressure....

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What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and...

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Octahedral complexes of copper (II) undergo structural distortion (Jahn-Teller). Which one of the given copper (II) complexes will show the...

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The pressure of a moist gas at $27^{\circ} \mathrm{C}$ is 4 atm . The volume of the container is doubled...

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Metal $M$ crystallizes into a FCC lattice with the edge length of $4.0 \times 10^{-8} \mathrm{~cm}$. The atomic mass of...

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Given below are two statements: one is labeled as Assertion (A) and the other is labeled as Reason (R) Assertion...

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Match List–I with List–II. Choose the correct answer from the options given below :

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The wavelength of an electron and a neutron will become equal when the velocity of the electron is x times...

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2 L of $0.2 \mathrm{M} \mathrm{H}_2 \mathrm{SO}_4$ is reacted with 2 L of 0.1 M NaOH solution, the molarity of...

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The enthalpy of combustion of propane, graphite and dihydrogen at 298 K are: $-2220.0 \mathrm{~kJ} \mathrm{~mol}^{-1},-393.5 \mathrm{~kJ}$ mol-1 and $...

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An element A of group 1 shows similarity to an element B belonging to group 2. If A has maximum...

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Find out the major product for the reaction.

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A mixture of hydrogen and oxygen contains 40% hydrogen by mass when the pressure is 2.2 bar. The partial pressure...

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Among the following species $$ \mathrm{N}_2, \mathrm{~N}_2^{+}, \mathrm{N}_2^{-}, \mathrm{N}_2^{2-}, \mathrm{O}_2, \mathrm{O}_2^{+}, \mathrm{O}_2^{-}, \mathrm{O}_2^{2-} $$ the number of species showing diamagnetism...

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Which of the following 3d-metal ion will give the lowest enthalpy of hydration $\left(\Delta_{\text {hyd }} \mathrm{H}\right)$ when dissolved in...

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Chlorophyll extracted from the crushed green leaves was dissolved in water to make 2 L solution of Mg of concentration...

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The formulas of A and B for the following reaction sequence are

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Outermost electronic configurations of four elements A, B, C, D are given below: (A) $3 \mathrm{~s}^2$ (B) $...

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Given below two statements i Statement I. On heating with $\mathrm{KHSO}_4$, glycerol is dehydrated and acrolein is formed. Statement II...

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)....

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Given below are two statements : One is labeled as Assertion A and the other is labeled as Reason R...

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A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40...

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When borax is heated with CoO on a platinum loop, blue coloured bead formed is largely due to:

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Given below are two statements: one is labeled as Assertion (A) and the other is labeled as Reason (R) Assertion...

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Drugs used to bind to receptors, inhibiting its natural function and blocking a message are called :

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Two statements in respect of drug–enzyme interaction are given below Statement I : Action of an enzyme can be blocked...

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Which of the following is reducing sugar?

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During the denaturation of proteins, which of these structures will remain intact ?

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In neutral or faintly alkaline medium, $\mathrm{KMnO}_4$ being a powerful oxidant can oxidize, thiosulphate almost quantitatively, to sulphate. In this...

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Given below are two statements: Statement I: For KI, molar conductivity increases steeply with dilution. Statement II: For carbonic acid,...

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Match List I with List II

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Stearic acid and polyethylene glycol react to form which one of the following soap/s detergents ?

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Portland cement contains 'X' to enhance the setting time. What is 'X'?

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Given below are two statements : one is labeled as Assertion A and the other is labeled as Reason R...

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The Plot of pH-metric titration of weak base $\mathrm{NH}_4 \mathrm{OH}$ vs strong acid HCl looks like:

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The correct stability order of the following diazonium salt is

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Compound I is heated with Conc. HI to give a hydroxy compound A which is further heated with Zn dust...

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Given below are two statements. Statement I : Stannane is an example of a molecular hydride. Statement II: Stannane is...

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The major product of the following reaction is

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Arrange the following in increasing order of reactivity towards nitration

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In following pairs, the one in which both transition metal ions are colourless is :

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Which reactant will give the following alcohol on reaction with one mole of phenyl magnesium bromide (PhMgBr) followed by acidic...

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The major product in the given reaction is

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The correct decreasing order of energy, for the orbitals having, following set of quantum numbers: (A) $\mathrm{n}=3, \ell=0, \mathrm{~m}=0$ (B)...

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Melamine polymer is formed by the condensation of :

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Dinitrogen and dioxygen. the main constituents of air do not react with each other in atmosphere to form oxides of...

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The products formed in the following reaction, A and B are

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Number of lone pairs of electrons in the central atom of $\mathrm{SCl}_2, \mathrm{O}_3, \mathrm{ClF}_3$ and $\mathrm{SF}_6$, respectively, are in

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An organic compound ' A ' on reaction with $\mathrm{NH}_3$ followed by heating gives compound B . Which on further...

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Match List I with List II

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Which of the following compounds is not aromatic?

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In liquation process used for tin (Sn), the metal :

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Given below are two statements : One is labeled as Assertion A and the other is labeled as Reason R...

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Which one of the following reactions does not represent correct combination of substrate and product under the given conditions ?

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Match List–I with List–II. Choose the correct answer from the options given below :

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Lithium nitrate and sodium nitrate, when heated separately, respectively, give :

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The difference in the reaction of phenol with bromine in chloroform and bromine in water medium is due to :

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Which of the following pair is not isoelectronic species? (At. no. Sm, 62; Er, 68: Yb, 70: Lu, 71; Eu,...

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A capacitor of capacitance 500 $\mu \mathrm{F}$is charged completely using a dc supply of 100 V. It is now connected...

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Most stable product of the following reaction is:

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Which of the following relation is not correct ?

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Which technique among the following, is most appropriate in separation of a mixture of 100 mg of p-nitrophenol and picric...

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Given below are the critical temperatures of some of the gases :

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Two radioactive materials A and B have decay constants $25 \lambda$ and $16 \lambda$ respectively. If initially they have the...

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Concentrated $\mathrm{HNO}_3$ reacts with lodine to give

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$ \dot{\mathrm{C}} \mathrm{l}+\mathrm{CH}_4 \rightarrow \mathrm{~A}+\mathrm{B} $ A and B in the above atmospheric reaction step are

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The reaction of zinc with excess of aqueous alkali, evolves hydrogen gas and gives :

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Identify the incorrect statement from the following.

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White phosphorus reacts with thionyl chloride to give

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A 8 V Zener diode along with a series resistance R is connected across a 20 V supply (as shown...

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In metallurgy the term "gangue" is used for:

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The dark purple colour of KMnO4 disappears in the titration with oxalic acid in acidic medium. The overall change in...

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Statement I : An alloy of lithium and magnesium is used to make aircraft plates. Statement II : The magnesium...

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The first ionization enthalpy of $\mathrm{Na}, \mathrm{Mg}$ and Si, respectively, are: 496,737 and $786 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The first ionization enthalpy...

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The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is 10 s....

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Which of the given reactions is not an example of disproportionation reaction ?

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The products obtained during treatment of hard water using Clark's method are:

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Borazine, also known as inorganic benzene, can be prepared by the reaction of 3-equivalents of "X" with 6-equivalents of "Y"....

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The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is$60 \mathrm{~ms}^{-1}$....

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100 mL of 5% (w/v) solution of NaCl in water was prepared in 250 mL beaker. Albumin from the egg...

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Given below are two statements :One is labeled as Assertion A and the other is labeled as Reason R Assertion...

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In an experiment to find acceleration due to gravity ( g ) using simple pendulum, time period of 0.5 s...

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200 mL of 0.01 M HCl is mixed with 400 mL of $0.01 \mathrm{M} \mathrm{H}_2 \mathrm{SO}_4$. The pH of the...

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In an experiment with a convex lens. The plot of the image distance ( $v^{\prime}$ ) against the object distance...

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Reaction of $\mathrm{BeCl}_2$ with $\mathrm{Li}_4 \mathrm{IH}_4$ gives :

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A compound 'A' on reaction with 'X' and 'Y' produces the same major product but different by product 'a' and...

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$\begin{aligned} & \mathrm{N}_{2(\mathrm{~g})}+3 \mathrm{H}_{2(\mathrm{~g})} \rightleftharpoons 2 \mathrm{NH}_{3(\mathrm{~g})} \\ & 20 \mathrm{~g} 5 \mathrm{~g}\end{aligned}$ Consider the above reaction, the limiting reagent...

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The correct decreasing order for metallic character is

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A modulating signal 2sin $\left(6.28 \times 10^6\right) \mathrm{t}$ is added to the carrier signal 4sin $\left(12.56 \times 10^9\right)$ t for...

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An object ‘o’ is placed at a distance of 100 cm in front of a concave mirror of radius of...

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Which of the following pair of molecules contain odd electron molecule and an expanded octet molecule?

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$$ \begin{aligned} & \mathrm{C}(\mathrm{~s})+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+400 \mathrm{~kJ} \\ & \mathrm{C}(\mathrm{~s})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}(\mathrm{~g})+100 \mathrm{~kJ} \end{aligned} $$ When coal of purity...

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For the given circuit the current through battery of 6V just after closing the switch ‘S’ will be ……….A.

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Which of the following can be used to prevent the decomposition of H2O2?

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The photochemical smog does not generally contain :

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The velocity of a small ball of mass 0.3 g and density 8 g/cc when dropped in a container filled...

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Given below are two statements : One is labeled as Assertion A and the other is labeled as Reason R...

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The interhalogen compound formed from the reaction of bromine with excess of fluorine is a :

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Refining using liquation method is the most suitable for metals with :

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A metal wire of length 0.5 m and cross-sectional area $10^{-4} \mathrm{~m}^2$ has breaking stress $5 \times 10^8 \mathrm{Nm}^{-2}$. A...

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Given below are the quantum numbers for 4 electrons. A. $\mathrm{n}=3, l=2, \mathrm{~m}_{\square}=1, \mathrm{~m}_{\mathrm{s}}=+1 / 2$ B. $...

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The geometry around boron in the product ' B ' formed from the following reaction is $$ \begin{aligned} & \mathrm{BF}_3+\mathrm{NaH}...

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Given two statements below : Statement I : In Cl2 molecule the covalent radius is double of the atomic radius...

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Nearly 10% of the power of a 110 W light bulb is converted to visible radiation. The change in average...

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Magnetic flux (in weber) in a closed circuit of resistance $20 \Omega$ varies with time $t(s)$ as $\phi=8 t^2-9 t+5$....

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A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at...

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A convex lens of focal length 20 cm is placed in front of convex mirror with principal axis coinciding each...

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Choose the correct order of density of the alkali metals :

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Light enters from air into a given medium at an angle of 45º with interface of the air-medium surface. After...

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Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference...

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The root mean square speed of smoke particles of mass $5 \times 10^{-17}$ kg their Brownian motion in air at...

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The reaction of $\mathrm{H}_2 \mathrm{O}_2$ with potassium permanganate in acidic medium leads to the formation of mainly:

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Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant...

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Consider the reaction $$ 4 \mathrm{HNO}_3(l)+3 \mathrm{KCl}(\mathrm{~s}) \rightarrow \mathrm{Cl}_2(\mathrm{~g})+\mathrm{NOCl}(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{~g})+3 \mathrm{KNO}_3(\mathrm{~s}) $$ The amount of $\mathrm{HNO}_3$ required to produce...

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In a potentiometer arrangement, a cell of emf 1.20 V gives a balance point at 36 cm length of wire....

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$\frac{x}{x+4}$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its...

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Match List - I with List - II. Choose the correct answer from the options given below :

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A block of ice of mass 120 g at temperature 0°C is put in 300 gm of water at 25°C....

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Match List - I with List - II. Choose the correct answer from the options given below :

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Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular...

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The vertical component of the earth’s magnetic field is$6 \times 10^{-5} T$ at any place where the angle of dip...

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A particle is moving in a straight line such that its velocity is increasing at $5 \mathrm{~ms}^{-1}$ per meter. The...

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The compound(s) that is(are) removed as slag during the extraction of copper is i. (1) CaO (2) FeO (3) $...

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Hydrogen atom from excited state comes to the ground by emitting a photon of wavelength $\lambda$. The value of principal...

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A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown...

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If the potential barrier across a p-n junction is 0.6 V . Then the electric field intensity, in the depletion...

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The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are...

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A ball is projected from the ground with a speed $15 \mathrm{~ms}^{-1}$ at an angle $\theta$ with horizontal so that...

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The $X-Y$ plane be taken as the boundary between two transparent media $M_1$ and $M_2 . M_1$ in $...

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A wire of length 314 cm carrying current of 14 A is bent to form a circle. The magnetic moment...

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A bad of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with...

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The torque of a force $5 \hat{i}+3 \hat{j}-7 \hat{k}$ about the origin is $\tau$. If the force acts on a...

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Two light beams of intensities 41 and 91 interfere on a screen. The phase difference between these beams on the...

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An object is taken to a height above the surface of earth at a distance $\frac{5}{4} R$ from the centre...

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A closely wounded circular coil of radius 5 cm produces a magnetic field of $37.68 \times 10^{-4} \mathrm{~T}$ at its...

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Let $\eta_1$ is the efficiency of an engine at $T_1=447^{\circ} \mathrm{C}$ and $T_2=147^{\circ} \mathrm{C}$ while $\eta_2$ is the efficiency at...

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If momentum of a body is increased by 20%, then its kinetic energy increases by :

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The current I flowing through the given circuit will be ________A.

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Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas...

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One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of...

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The length of a seconds pendulum at a height h = 2R from earth surface will be: (Given: $R=$ Radius...

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The pressure $\mathrm{P}_1$ and density $\mathrm{d}_1$ of diatomic gas $\left(\gamma=\frac{7}{5}\right)$ changes suddenly to $\mathrm{P}_2\left(>\mathrm{P}_1\right)$ and $\mathrm{d}_2$ respectively during an adiabatic...

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A current of 15 mA flows in the circuit as shown in figure. The value of potential difference between the...

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If the acceleration due to gravity experienced by a point mass at a height $h$ above the surface of earth...

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An electron with energy 0.1 keV moves at right angle to the earth's magnetic field of $1 \times 10^{-4} \mathrm{Wbm}^{-2}$....

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An object is projected in the air with initial velocity u at an angle $\theta$. The projectile motion is such...

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The IUPAC nomenclature of an element with electronic configuration $[\mathrm{Rn}] 5 \mathrm{f}^{14} 6 \mathrm{~d}^1 7 \mathrm{~s}^2$ is:

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Match list- I with list-ll

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An electrical bulb rated 220 V, 100 W, is connected in series with another bulb rated 220V, 60 W. If...

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20 mL of $0.1 \mathrm{M} \mathrm{NH}_4 \mathrm{OH}$ is mixed with 40 mL of 0.05 M HCl . The pH of...

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The potential energy of a particle of mass 4 kg in motion along the $x$-axis is given by $...

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The depression in freezing point observed for a formic acid solution of concentration $0.5 \mathrm{~mL} \mathrm{~L}^{-1}$ is $0.0405^{\circ} \mathrm{C}$. Density...

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At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of...

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A string of area of cross-section $4 \mathrm{~mm}^2$ and length 0.5 is connected with a rigid body of mass 2...

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Which of the following sets of quantum numbers is not allowed ?

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The distance of centre of mass from end $A$ of a one dimensional rod (AB) having mass density $...

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Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below: $$ { }_1^2 \mathrm{X}+{ }_1^2...

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A ball is thrown vertically upwards with a velocity of $19.6 \mathrm{~ms}^{-1}$ from the top of a tower. The ball...

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$\mathrm{SO}_2 \mathrm{Cl}_2$ on reaction with excess of water results into acidic mixture $$ \mathrm{SO}_2 \mathrm{Cl}_2+2 \mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{H}_2 \mathrm{SO}_4+2...

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A FM Broad cast transmitter, using modulating signal of frequency 20 kHz has a deviation ratio of 10. The Bandwidth...

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In the given reaction, The number of $\alpha$ electrons present in the product ' P ' is $\_\_\_\_$ .

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Two bodies of masses $\mathrm{m}_1=5 \mathrm{~kg}$ and $\mathrm{m}_2=3 \mathrm{~kg}$ are connected by a light string going over a smooth light...

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An n.p.n transistor with current gain $\beta=100$ in common emitter configuration is shown in figure. The output voltage of the...

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Four identical discs each of mass ' $M$ ' and diameter ' $a$ ' are arranged in a small plane...

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A radioactive sample decays $\frac{7}{4}$ times its original quantity in 15 minutes. The half-life of the sample is

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A ball is released from a height $h$. If $t_1$ and $t_2$ be the time required to complete first half...

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A block of mass m (as shown in figure) moving with kinetic energy E compresses a spring through a distance...

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Two streams of photons, possessing energies to five and ten times the work function of metal are incident on the...

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In the given reaction (i) $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ the number of $\mathrm{sp}^2$ hybridised carbon ( s ) in compound '...

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An object of mass 1 kg is taken to a height from the surface of earth which is equal to...

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The power of a lens (biconvex) is $1.25 \mathrm{~m}^{-1}$ in particular medium. Refractive index of the lens is 1.5 and...

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The diameter of an air bubble which was initially 2 mm , rises steadily through a solution of density $...

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In the given figure, the face $A C$ of the equilateral prism is immersed in a liquid of refractive index...

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Sun light falls normally on a surface of area $36 \mathrm{~cm}^2$ and exerts an average force of $...

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The frequency of echo will be _______ Hz if the train blowing a whistle of frequency 320 Hz is moving...

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Read the following statements : (A) Volume of the nucleus is directly proportional to the mass number. (B) volume o...

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Which statements are correct about degrees of freedom? A. A molecule with n degrees of freedom has $\mathrm{n}^2$ different ways...

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The number of chiral alcohol(s) with molecular formula $\mathrm{C}_4 \mathrm{H}_{10} \mathrm{O}$ is $\_\_\_\_$

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The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through...

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Two electric dipoles of dipole moments $1.2 \times 10^{-30} \mathrm{~cm}$ and $2.4 \times 10^{-30} \mathrm{~cm}$ are placed in two difference...

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A transformer operating at primary voltage 8 kV and secondary voltage 160 V serves a load of 80 kW. Assuming...

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An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta...

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As shown in the figure, a potentiometer wire of resistance $20 \Omega$ and length 300 cm is connected with resistance...

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If $\vec{A}=(2 \hat{i}+3 \hat{j}-\hat{k}) \mathrm{m}$ and $\vec{B}=(\hat{i}+2 \hat{j}+2 \hat{k}) \mathrm{m}$. The magnitude of component of vector $\vec{A}$ along vector $\vec{B}$...

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For the reaction given below: $$ \mathrm{CoCl}_{3 m} \times \mathrm{NH}_3+\mathrm{AgNO}_3(\mathrm{ag}) \rightarrow $$ If two equivalents of AgCl precipitate out, then...

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The magnetic field at the center of current carrying circular loop is $\mathrm{B}_1$. The magnetic field at a distance of...

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In $1^{\text {st }}$ case, Carnot engine operates between temperatures 300 K and 100 K. In $2^{\text {nd }}$ case,...

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An unpolarised light beam of intensity 2I0 is passed through a polaroid P and then through another polaroid Q which...

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The frequencies at which the current amplitude in an LCR series circuit becomes $\frac{1}{\sqrt{2}}$ times its maximum value, are $...

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The area of cross section of the rope used to lift a load by a crane is $...

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A triangular shaped wire carrying 10A current is placed in a uniform magnetic field of 0.5T, as shown in figure....

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In a Young’s double slit experiment, a laser light of 560 nm produces an interference pattern with consecutive bright fringes...

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A circuit element X when connected to an a.c. supply of peak voltage 100 V gives a peak current of...

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A steel wire of length 3.2 m $\left(\mathrm{Y}_{\mathrm{s}}=2.0 \times 10^{11} \mathrm{Nm}^{-2}\right)$ and a copper wire of length 4.4 M $...

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Given below are two statements : Statement I: A uniform wire of resistance $80 \Omega$ is cut into four equal...

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Mass numbers of two nuclei are in the ratio of $4: 3$. Their nuclear densities will be in the ratio...

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A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible...

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A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position,...

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If the projection of $2 \hat{i}+4 \hat{j}-2 \hat{k}$ on $\hat{i}+2 \hat{j}+\alpha \hat{k}$ is zero. Then, the value of $\alpha$ will...

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In an experiment to find out the diameter of wire using screw gauge, the following observation were noted :

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A uniform electric field E = (8 m/e) V/m is created between two parallel plates of length 1m as shown...

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A body of mass m is projected with velocity $\lambda V_e$ in vertically upward direction from the surface of the...

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A wire X of length 50 cm carrying a current of 2 A is placed parallel to a long wire...

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In the case of amplitude modulation to avoid distortion the modulation index $(\mu)$ should be ${ }_{\text {in }}$

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Two masses $M_1$ and $M_2$ are tied together at the two ends of a light inextensible string that passes over...

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A slab of dielectric constant $K$ has the same cross-sectional area as the plates of a parallel plate capacitor and...

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A 1 m long wire is broken into two unequal parts X and Y The X part of the wire...

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Identify the solar cell characteristics from the following options :

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Spin only magnetic moment of $[\mathrm{MnBr} \mathbf{r}]^{4-}$ is $\_\_\_\_$ B.M. (round off to the closest integer)

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Given below are two statements : one is labeled as Assertion A and the other is labeled as Reason R....

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A velocity selector consists of electric field $\vec{E}=E \hat{k}$ and magnetic field $\vec{B}=B \hat{j}$ with $B=12 m T$. The value...

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A vessel contains 14 g of nitrogen gas at a temperature of $27^{\circ} \mathrm{C}$. The amount of heat to be...

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Two identical thin metal plates has charge $\mathrm{q}_1$ and $\mathrm{q}_2$ respectively such that $q_1>q_2$. The plates were brought close to...

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The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet...

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The equation $$ k=\left(6.5 \times 10^{12} \mathrm{~s}^{-1}\right) \mathrm{e}^{-28000 \mathrm{kJT}} $$ is followed for the decomposition of compound A . The...

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The half life period of a radioactive substance is 60 days. The time taken for $\frac{7}{8}$ th of its original...

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Consider a cylindrical tank of radius 1 m is filled with water. The top surface of water is at 15...

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Match List I with List II. Choose the correct answer from the options given below :

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The equation $\lambda=\frac{1.227}{\mathrm{x}} \mathrm{nm}$ can be used to find the de-Brogli wavelength of an electron. In this equation x stands...

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Two concentric circular loops of radii $r_1=30 \mathrm{~cm}$ and $r_2=50 \mathrm{~cm}$ are placed in $X-Y$ plane as shown in the...

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A block ‘A’ takes 2 s to slide down a frictionless incline of $30^{\circ}$ and length ‘l’ kept inside a...

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Assume there are two identical simple pendulum Clocks-1 is placed on the earth and Clock-2 is placed on a space...

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In normal adjustment, for a refracting telescope, the distance between objective and eye piece is 30 cm. The focal length...

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The cell potential for the given cell at $298 \mathrm{~K} \mathrm{Pt}\left|\mathrm{H}_2(\mathrm{~g}, 1 \mathrm{bar})\right| \mathrm{H}^{+}(\mathrm{ag}) \| \mathrm{Cu}^{2+}(\mathrm{aq}) \mid \mathrm{Cu}(\mathrm{s})$ is 0.31...

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A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as...

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Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force...

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A travelling microscope has 20 divisions per cm on the main scale while its Vernier scale has total 50 divisions...

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A source of potential difference V is connected to the combination of two identical capacitors as shown in the figure....

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A uniform metal chain of mass $m$ and length ' $L$ ' passes over a massless and frictionless pulley. It...

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A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the...

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Elevation in boiling point for 1.5 molal solution of glucose in water is 4 K . The depression in freezing...

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As shown in the figure, after passing through the medium 1 . The speed of light $v_2$ in medium 2...

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A pressure-pump has a horizontal tube of cross-sectional area $10 \mathrm{~cm}^2$ for the outflow of water at a speed of...

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In the circuit shown below, maximum zener diode current will be ____mA

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A battery of 6 V is connected to the circuit as shown below. The current I drawn from the battery...

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A body of mass 10 kg is projected at an angle of $45^{\circ}$ with the horizontal. The trajectory of the...

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At time $t=0$ a particle starts travelling from a height $7 \hat{z} \mathrm{~cm}$ in a plane keeping z coordinate constant....

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The equation of current in a purely inductive circuit is $5 \sin \left(49 \pi t-30^{\circ}\right)$. If the inductance is 30...

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Find the modulation index of an AM wave having 8V variation where maximum amplitude of the AM wave is 9...

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Consider the efficiency of Carnot's engine is given by $\eta=\frac{\alpha \beta}{\sin \theta} \log _{\mathrm{e}} \frac{\beta \mathrm{x}}{\mathrm{kT}}$, where $\alpha$ and $\beta$...

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In a hydrogen spectrum, $\lambda$ be the wavelength of first transition line of Lyman series. The wavelength difference will be...

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Find the ratio of energies of photons produced due to transition of an election of hydrogen atoms from its (i)...

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2.2 g of nitrous oxide $\left(\mathrm{N}_2 \mathrm{O}\right)$ gas is cooled at a constant pressure of 1 atm from 310 K...

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A ball of mass m is thrown vertically upward. another ball of mass 2 m is thrown an angle ...

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A gas has n degrees of freedom. The ratio of specific heat of gas at constant volume to the specific...

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As shown in the figure, a metallic rod of linear density $0.45 \mathrm{~kg} \mathrm{~m}^{-1}$ is lying horizontally on a smooth...

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The graph between $\frac{1}{u}$ and $\frac{1}{v}$ for a thin convex lens in order to determine its focal length is plotted...

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A pulley of radius 1.5 m is rotated about its axis by a force $\mathrm{F}=\left(12 \mathrm{t}-3 \mathrm{t}^2\right) \mathrm{N}$ applied tangentially...

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The required height of a TV tower which can cover the population of 6.03 lakh is h. If the average...

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The kinetic energy of emitted electron is E when the light incident on the metal has wavelength $\lambda$. To double...

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A square aluminium (shear modulus is $25 \times 10^9 \mathrm{Nm}^{-2}$ ) slab of side 60 cm and thickness 15 cm...

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29. The energy band gap of semiconducting material to produce violet (wavelength = 4000 Å) LED is _____ eV. (Round...

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A box contains 0.90 g of liquid water in equilibrium with water yapour at $27^{\circ} \mathrm{C}$. The equilibrium vapour pressure...

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An ice cube of dimensions $60 \mathrm{~cm} \times 50 \mathrm{~cm} \times 20 \mathrm{~cm}$ is placed in an insulation box of...

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The current sensitivity of a galvanometer can be increased by : (A) decreasing the number of turns (B) increasing the...

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Eight copper wire of length l and diameter d are joined in parallel to form a single composite conductor of...

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The effective current I in the given circuit at very high frequencies will be ____A.

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Match List – I with List –II Choose the correct answer from the options given below :

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A mass 0.9 kg , attached to a horizontal spring, executes SHM with an amplitude $\mathrm{A}_1$. When this mass passes...

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In the given figure, the value of $V_0$ will be $\_\_\_\_$ V.

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A wire of resistance R1 is drawn out so that its length is increased by twice of its original length....

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An expression of energy density is given by $\mathrm{u}=\frac{\alpha}{\beta} \sin \left(\frac{\alpha \mathrm{x}}{\mathrm{kt}}\right)$ , where $\alpha, \beta$ are constants, x is...

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A long cylindrical volume contains a uniformly distributed charge of density $\rho \mathrm{Cm}^{-3}$. The electric field inside the cylindrical volume...

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Resistance are connected in a meter bridge circuit as shown in the figure. The balancing length $\mathrm{l}_1$ is 40cm. Now...

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A 1 m long copper wire carries a current of 1 A . If the cross section of the wire...

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A nucleus of mass $M$ at rest splits into two parts having masses $\frac{M^{\prime}}{3}$ and $\frac{2 M^{\prime}}{3}\left(M^{\prime}

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Two capacitors, each having capacitance $40 \mu \mathrm{~F}$ are connected in series. The space between one of the capacitors is...

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To light, a $50 \mathrm{~W}, 100 \mathrm{~V}$ lamp is connected, in series with a capacitor of capacitance $...

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The volume charge density of a sphere of radius 6 m is $2 \mu \mathrm{C} \mathrm{cm}^{-3}$. The number of lines...

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A composite parallel plate capacitor is made up of two different dielectric materials with different thickness $\left(\mathrm{t}_1\right.$ and $\left.\mathrm{t}_2\right)$ as...

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The maximum and minimum voltage of an amplitude modulated signal are 60 V and 20 V respectively. The percentage modulation...

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An observer is riding on a bicycle and moving towards a hill at $18 \mathrm{kmh}^{-1}$. He hears a sound from...

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In the wave equation $y=0.5 \sin \frac{2 \pi}{\lambda}(400 t-x) m$ the velocity of the wave will be

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A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape...

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When a car is approaching the observer, the frequency of horn is 100 Hz. After passing the observer, it is...

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A unit scale is to be prepared whose length does not change with temperature and remains 20 cm , using...

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In an experiment of determine the Young’s modulus of wire of a length exactly 1m, the extension in the length...

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Light travels in two media $M_1$ and $M_2$ with speeds $1.5 \times 108 \mathrm{~ms}^{-1}$ and $2.0 \times 10^8 \mathrm{~ms}^{-1}$ respectively....

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Given below are two statements : Statement I : The average momentum of a molecule in a sample of an...

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A white precipitate was formed when $\mathrm{BaCl}_2$ was added to water extract of an inorganic salt. Further, a gas '...

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A coil of inductance 1 H and resistance $100 \Omega$ is connected to a battery of 6 v . Determine...

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A disc of mass 1 kg and radius R is free of rotate about a horizontal axis passing through its...

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A wire of length L and radius r is clamped rigidly at one end. When the other end of the...

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Two beam of light having intensities 1 and 41 interfere to produce a fringe pattern on a screen. The phase...

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The oscillating magnetic field in a plane electromagnetic wave is given by $...

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The one division of main scale of vernier calipers reads 1mm and 10 division of Vernier scale is equal to...

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An alternating emf $E=440 \sin 100 \pi t$ is applited to a circuit containing an inductance of $\frac{\sqrt{2}}{\pi} H$. If...

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In meter bridge experiment for measuring unknown resistance ' S ', the null point is obtained at a distance 30...

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Two metallic wires of identical dimensions are connected is series. If $\sigma_1$ and $\sigma_2$ are the conductivities of the these...

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A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio...

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At a particular station, the TV transmission tower has a height of 100 m. To triple its coverage range, height...

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Given below are two statements. Statement I : Electric potential is constant within and at the surface of each conductor....

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If the initial velocity in horizontal direction of a projectile is unit vector $\hat{\mathrm{i}}$ and the equation of trajectory is...

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0.01 M KMnO4 solution was added to 20.0 mL of 0.05 M Mohr’s salt solution through a burette. The initial...

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A logic gate circuit has two inputs A and B and output Y. The voltage waveforms of A, B and...

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A Carnot engine has efficiency of 50%. If the temperature of sink is reduced by 40ºC, its efficiency increases by...

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A ball of mass 0.15 kg hits the wall with its initial speed of $12 \mathrm{~ms}^{-1}$ and bounces back without...

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A screw gauge of pitch 0.5mm is used to measure the diameter of uniform wire of length 6.8cm, the main...

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The major product of the following reaction contains _______ bromine atom(s).

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The mixture of chloroxylenol and terpineol is an example of :

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Four forces are acting at a point $P$ in equilibrium as shown in figure. The ratio of force $F_1$ to...

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The force required to stretch a wire of cross-section $1 \mathrm{~cm}^2$ to double its length will be.i(Given Youg's modulus of...

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What is the half-life period of a radioactive material if its activity drops to $1 / 16^{\text {th }}$ of...

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A spherically symmetric charge distribution is considered with charge density varying as

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The complete combustion of 0.492 g of an organic compound containing ‘C’, ‘H’ and ‘O’ gives 0.793g of $\mathrm{CO}_2$ and...

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A car is moving with speed of 150 km/h and after applying the brake it will move 27 m before...

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An electron (mass $m$ ) with an initial velocity $\vec{v}=v_0 \hat{i}\left(v_0>0\right)$ is moving in an electric field $\vec{E}=-E_0 \hat{i}\left(E_0>0\right)$ where...

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Two projectile thrown at 30º and 45º with the horizontal respectively, reach the maximum height in same time. The ratio...

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In a Vernier Calipers. 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both...

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The structure of protein that is unaffected by heating is :

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In the circuit, the logical value of A = 1 or B = 1 when potential at A or B...

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If the radius of earth shrinks by 2% while its mass remains same. The acceleration due to gravity on the...

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The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which...

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(a) $\mathrm{CoCl}_3 \cdot 4 \mathrm{NH}_3$ (b) $\mathrm{CoCl}_3 \cdot 5 \mathrm{NH}_3$ (c) $\mathrm{CoCl}_3 \cdot .6 \mathrm{NH}_3$ and (d) $...

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A monkey of mass 50kg climbs on a rope which can withstand the tension (T) of 350N. If monkey initially...

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Two projectiles are thrown with same initial velocity making an angle of $45^{\circ}$ and $30^{\circ}$ with the horizontal respectively. The...

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A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with...

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The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given...

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The momentum of an electron revolving in $\mathrm{n}^{\text {th }}$ orbit is given by :

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As per the given figure, two blocks each of mass 250g are connected to a spring of spring constant $...

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R....

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In two different experiments, an object of mass 5 kg moving with a speed of $25 \mathrm{~ms}^{-1}$ hits two different...

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When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon...

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A metal exposed to light of wavelength 800 nm and emits photoelectrons with a certain kinetic energy. The maximum kinetic...

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The moles of methane required to produce 81 g of water after complete combustion is $\_\_\_\_$ $\times 10^{-2} \mathrm{~mol}$. [nearest...

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The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface...

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Time taken by light to travel in two different materials $A$ and $B$ of refractive indices $\mu_A$ and $\mu_B$ of...

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For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a...

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If the length of a wire is made double and radius is halved of its respective values. Then, the Young’s...

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Reaction of $\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$ with excess ammonia and in the presence of oxygen results into a diamagnetic product. Number of...

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In Friedel-Crafts alkylation of aniline, one gets :

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A NCC parade is going at a uniform speed of $9 \mathrm{~km} / \mathrm{h}$ under a mango tree on which...

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A water drop of radius 1cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm,...

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Which of the following statement is correct ?

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The ratio of wavelengths of proton and deuteron accelerated by potential $V_p$ and $V_d$ is $1: \sqrt{2}$. Then, the ratio...

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Let $S=\left\{E, E_2 \ldots E_8\right\}$ be a sample space of random experiment such that $P\left(E_n\right)=\frac{n}{36}$ for every $...

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A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For...

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Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R)....

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Catalyst A reduces the activation energy for a reaction by $10 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at 300 K . The ratio of...

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A radioactive element has a half life of 200 days. The percentage of original activity remaining after 83 days is...

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Let a circle $C$ of radius 5 lie below the $x$-axis. The line $L_1=4 x+3 y-2$ passes through the centre...

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A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The...

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Capacitance of an isolated conducting sphere of radius $R_1$ becomes $n$ times when it is enclosed by a concentric conducting...

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The rms value of conduction current in a parallel plate capacitor is $6.9 \mu \mathrm{~A}$. The capacity of this capacitor,...

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The dimension of $\left(\frac{B^2}{\mu_0}\right)$ will be : (if $\mu_0$; permeability of free space and $B$ : magnetic field)

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$$ \mathrm{Cu}(\mathrm{~s})+\mathrm{Sn}^{2+}(0.001 \mathrm{M}) \rightarrow \mathrm{Cu}^{2+}(0.01 \mathrm{M})+\mathrm{Sn}(\mathrm{~s}) $$ The Gibbs free energy change for the above reaction at 298 K is...

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Two isomers (A) and (B) with Molar mass $184 \mathrm{~g} / \mathrm{mol}$ and elemental composition $...

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7 mole of certain monoatomic ideal gas undergoes a temperature increase of 40K at constant pressure. The increase in the...

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A small square loop of wire of side l is placed inside a large square loop of wire L (L...

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A beam of light travelling along $X$-axis is described by the electric field $E_y=900 \sin \omega(t-x / c)$. The ratio...

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For a free body diagram shown in the figure, the four forces are applied in the 'x' and 'y' directions....

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For the given reactions $\mathrm{Sn}^{2+}+2 \mathrm{e}-\rightarrow \mathrm{Sn}$ $\mathrm{Sn}^{4+}+4 \mathrm{e}-\rightarrow \mathrm{Sn}$ The electrode potentials are; $\mathrm{E}_{\mathrm{Sn}^{2+} / \mathrm{Sn}}^{\circ}=-0.140 \mathrm{~V}$ and $...

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A direct current of 4 A and an alternating current of peak value 4A flow through resistance of $3 \Omega$...

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When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be :

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If the area of the region $\left\{(x, y): x^{\frac{2}{3}}+y^{\frac{2}{3}} \leq 1, x+y \leq 0, y \geq 0\right\}$ is $A$, then...

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To increase the resonant frequency in series LCR circuit,

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Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms–1 collide and rebound with the...

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A magnet hung at $45^{\circ}$ with magnetic meridian makes an angle of $60^{\circ}$ with the horizontal. The actual value of...

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$40^{\circ}$ of HI undergoes decomposition to $\mathrm{H}_2$ and $\mathrm{I}_2$ at $300 \mathrm{~K} . \Delta \mathrm{G}^{\ominus}$ for this decompostion reaction at...

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Two bodies of mass 1 kg and 3 kg have position vectors $\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $-3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ respectively. The...

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2.5 g of protein containing only glycine $\left(\mathrm{C}_2 \mathrm{H}_5 \mathrm{NO}_2\right)$ s dissolved in water to make 500 mL of solution....

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If $y(x)=\left(x^{x^x}\right), x>0$ then $\frac{d^2 x}{d y^2}+20$ at $x=1$ is equal to :

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Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction...

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The total charge on the system of capacitance $\mathrm{C}_1=1 \mu \mathrm{~F}, \mathrm{C}_2=2 \mu \mathrm{~F}, \mathrm{C}_3=4 \mu \mathrm{~F}$ and $...

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A drop of liquid of density $\rho$ is floating half immersed in a liquid of density $\sigma$ and surface tension...

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Two bar magnets oscillate in a horizontal plane in earth’s magnetic field with time periods of 3 s and 4...

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For combustion of one mole of magnesium in an open container at 300 K and 1 bar pressure, $...

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Let $[t]$ denote the greatest integer $\leq t$ and $\{t\}$ denote the fractional part of $t$. Then integral value of...

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A condenser of $2 \mu \mathrm{~F}$ capacitance is charged steadily from 0 to 5C. Which of the following graph represents...

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A ball is projected with kinetic energy E, at an angle of 60º to the horizontal. The kinetic energy of...

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The osmotic pressure exerted by a solution prepared by dissolving 2.0 g of protein of molar mass $60 \mathrm{~kg} \mathrm{~mol}^{-1}$...

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Two sources of equal emfs are connected in series. This combination is connected to an external resistance $R$. The internal...

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The electric current in a circular coil of 2 turns produces a magnetic induction $B_1$ at its centre. The coil...

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The current I in the given circuit will be :

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If the sum of the coefficients of all the positive powers of $x$, in the binomial expansion of $\left(x^n+\frac{2}{x^5}\right)^7$ is...

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Two identical positive charges $Q$ each are fixed at a distance of '2a' apart from each other. Another point charge...

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Let A be a matrix of order 2 × 2, whose entries are from the set {0, 1, 2, 3,...

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A fish swimming in water body when taken out from the water body is covered with a film of water...

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A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against...

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In AM modulation, a signal is modulated on a carrier wave such that maximum and minimum amplitude are found to...

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Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the...

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$B_X$ and $B_Y$ are the magnetic field at the centre of two coils of two coils X and Y respectively,...

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Let $\alpha, \beta$ be the roots of the equation $x^2-4 \lambda x+5=0$ and $\alpha, \gamma$ be the roots of the...

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The stable carbocation formed in the above reaction is :

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Read the following statements; A. When small temperature difference between a liquid and its surrounding is doubled the rate of...

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Let $S=\{1,2,3,4,5,6,7,8,9,10\}$. Define $$ f: S \rightarrow S \text { as } f(n)=\left\{\begin{array}{cc} 2 n, & \text { if }...

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Amongst $\mathrm{SF}_4, \mathrm{XeF}_4, \mathrm{CF}_4$ and $\mathrm{H}_2 \mathrm{O}$, the number of species with two lone pairs of electrons $\_\_\_\_$

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If $t=\sqrt{x}+4$, then $\left(\frac{d x}{d t}\right)_{t-4}$

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A charge particle is moving in a uniform magnetic field $(2 \hat{i}+3 \hat{j}) T$ . If it has an acceleration...

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Which of the following statement is a tautology?

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The drug tegamet is :

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If $K_1$ and $K_2$ are the thermal conductivities $L_1$ and $L_2$ are the lengths and $A_1$ and $A_2$ are the...

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In a solid A B. A atoms are in ccp arrangement and $B$ atoms occupy all the octahedral sites. If...

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In a series LR circuit $X_L=R$ and power factor of the circuit is $\mathrm{P}_1$. When capacitor with capacitance C such...

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When sugar ‘X’ is boiled with dilute $\mathrm{H}_2 \mathrm{SO}_4$ in alcoholic solution, two isomers ‘A’ and ‘B’ are formed. ‘A’...

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A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height $h$. Find the...

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CNG is an important transportation fuel. When 100 g CNG is mixed with 208 oxygen in vehicles, it leads to...

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Which of the following carbocations is most stable :

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Two satellites A and B having masses in the ratio 4 : 3 are revolving in circular orbits of radii...

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$\alpha=\sin 36^{\circ}$ is a root of which of the following equation

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The magnetic field of a plane electromagnetic wave is given by $...

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Given below are two statements : One is labeled as Assertion (A) and other is labeled as Reason (R). Assertion...

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Which one of the following is a water soluble vitamin, that is not excreted easily?

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Two cylindrical vessels of equal cross=sectional area $16 \mathrm{~cm}^2$ contain water upto heights 100 cm and 150 cm respectively. The...

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The value of $\cot \left(\sum_{n=1}^{50} \tan ^{-1}\left(\frac{1}{1+n+n^2}\right)\right)$ is :

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Given below are two statements, one is Assertion (A) and other is Reason (R). Assertion (A) : Natural rubber is...

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Let $f(x)$ and $g(x)$ be two real polynomials of degree 2 and 1 respectively. If $f(g(x))=8 x^2-2 x$, and $...

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In young’s double slit experiment, the fringe width is 12 mm. If the entire arrangement is placed in water of...

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If a point $A(x, y)$ lies in the region bounded by the $y$-axis, straight lines $2 y+x=6$ and $...

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In figure (A), mass ' 2 m ' is fixed on mass ' m ' which is attached to two...

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Let $M=\left[\begin{array}{cc}0 & -\alpha \\ \alpha & 0\end{array}\right]$, where $\alpha$ is a non-zero real number an $N=\sum_{k=1}^{49} M^{2 k}$. If...

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The mean and variance of the data $4,5,6,6,7,8, x, y$ where $x

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A bag is gently dropped on a conveyor belt moving at a speed of 2 m/s. The coefficient of friction...

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A parallel beam of light of wavelength 900 nm and intensity 100 $\mathrm{Wm}^{-2}$ is incident on a surface perpendicular to...

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With respect to the following reaction, consider the given statements : (A) o-Nitroaniline and p-nitroaniline are the predominant products (B)...

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Which of the following is NOT an example of synthetic detergent?

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Sand is being dropped from a stationary dropper at a rate of $0.5 \mathrm{kgs}^{-1}$ on a conveyor belt moving with...

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Let $\vec{a}$ and $\vec{b}$ be the vectors along the diagonal of a parallelogram having area $2 \sqrt{2}$. Let the angle...

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The maximum number of compound propositions, out of $...

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Following statements are given : (1) The average kinetic energy of a gas molecule decreases when the temperature is reduced....

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The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the...

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Isobutyraldehyde on reaction with formaldehyde and $\mathrm{K}_2 \mathrm{CO}_3$ gives compound ‘A’. Compound ‘A’ reacts with KCN and yields compound ‘B’,...

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The shortest distance between the lines $\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{-1}$ and $\frac{x+3}{2}=\frac{y-6}{1}=\frac{z-5}{3}$ is :

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A certain amount of gas of volume V at $27^{\circ} \mathrm{C}$ temperature and pressure $2 \times 10^7 \mathrm{Nm}^{-2}$ expands isothermally...

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Sulphur dioxide is one of the components of polluted air. $\mathrm{SO}_2$ is also a major contributor to acid rain. The...

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A bullet is shot vertically downwards with an initial velocity of 100 m/s from a certain height. Within 10 s,...

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Let $S=\{1,2,3,4\}$. Then the number of elements in the set $\{f: S \times S \rightarrow S: f$ is onto and...

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The total number of four digit numbers such that each of the first three digits is divisible by the last...

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A radio can tune to any station in 6 MHz to 10 MHz band. the value of corresponding wavelength bandwidth...

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Sum of squares of modulus of all the complex numbers $z$ satisfying $\bar{z}=i z^2+z^2-z$ is equal to

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Three identical particle A, B and C of mass 100 kg each are placed in a straight line with AB...

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A $\xrightarrow[\substack{\text { (ii) } \mathrm{CN}^{-} \\ \text {(ii) } \mathrm{H}_2 \mathrm{O} / \mathrm{H}^{+}}]{\text {(i) } \mathrm{Cl}_2 \Delta} 4$-Bromophenyl acetic...

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Three masses M = 100 kg, m1 = 10 kg and m2 = 20 kg are arranged in a system...

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Given $\pi a^2-\pi a b=30 \pi$ and $\pi a b-\pi b^2=18 \pi$ on subtracting, we get $(a-b)^2=a^2-2 a b+b^2=12$ Let...

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Let $A=\left(\begin{array}{cc}1+i & 1 \\ -i & 0\end{array}\right)$ where $i=\sqrt{-1}$. Then, the number of elements in the set $...

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A torque meter is calibrated to reference standards of mass, length and time each with 5% accuracy. After calibration, the...

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A solid cylinder and a solid sphere, having same mass M and radius R, roll down the same inclined plane...

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If the system of linear equations $2 x-3 y=\gamma+5, \alpha x+5 y=\beta+1$ where $\alpha, \beta, \gamma \in \mathbf{R}$ has infinitely...

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For real numbers a, b (a > b > 0), let

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Aqueous solution of which of the following boron compounds will be strongly basic in nature?

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The major product (P) of the given reaction is (where, Me is – $\left.\mathrm{CH}_3\right)$

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A body of mass 0.5 kg travels on straight line path with velocity $\mathrm{v}=\left(3 x^2+4\right) \mathrm{m} / \mathrm{s}$. The net...

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If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple...

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The number of solutions of the equation $\sin x=\cos ^2 x$ in the interval $(0,10)$ is $\_\_\_\_$ .

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Let for $\mathrm{n}=1,2, \ldots, 50, \mathrm{~S}_{\mathrm{n}}$ be the sum of the infinite geometric progression whose first term is $\mathrm{n}^2$ and...

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The final product ‘C’ is the following series series of reactions

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Number of lone pair (s) of electrons on central atom and the shape of $\mathrm{BrF}_3$ molecule respectively, are.

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Let a line $L_1$ be tangent to the hyperbola $\frac{x^2}{16}-\frac{y^2}{4}=1$ and let $L_2$ be the line passing through the origin...

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Let 3, 6, 9, 12, ... upto 78 terms and 5, 9, 13, 17, ... upto 59 terms be two...

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A person moved from A to B on a circular path as shown in figure. If the distance travelled by...

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If $\lim _{x \rightarrow 1} \frac{\sin \left(3 x^2-4 x+1\right)-x^2+1}{2 x^3-7 x^2+a x+b}=-2$, then the value of $(a-b)$ is equal to

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Let P1 be a parabola with vertex (3, 2) and focus (4, 4) and P2 be its mirror image with...

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Let $y=y(x), x>1$, be the solution of the differential equation $(x-1) \frac{d y}{d x}+2 x y=\frac{1}{x-1}$, with $y(2)=\frac{1+e}{2 e^4}$. If...

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The integral $\frac{24}{\pi} \int_0^{\sqrt{2}} \frac{\left(2-x^2\right) d x}{\left(2+x^2\right) \sqrt{4+x^4}}$ is equal to

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The correct IUPAC name of the following compound is :

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If $a_1(>0), a_2, a_3, a_4, a_5$ are in a G.P., $a_2+a_4=2 a_3+1$ and $3 a_2+a_3=2 a_4$, then $a_2+a_4+2 a_6$ is...

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If one of the diameters of the circle $x^2+y^2-2 \sqrt{2} x-6 \sqrt{2} y+14=0$ is a chord of the circle $...

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Which of the following physical quantities have the same dimensions ?

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Let $\vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}, \vec{b}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{c}$ be a vector such that $\vec{a}+(\vec{b} \times \vec{c})=\overrightarrow{0}$ and $\vec{b} \cdot \vec{c}=5$. Then,...

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Correct statement about photo-chemical smog is :

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Let the hyperbola H : $\frac{x^2}{a^2}-y^2=1$ and the ellipse E : $3 x^2+4 y^2=12$ be such that the length of...

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If $\left({ }^{40} \mathrm{C}_0\right)+\left({ }^{41} \mathrm{C}_1\right)+\left({ }^{42} \mathrm{C}_2\right)+\ldots .+\left({ }^{60} \mathrm{C}_{20}\right)=\frac{m}{n}{ }^{60} \mathrm{C}_{20}, m$ and $n$ are coprime, then $m+n$...

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Amongst baking soda, caustic soda and washing soda carbonate anion is present in :

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Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their...

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Which statement is NOT correct for p-toluenesulphonyl chloride?

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If momentum [P], area [A] and time [T] are taken as fundamental quantities, then the dimensional formula for coefficient of...

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The total number of 3–digit numbers, whose greatest common divisor with 36 is 2, is ______ .

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Let $n \geq 5$ be an integer. If $9^n-8 n-1=64 \alpha$ and $6^n-5 n-1=25 \beta$, then $\alpha-\beta$ is equal to...

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Which of the following oxoacids of sulphur contains “S” in two different oxidation states?

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In an examination, there are 10 true-false type questions. Out of 10, a student can guess the answer of 4...

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Let the image of the point $P(1,2,3)$ in the line $L: \frac{x-6}{3}=\frac{y-1}{2}=\frac{z-2}{3}$ be $Q$. let $R(\alpha, \beta, \gamma)$ be a...

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Let $...

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The final product ‘A’ in the following reaction sequence

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Given below are two statements . Statement I: In $\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}, \mathrm{Cu}-\mathrm{O}$ bonds are present. Statement II:...

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If $\cot \alpha=1$ and $\sec \beta=-\frac{5}{3}$, where $\pi

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Let a circle C : $(x-h)^2+(y-k)^2=r^2, k>0$,, touch the x-axis at (1, 0). If the line x + y =...

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If $z^2+z+1=0, z \in \mathbb{C}$, then $\left|\sum_{n=1}^{15}\left(z^n+(-1)^n \frac{1}{z^n}\right)^2\right|$ is equal to

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Negation of the Boolean statement $(p \vee q) \Rightarrow((\sim r) \vee p)$ is equivalent to :

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Let $p$ and $q$ be two real numbers such that $p+q=3$ and $p^4+q^4=369$. Then $\left(\frac{1}{p}+\frac{1}{q}\right)^{-2}$ is equal to . $\_\_\_\_$

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Among the given oxides of nitrogen; $\mathrm{N}_2 \mathrm{O}, \mathrm{N}_2 \mathrm{O}_3, \mathrm{~N}_2 \mathrm{O}_4$ and $\mathrm{N}_2 \mathrm{O}_5$ the number of compound/(s) having...

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The area (in sq. units) of the region enclosed between the parabola $y^2$ = 2x and the line x +...

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Let the foot of the perpendicular from the point $(1,2,4)$ on the line $\frac{x+2}{4}=\frac{y-1}{2}=\frac{z+1}{3}$ be $P$. Then the distance of...

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Let $\vec{a}$ be a vector which is perpendicular to the vector $3 \hat{i}+\frac{1}{2} \hat{j}+2 \hat{k}$. If $...

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From the base of a pole of height 20 meter, the angle of elevation of the top of a tower...

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The reagent, from the following, which converts benzoic acid to benzaldehyde in one step is

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Among the following basic oxide is :

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The set of values of $k$ for which the circle $C: 4 x^2+4 y^2-12 x+8 y+k=0$ lies inside the fourth...

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The remainder on dividing $1+3+3^2+3^3+\ldots+3^{2021}$ by 50 is $\_\_\_\_$

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The value of $\lim _{n \rightarrow \infty} 6 \tan \left\{\sum_{r=1}^n \tan ^{-1}\left(\frac{1}{r^2+3 r+3}\right)\right\}$

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The number of values of $a \in \mathbb{N}$ such that the variance of $3,7,12 a, 43-a$ is a natural number...

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The sum of all the elements of the set $\{\alpha \in\{1,2, \ldots, 100\}: \operatorname{HCF}(\alpha, 24)=1\}$ is $\_\_\_\_$

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The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to:

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The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2,...

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The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3,...

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Let the plane ax + by + cz = d pass through (2, 3, –5) and is perpendicular to the...

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Let $Q$ be the mirror image of the point $P(1,2,1)$ with respect to the plane $x+2 y+2 z=16$. Let $T$...

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If vertex of a parabola is (2, –1) and the equation of its directrix is 4x – 3y = 21,...

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The distance of the origin from the centroid of the triangle whose two sides have the equations $x-2 y+1=0$ and...

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Let $\frac{x-2}{3}=\frac{y+1}{-2}=\frac{z+3}{-1}$ lie on the plane $p x-q y+z=5$, for some $p, q \in \mathbb{R}$. The shortest distance of the...

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Let a triangle $A B C$ be inscribed in the circle $x^2-\sqrt{2}(x+y)+y^2=0$ such that $\angle B A C=\frac{\pi}{2}$. If the...

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Let $P: y^2=4 a x, a>0$ be a parabola with focus $S$. Let the tangents to the parabola $P$ make...

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If $y=y(x)$ is the solution of the differential equation $\left(1+e^{2 x}\right) \frac{d y}{d x}+2\left(1+y^2\right) e^x=0$ and $y(0)=0$, then $...

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If $\int_0^2\left(\sqrt{2 x}-\sqrt{2 x-x^2}\right) d x=\int_0^1\left(1-\sqrt{1-y^2}-\frac{y^2}{2}\right) d y+\int_1^2\left(2-\frac{y^2}{2}\right) d y+1$

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Let $f$ be a real valued continuous function on $[0,1]$ and $f(x)=x+\int_0^1(x-t) f(t) d t$. Then which of the following...

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Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function defined by $f(x)=(x-3)^{n_1}(x-5)^{n_2}, n_1, n_2 \in N$. The, which of the following...

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Halogenation of which one of the following will yield m-substituted product with respect to methyl group as a major product?

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The value of $\lim _{x \rightarrow 1} \frac{\left(x^2-1\right) \sin ^2(\pi x)}{x^4-2 x^3+2 x-1}$ is equal to:

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Let $\mathrm{S}=\left\{\left(\begin{array}{cc}-1 & \mathrm{a} \\ 0 & \mathrm{~b}\end{array}\right) ; \mathrm{a}, \mathrm{b} \in\{1,2,3, \ldots 100\}\right\}$ and let $\mathrm{T}_{\mathrm{n}}=\left\{\mathrm{A} \in \mathrm{S}: \mathrm{A}^{\mathrm{n}(\mathrm{n}+1)}=\mathrm{I}\right\}$....

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The sum of the infinite series $1+\frac{5}{6}+\frac{12}{6^2}+\frac{22}{6^3}+\frac{35}{6^4}+\frac{51}{6^5}+\frac{70}{6^6}+\ldots .$. is equal to :

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Let $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfy $f(x+y)=2 x f(y)+4 y f(x), \forall x, y \in \mathbb{R}$. If $f(2)=3$, then 14...

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Hydrogen has three isotopes : protium $\left({ }^1 \mathrm{H}\right)$ deuterium $\left({ }^2 \mathrm{H}\right.$ or D$)$ and tritium $\left({ }^3 \mathrm{H}\right.$...

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Let $\vec{a}=\alpha \hat{i}+2 \hat{j}-\hat{k}$ and $\vec{b}=-2 \hat{i}+\alpha \hat{j}+\hat{k}$, where $a \in \mathbf{R}$. If the area of the parallelogram whose adjacent...

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Let $S=\{z \in \mathbb{C}:|z-3| \leq$ and $z(4+3 i)+\bar{z}(4-3 i) \leq 24\}$. if $\alpha+\mathrm{i} \beta$ is the point in S which...

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Let $\mathrm{A}=\left(\begin{array}{cc}2 & -1 \\ 0 & 2\end{array}\right)$. If $\mathrm{B}=1-{ }^5 \mathrm{C}_1(\operatorname{adj} \mathrm{~A})+{ }^5 \mathrm{C}_2(\operatorname{adj} \mathrm{~A})^2-\ldots \ldots-{ }^5 \mathrm{C}_5(\operatorname{adj} \mathrm{~A})^5$,...

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Let $r \in\{p, q, \sim p, \sim q\}$ be such that the logical statement $...

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Let $\mathrm{a}>0, \mathrm{~b}>0$. Let e and $\ell$ respectively be the eccentricity and length of the latus rectum of the hyperbola...

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Let $\arg (z)$ represent the principal argument of the complex number $z$. The, $|z|=3$ and $\arg (z-1)-\arg (z+1) =\frac{\pi}{4}$ intersect:

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Let a triangle be bounded by the lines $L_{1 i} 2 x+5 y=10 ; L_{2 i}-4 x+3 y=12$ and the...

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Let $\alpha$ be a root of the equation $1+x^2+x^4=0$. Then the value of $\alpha^{1011}+\alpha^{2022}-\alpha^{3033}$ is equal to:

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Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion...

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Let the slope of the tangent to a curve $y=f(x)$ at $(x, y)$ be given by $2 \tan (\cos x-y)$....

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Let $l_1$ be the line in xy - plane with x and y intercepts $\frac{1}{8}$ and $\frac{1}{4 \sqrt{2}}$ respectively, and...

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Match List-I with List-II. Choose the correct answer from the options given below :

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0.25 g of an organic compound containing chlorine gave 0.40 g of silver chloride in Carius estimation. The percentage of...

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If the inverse trigonometric functions take principal values, then $\cos ^{-1}\left(\frac{3}{10} \cos \left(\tan ^{-1}\left(\frac{4}{3}\right)\right)+\frac{2}{5} \sin \left(\tan ^{-1}\left(\frac{4}{3}\right)\right)\right)$ is equal to...

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Let the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be $\frac{5}{4}$. If the equation of the normal at the point $\left(\frac{8}{\sqrt{5}}, \frac{12}{5}\right)$...

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Solve the fig-:

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Let $\mathrm{x}=\mathrm{x}(\mathrm{y})$ be the solution of the differential equation $2 \mathrm{ye}^{\mathrm{x} / \mathrm{y}^2} \mathrm{dx}+\left(\mathrm{y}^2-4 \mathrm{xe}^{\mathrm{x} / \mathrm{y}^2}\right) \mathrm{dy}=0$ such that...

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Match List-I with List-II. Choose the correct answer from the options given below:

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Let $f(x)=\left\lfloor(x-1)\left(x^2-2 x-3\right)\right\rfloor+x-3, x \in R$. If $m$ and $M$ are respectively the number of points of local minimum and...

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The slope of normal at any point (x, y), x > 0, y > 0 on the curve y =...

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$16 \sin \left(20^{\circ}\right) \sin \left(40^{\circ}\right) \sin \left(80^{\circ}\right)$ is equal to :

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It has been found that for a chemical reaction with rise in temperature by 9K the rate constant gets doubled....

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The total number of three-digit numbers, with one digit repeated exactly two times, is

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The area of the bounded region enclosed by the curve $y=3-\left|x-\frac{1}{2}\right|-|x+1|$ and the $x$-axis is

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The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation...

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A student needs to prepare a buffer solution of propanoic acid and its sodium salt with pH 4. The ratio...

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For the reaction taking place in the cell: $$ \begin{aligned} & \mathrm{Pt}(\mathrm{~s})\left|\mathrm{H}_2(\mathrm{~g})\right| \mathrm{H}^{+}(\mathrm{aq}) \| \mathrm{Ag}^{+}(\mathrm{aq}) \mid \mathrm{Ag}(\mathrm{~s}) \\ & \mathrm{E}_{\text...

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Consider the following statements : A : Rishi is a judge. B : Rishi is honest. C : Rishi is...

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pH value of 0.001 M NaOH solution is______.

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Let $f: R \rightarrow R$ be continuous function satisfying $f(x)+f(x+k)=n$, for all $x \in R$ where $k>0$ and $n$ is...

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Let $\vec{a}=\hat{i}+\hat{j}+2 \hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}+\hat{k}$ be three given vectors. Let $\vec{v}$ be a vector in the plane...

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Let $\vec{b}=\hat{i}+\hat{j}+\lambda \hat{k}, \lambda \in R$. If $\vec{a}$ is a vector such that $\vec{a} \times \vec{b}=13 \hat{i}-\hat{j}-4 \hat{k}$ and $...

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A solution containing $2.5 \times 10^{-3} \mathrm{~kg}$ of a solute dissolved in $75 \times 10^{-3} \mathrm{~kg}$ of water boils at...

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If $y=\tan ^{-1}\left(\sec x^3-\tan x^3\right)$. $\frac{\pi}{2}$< $x^3$< $\frac{3 \pi}{2}$, then

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In the structure of $\mathrm{SF}_4$ , the lone pair of electrons on S is in.

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4.0 moles of argon and 5.0 moles of $\mathrm{PCl}_5$ are introduced into an evacuated flask of 100 litre capacity at...

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If the mean deviation about the mean of the numbers $1,2,3$, $\_\_\_\_$ $n$, where $n$ is odd, is $\frac{5(n+1)}{n}$, then...

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If the lines and $\vec{r}=(\hat{i}-\hat{j}+\hat{k})+\lambda(3 \hat{j}-\hat{k})$ and $\vec{r}=(\alpha \hat{i}-\hat{j})+\mu(2 \hat{i}-3 \hat{k})$ are co-planar, then distance of the plane containing these...

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When 5 moles of He gas expand isothermally and reversibly at 300 K from 10 litre to 20 litre, the...

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Let $f: R \rightarrow R$ be a differentiable function such that $f\left(\frac{\pi}{4}\right)=\sqrt{2}, f\left(\frac{\pi}{2}\right)=0$ and $f\left(\frac{\pi}{2}\right)=1$ and let $...

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BeO reacts with HF in presence of ammonia to give [A] which on thermal decomposition produces [B] and ammonium fluoride....

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Let $f, g: R \rightarrow R$ be functions defined by $f(x)=\left\{\begin{array}{cc}{[x],} & x

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If the plane 2x + y – 5z = 0 is rotated about its line of intersection with the plane...

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If the sum of the coefficients of all the positive even powers of $x$ in the binomial expansion of $...

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If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the...

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116 g of a substance upon dissociation reaction, yields 7.5 g of hydrogen, 60g of oxygen and 48.5 g of...

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The value of $b>3$ for which $12 \int_3^b \frac{1}{\left(x^2-1\right)\left(x^2-4\right)} d x=\log _e\left(\frac{49}{40}\right)$, is equal to

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The normal to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{9}=1$ at the point $(8,3 \sqrt{3})$ on it passes through the point :

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Consider the following statements : (A) The principal quantum number ‘n’ is a positive integer with values of ‘n’ =...

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Let $f(x)=\left[2 x^2+1\right]$ and $g(x)=\left\{\begin{array}{ll}2 x-3, & x

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The locus of the mid point of the line segment joining the point (4, 3) and the points on the...

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The term independent of $x$ in the expression of $\left(1-x^2+3 x^3\right)\left(\frac{5}{2} x^3-\frac{1}{5 x^2}\right)^{11}, x \neq 0$ is

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Let $A=\left(\begin{array}{ll}2 & -2 \\ 1 & -1\end{array}\right)$ and $B=\left(\begin{array}{ll}-1 & 2 \\ -1 & 2\end{array}\right)$. Then the number of...

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Match List I with List II

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Let the points on the plane P be equidistant from the points (.4, 2, 1) and (2, .2, 3). Then...

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Consider the species $\mathrm{CH}_4, \mathrm{NH}_4^{+}$and $\mathrm{BH}_4^{-}$. Choose the correct option with respect to the there species:

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The number of ways to distribute 30 identical candies among four children $\mathrm{C}_1, \mathrm{C}_2, \mathrm{C}_3$ and $\mathrm{C}_4$ so that $\mathrm{C}_2$...

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The line $y=x+1$ meets the ellipse $\frac{x^2}{4}+\frac{y^2}{2}=1$ at two points $P$ and $Q$. If $r$ is the radius of the...

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Match List I with List Ii

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If m is the slope of a common tangent to the curves $\frac{x^2}{16}+\frac{y^2}{9}=1$ and $x^2+y^2=12$, then $12 m^2$ is equal...

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Let f(x) be a quadratic polynomial such that f(–2) + f(3) = 0. If one of the roots of f(x)...

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If the shortest distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{\lambda}$ and $\frac{x-2}{1}=\frac{y-4}{4}=\frac{z-5}{5}$ is $\frac{1}{\sqrt{3}}$, then the sum of all possible values of...

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If the equation of the parabola, whose vertex is at $(5,4)$ and the directrix is $...

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If the solution of the differential equation $\frac{d y}{d x}+e^x\left(x^2-2\right) y=\left(x^2-2 x\right)\left(x^2-2\right) e^{2 x}$ satisfies y(0) = 0, then the...

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Let $\mathrm{R}_1=\{(\mathrm{a}, \mathrm{b}) \in \mathrm{N} \times \mathrm{N}:|\mathrm{a}-\mathrm{b}| \leq 13\}$ and $R_2=\{(a, b) \in N \times N:|a-b| \neq 13\}$. Then on...

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The value of $\tan ^{-1}\left(\frac{\cos \left(\frac{15 \pi}{4}\right)-1}{\sin \left(\frac{\pi}{4}\right)}\right)$ is equal to :

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If the solution curve of the differential equation $\left(\left(\tan ^{-1} y\right)-x\right) d y=\left(1+y^2\right) d x$ passes through the point $(1,0)$...

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If $y=y(x)$ is the solution of the differential equation $x \frac{d y}{d x}+2 y=x e^x, y(1)=0$, then the local maximum...

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Which of the following is the correct plot for the probability density $\psi^2(r)$ as a function of distance ' $r$...

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The number of solutions of the equation cos $\left(x+\frac{\pi}{3}\right) \cos \left(\frac{\pi}{3}-x\right)=\frac{1}{4} \cos ^2 2 x, x \in[-3 \pi, 3 \pi]$...

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The integral $\int_0^1 \frac{1}{7^{\left[\frac{1}{x}\right]}} \mathrm{dx}$, where [.] denotes the greatest integer function is equal to :

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If the line $y=4+k x, k>0$, is the tangent to the parabola $y=x-x^2$ at the point $P$ and $V$ is...

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Given below are two statements. Statement I: Maltose has two $\alpha$-D-glucose units linked at $\mathrm{C}_1$ and $\mathrm{C}_4$ and is a...

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Let $\mathrm{b}_1 \mathrm{~b}_2 \mathrm{~b}_3 \mathrm{~b}_4$ be a 4 -element permutation with $\mathrm{b}_{\mathrm{i}} \in\{1,2,3, \ldots \ldots \ldots, 100\}$ for $...

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Let $f$ be a differentiable function in $\left(0, \frac{\pi}{2}\right)$. If $\int_{\cos x}^1 t^2 f(t) d t=\sin ^3 x+\cos x$ then...

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The negation of the Boolean expression $((\sim q) \wedge p) \Rightarrow((\sim p) \vee q)$ is logically equivalent to

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Let $P_1: \bar{r} .(2 \hat{i}+\hat{j}-3 \hat{k})=4$ be a plane. Let $P_2$ be another plane which passes through the points $(2,-3,2)(2$,...

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The major product in the following reaction

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If $m$ and $n$ respectively are the number of local maximum and local minimum points of the function $...

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Which is true about Buna-N?

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Let $c, k \in R$. If $f(x)=(c+1) x^2+\left(1-c^2\right) x+2 k$ and $f(x+y)=f(x)+f(y)-x y$, for all $x, y \in R$, then...

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If $a_1, a_2, a_3 \ldots$. and $b_1, b_2, b_3 \ldots$. are A.P. and $a_1,=2, a_{10}=3, a_1 b_1=1=a_{10} b_{10}$ then $...

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Decarboxylation of all six possible forms of diaminobenzoic acids $\mathrm{C}_6 \mathrm{H}_3\left(\mathrm{NH}_2\right)_2 \mathrm{COOH}$ yields three products A, B and C. Three...

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$50 \tan \left(3 \tan ^{-1}\left(\frac{1}{2}\right)+2 \cos ^{-1}\left(\frac{1}{\sqrt{5}}\right)\right)+4 \sqrt{2} \tan \left(\frac{1}{2} \tan ^{-1}(2 \sqrt{2})\right)$ is equal to $\_\_\_\_$

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Let $S=2+\frac{6}{7}+\frac{12}{7^2}+\frac{20}{7^3}+\frac{30}{7^4}+\ldots$. then $4 S$ is equal to

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If $\int \frac{1}{x} \sqrt{\frac{1-x}{1+x}} d x=g(x)+c, g(1)=0$, then $g\left(\frac{1}{2}\right)$ is equal to :

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Match List I with List II

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Using the rules for significant figures, the correct answer for the expression $\frac{0.02858 \times 0.112}{0.5702}$ will be:

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Let $A$ and $B$ be two $3 \times 3$ matrices such that $A B=I$ and $|A|=\frac{1}{8}$ then $|\operatorname{adj}(\operatorname{Badj}(2 A))|$ is...

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The number of solutions of the equation $2 \theta-\cos ^2 \theta+\sqrt{2}=0$ is $R$ is equal to $\_\_\_\_$ .

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The number of elements in the set $...

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Let for some real numbers $\alpha$ and $\beta, \mathrm{a}=\alpha-\mathrm{i} \beta$. If the system of equations 4ix $+(1+\mathrm{i}) \mathrm{y}=0$ and $...

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Product ‘A’ of following sequence of reactions is

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Let $d$ be the distance between the foot of perpendiculars of the points $P(1,2-1)$ and $Q(2,-1,3)$ on the plane $-x+y+z=1$....

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The number of distinct real roots of the equation $x^7-7 x-2=0$ is

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What will be the major product of following sequence of reactions?

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Let $...

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The area of the region bounded by $y^2=8 x$ and $y^2=16(3-x)$ is equal to:-

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Let the area of the triangle with vertices $\mathrm{A}(1, \alpha), \mathrm{B}(\alpha, 0)$ and $\mathrm{C}(0, \alpha)$ be 4 sq. units. If...

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The number of points of intersection of $|z-(4+3 i)|=2$ and $|z|+|z-4|=6, z \in C$ is :

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Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of...

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Which of the following is most stable?

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Let the maximum area of the triangle that can be inscribed in the ellipse $\frac{x^2}{a^2}+\frac{y^2}{4}=1, a>2$, having one of its...

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On the surface of polar stratospheric clouds, hydrolysis of chlorine nitrate gives A and B while its reaction with HCl...

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Let $f(x)=\min \{1,1+x \sin x\}, 0 \leq x \leq 2 \pi$. If m is the number of points, where f...

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Oxidation of toluene to Benzaldehyde can be easily carried out with which of the following reagents?

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Let $S=\{z \in C:|z-2| \leq 1, z(1+i)+\bar{z}(1-i) \leq 2\}$. Let $|z-4 i|$ attains minimum and maximum values, respectively, at $...

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Arrange the following coordination compounds in the increasing order of magnetic moments. (Atomic numbers: Mn = 25; Fe = 26)

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A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to...

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Let the mean and the variance of 5 observations $x_1, x_2, x_3, x_4, x_5$ be $\frac{24}{5}$ and $\frac{194}{25}$ respectively. If...

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Let the tangent to the circle $C_1: x^2+y^2=2$ at the point $M(-1,1)$ intersect the circle $C_2:(x-3)^2+(y-2)^2=5$ at two distinct points...

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Compound A contains 8.7% Hydrogen, 74% Carbon and 17.3% Nitrogen. The molecular formula of the compound is, Given: Atomic masses...

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$\lim _{n \rightarrow \infty}\left(\frac{n^2}{\left(n^2+1\right)(n+1)}+\frac{n^2}{\left(n^2+4\right)(n+2)}+\frac{n^2}{\left(n^2+9\right)(n+3)}+\ldots+\frac{n^2}{\left(n^2+n^2\right)(n+n)}\right)$ is equal to

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The ‘f’ orbitals are half and completely filled, respectively in lanthanide ions (Given: Atomic no. Eu, 63; Sm, 62; Tm,...

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Let $P Q$ be a focal chord of the parabola $y^2=4 x$ such that it subtends an angle of $\frac{\pi}{2}$...

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$\lim _{x \rightarrow 0} \frac{\cos (\sin x)-\cos x}{x^4}$ is equal to :

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$\int_0^5 \cos \left(\pi\left(x-\left[\frac{x}{2}\right]\right)\right) d x$, Where $[t]$ denotes greatest integer less than or equal to $t$, is equal to :

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In 3d series, the metal having the highest $\mathrm{M}^{2+} / \mathrm{M}$ standard electrode potential is

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The value of the integral $\int_{-\pi / 2}^{\pi / 2} \frac{d x}{\left(1+e^x\right)\left(\sin ^6 x+\cos ^6 x\right)}$ is equal to

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If the constant term in the expansion of $\left(3 x^3-2 x^2+\frac{5}{x^5}\right)^{10}$ is $2^k . l$, where $l$ is an odd...

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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion...

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If $A=\sum_{n=1}^{\infty} \frac{1}{\left(3+(-1)^n\right)^n}$ and $B \sum_{n=1}^{\infty} \frac{(-1)^n}{\left(3+(-1)^n\right)^n}$, then $\frac{A}{B}$ is equal to :

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Let $f(x)=\left\{\begin{array}{ccc}\frac{\sin (x-[x])}{x-[x]}, & x \in(-2,-1) \\ \{\max 2 x, 3[|x|]\}, & |x|

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The domain of the function $\cos ^{-1}\left(\frac{2 \sin ^{-1}\left(\frac{1}{4 x^2-1}\right)}{\pi}\right)$ is

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The gas produced by treating an aqueous solution of ammonium chloride with sodium nitrite is

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The correct order of nucleophilicity is

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A wire of length 22 m is to be cut into two pieces. One of the pieces is to be...

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The correct order of increasing ionic radii is

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If the system of equations $\alpha x+y+z=5, x+2 y+3 z=4, x+3 y+5 z=\beta$, has infinitely many solutions, then the ordered...

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The correct order of increasing intermolecular hydrogen bond strength is

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The distance between the two points $A$ and $A^{\prime}$ which lie on $y=2$ such that both the line segments $...

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Let $x, y>0$. If $x^3 y^2=2^{15}$, then the least value of $3 x+2 y$ is

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Statement I : Leaching of gold with cyanide ion in absence of air / O2 leads to cyano complex of...

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Let $\left\{a_n\right\}_{n-0}^{\infty}$ be a sequence such that $a_0=a_1=0$ and $a_{n+2}=2 a_{n+1}-a_n+1$ for all $n \geq 0$. Then, $\sum_{n-2}^{\infty} \frac{a_n}{7^n}$ is...

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Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as $f(x)=x-1$ and $g: \mathbb{R}-\{1,-1\}$ be defined as $g(x)=\frac{x^2}{x^2-1}$ Then the function fog...

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Identify the incorrect statement for $\mathrm{PCl}_5$ from the following.

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Let a set $A=A_1 \cup A_2 \cup \ldots \cup A_{k^{\prime}}$ where $A_i \cap A_j=\phi$ for $...

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Let $\mathrm{A}=\left[a_{i j}\right]$ be a square matrix of order 3 such that $a_{i j}=2^{i-i}$, for all $\mathrm{i}_{\text {and }} \mathrm{j}=1,2,3$....

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Which amongst the given plots is the correct plot for pressure (p) vs density (d) for an ideal gas?

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The neutralization occurs when 10 mL of 0.1 M acid ‘A’ is allowed to react with 30 mL of 0.05...

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How many of the given compounds will give a positive Biuret test ______ ? Glycine, Glycylalanine, Tripeptide, Biuret

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The Novolac polymer has mass of 963 g. The number of monomer units present in it are

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Amongst $\mathrm{FeCl}_3 .3 \mathrm{H}_2 \mathrm{O}, \mathrm{K}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right]$ and $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right] \mathrm{Cl}_3$, the spin-only magnetic moment value of the inner-orbital complex that absorbs...

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A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of...

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The value of $2 \sin \left(12^{\circ}\right)-\sin \left(72^{\circ}\right)$ is :

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If the angle made by the tangent at the point $\left(x_0, y_0\right)$ on the curve $...

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If $y=y(x)$ is the solution of the differential equation $2 x^2 \frac{d y}{d x}-2 x y+3 y^2=0$ such that $y(e)=\frac{e}{3}$,...

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If $b_n=\int_0^{\frac{\pi}{2}} \frac{\cos ^2 n x}{\sin x} d x, n \in N$, then

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In alanylglycylleucylalanylvaline, the number of peptide linkages is______.

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Consider the above reaction. The number of $\pi$ electrons present in the product ' P ' is $\_\_\_\_$

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Water is being filled at the rate of $1 \mathrm{~cm}^3 / \mathrm{sec}$ in a right circular conical vessel (vertex downwards)...

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0.2 g of an organic compound was subjected to estimation of nitrogen by Dumas method in which volume of $\mathrm{N}_2$...

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Manganese (VI) has ability to disproportionate in acidic solution. The difference in oxidation states of two ions it forms in...

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A circle touches both the y-axis and the line x + y = 0. Then the locus of its center...

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(a) Baryte, (b) Galena, (c) Zinc blende and (d) Copper pyrites. How many of these minerals are sulphide based?

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When 200 mL of 0.2 M acetic acid is shaken with 0.6 g of wood charcoal, the final concentration of...

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Let $P$ be the plane passing through the intersection of the planes $\vec{r} \cdot(\hat{i}+3 \hat{j}-\hat{k})=5$ and $\vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=3$, and...

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The resistance of conductivity cell containing 0.01 M KCl solution at 298 K is $1750 \Omega$. If the conductivity of...

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The measured BOD values for four different water samples (A-D) are as follows: $...

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The sum $1+2 \cdot 3+3 \cdot 3^2+\ldots \ldots+10 \cdot 3^9$ is equal to

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$\mathrm{PCl}_5$ dissociates as $$ \mathrm{PCl}_5(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_3(\mathrm{~g})+\mathrm{Cl}_2(\mathrm{~g}) $$ 5 moles of PCl 5 are placed in a 200 litre vessel...

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The coefficient of $x^{101}$ in the expression $(5+x)^{500}+x(5+x)^{499}+x^2(5+x)^{498}+\ldots . . x^{500} \ldots>0$, is

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A company dissolves ' X ' amount of $\mathrm{CO}_2$ at 298 K in 1 litre of water to prepare soda...

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The most common oxidation state of Lanthanoid elements is +3. Which of the following is likely to deviate easily from...

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The area of the region enclosed between the parabolas $y^2=2 x-1$ and $y^2=4 x-3$ is

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$\lim _{x \rightarrow \frac{\pi}{2}}\left(\tan ^2 x\left(\left(2 \sin ^2 x+3 \sin x+4\right)^{\frac{1}{2}}-\left(\sin ^2 x+6 \sin x+2\right)^{\frac{1}{2}}\right)\right)$ is equal to

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At 300 K , a sample of 3.0 g of gas A occupies the same volume as 0.2 g of...

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Which one of the following is an example of disproportionation reaction?

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Let the system of linear equations $$ \begin{aligned} & x+y+\alpha z=2 \\ & 3 x+y+z=4 \\ & x+2 z=1 \end{aligned}...

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The system of equations $$ \begin{aligned} & -k x+3 y-14 z=25 \\ & -15 x+4 y-k z=3 \\ & -4...

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In the flame test of a mixture of salts, a green flame with blue centre was observed. Which one of...

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The oxide which contains an odd electron at the nitrogen atom is

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Two objects of equal masses placed at certain distance from each other attracts each other with a force of F....

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Let $z_1$ and $z_2$ be two complex numbers such that $\bar{z}_1=i \bar{z}_2$ and arg $\left(\frac{z_1}{\bar{z}_2}\right)=\pi$. Then

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The structure shown below is of which well-known drug molecule?

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The sum of all the real roots of the equation $\left(e^{2 x}-4\right)\left(6 e^{2 x}-5 e^x+1\right)=0$ is

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Let $a, b \in R$ be such that the equation $a x^2-2 b x+15=0$ has a repeated root $\alpha$. If...

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Which of the following is not an example of a condensation polymer?

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Let $\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$ be such that $(p \wedge q) \Delta((p \vee q) \Rightarrow q)$ is a tautology....

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Water fall from a 40 m high dam at the rate of $9 \times 10^4 \mathrm{~kg}$ per hour. Fifty percentage...

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s-block element which cannot be qualitatively confirmed by the flame test is

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Let $A=\{x \in R:|x+1|

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Let $x * y=x^2+y^3$ and $(x * 1) * 1=x *(1 * 1)$. Then a value of $2 \sin ^{-1}\left(\frac{x^4+x^2-2}{x^4+x^2+2}\right)$

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The conversion of propan-1-ol to n-butylamine involves the sequential addition of reagents. The correct sequential order of reagents is.

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Let the lines $y+2 x=\sqrt{11}+7 \sqrt{7}$ and $2 y+x=2 \sqrt{11}+6 \sqrt{7}$ be normal to a circle $C:(x-h)^2+(y-k)^2=r^2$. If the line...

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Boiling of hard water is helpful in removing the temporary hardness by converting calcium hydrogen carbonate and magnesium hydrogen carbonate...

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An inductor of $0.5 \mu \mathrm{H}$, a capacitor of $200 \mu \mathrm{~F}$ and a resistor of $2 \Omega$ are connected...

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The number of elements in the set $\{z=a+i b \in \mathbb{C}: a, b \in \mathbb{Z}$ and $1

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Hex-4-ene-2-ol on treatment with PCC gives 'A'. 'A' on reaction with sodium hypoiodite gives 'B', which on further heating with...

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The number of positive integers $k$ such that the constant term in the binomial expansion of $...

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A $\sqrt{34} \mathrm{~m}$ long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3...

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Let the mirror image of the point $(a, b, c)$ with respect to the plane $3 x-4 y+12 z+19=0$ be...

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Which of the following reagents/ reactions will convert 'A' to 'B'?

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The role of depressants in Froth Flotation method* is to

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Let $\mathrm{A}=\left\{1, \mathrm{a}_1, \mathrm{a}_2 \ldots . . \mathrm{a}_{18}, 77\right\}$ be a set of integers with $1

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A circle of radius 2 unit passes through the vertex and the focus of the parabola $y^2=2 x$ and touches...

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A rectangle R with end points of the one of its dies as (1, 2) and (3, 6) is inscribed...

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Given below are two statements. Statement I : The presence of weaker - bonds make alkenes less stable than alkanes....

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If the sum of the first ten terms of the series $\frac{1}{5}+\frac{2}{65}+\frac{3}{325}+\frac{4}{1025}+\frac{5}{2501}+\ldots .$. is $\frac{m}{n}$, where $m$ and $n$ are...

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Arrange the following carbocations in decreasing order of stability.

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A ray of light passing through the point $P(2,3)$ reflects on the $x$-axis at point $A$ and the reflected ray...

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The cut-off voltage of the diodes (shown in figure) in forward bias is 0.6 V. The current through the resister...

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Let $A_1=\left\{(x, y):|x| \leq y^2,|x|+2 y \leq 8\right\}$ and $A_2=\{(x, y):|x|+|y| \leq k\}$. If $27\left(\operatorname{Area} A_1\right)=5\left(\operatorname{Area} A_2\right)$, then $k$ is...

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Which of the following elements in considered as a metalloid?

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If $\vec{a}=2 \hat{i}+\hat{j}+3 \hat{k}, \vec{b}=3 \hat{i}+3 \hat{j}+\hat{k}$ and $\vec{c}=c_1 \hat{i}+c_2 \hat{j}+c_3 \hat{k}$ are coplanar vectors and $...

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A ball is spun with angular acceleration $\alpha=6 t^2-2 t$ where $t$ is in second and $\alpha$ is in rads-2....

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The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was...

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If the coefficient of $x^{10}$ in the binomial expansion of $\left(\frac{\sqrt{x}}{5^{\frac{1}{4}}}+\frac{\sqrt{5}}{x^{\frac{1}{3}}}\right)^{60}$ is $5^k l$, where $l, k \in N$ and...

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In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the...

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The number of real solutions of the equation $\mathrm{e}^{4 \mathrm{x}}+4 \mathrm{e}^{3 \mathrm{x}}-58 \mathrm{e}^{2 \mathrm{x}}+4 \mathrm{e}^{\mathrm{x}}+1=0$ is $\_\_\_\_$ .

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The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in...

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A metallic rod of length 20 cm is palced in North- South direction and is moved at a constant speed...

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The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance...

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The positive value of the determinant of the matrix $A$, whose $...

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Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as $v_2=\frac{n}{m^2} v_1$ and $...

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Let $R_1$ and $R_2$ be relations on the set $\{1,2, \ldots \ldots, 50\}$ such that $\mathrm{R}_1=\left\{\left(\mathrm{p}, \mathrm{p}^{\mathrm{n}}\right): \mathrm{p}\right.$ is a...

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The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is $\mathrm{l}_{1 .}$....

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If the sum of all the roots of the equation $e^{2 x}-11 e^x-45 e^{-x}+\frac{81}{2}=0$ is $\log _e P$, then $p$...

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A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle...

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Let p, q, r be three logical statements. Consider the compound statements Then, which of the following is NOT true?

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Let $\alpha$ and $\beta$ be the roots of the equation $x^2+(2 i-1)=0$. Then, the value of $\left|\alpha^8+\beta^8\right|$ is equal to...

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The displacement current of $4.425 \mu \mathrm{~A}$ is developed in the space between the plates of parallel plate capacitor when...

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In the given circuit 'a' is an arbitrary constant. The value of m for which the equivalent circuit resistance is...

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Let $f: R \rightarrow R$ be a function defined $f(x)=\frac{2 e^{2 x}}{e^{2 x}+e}$. Then $f\left(\frac{1}{100}\right)+f\left(\frac{2}{100}\right)+f\left(\frac{3}{100}\right)+\ldots . .+f\left(\frac{99}{100}\right)$ is equal to

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Let $A B$ and $P Q$ be two vertical poles, 160 m apart from each other. Let $C$ be the...

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A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the n-side with...

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Some gases are responsible for heating of atmosphere (green house effect). Identify from the following the gaseous species which does...

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The Boolean expression $\left(\sim\left(p^{\wedge} q\right)\right) \vee q$ is equivalent to :

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The probability, that in a randomly selected 3-digit number at least two digits are odd, is

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The current density in a cylindrical wire of radius r = 4.0 mm is $1.0 \times 10^6 \mathrm{~A} / \mathrm{m}^2$....

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The number of radial and angular nodes in 4d orbital are. Respectively

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Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance $2000 \Omega$...

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A block of mass 2 kg moving on a horizontal surface with speed of $4 \mathrm{~ms}^{-1}$ enters a rough surface...

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Let the plane $P: \vec{r} \cdot \vec{a}=d$ contain the line of intersection of two planes $\vec{r} \cdot(\hat{i}+3 \hat{j}-\hat{k})=6$ and $...

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$\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)+\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)+\tan ^{-1}\left(\tan \frac{3 \pi}{4}\right)$ is equal to :

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Transition metal complex with highest value of crystal field splitting ( $\Delta_0$ ) will be

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A paralle plate capacitor is made up of stair like structure with a palte area A of each stair and...

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The acute angle between the planes $\mathrm{P}_1$ and $\mathrm{P}_2$, when $\mathrm{P}_1$ and $\mathrm{P}_2$ are the planes passing through the intersection...

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The value of $\cos \left(\frac{2 \pi}{7}\right)+\cos \left(\frac{4 \pi}{7}\right)+\cos \left(\frac{6 \pi}{7}\right)$ is equal to:

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Consider the following reactions : $$ \begin{aligned} & \mathrm{PCl}_3+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{~A}+\mathrm{HCl} \\ & \mathrm{~A}+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{~B}+\mathrm{HCl} \end{aligned} $$...

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A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6s. The time it will...

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Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(X = 4), then...

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If two distinct point $Q, R$ lie on the line of intersection of the planes $-x+2 y-z=0$ and $...

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In an experiment to determine the velocity of sound in air at room temperature using a resonance is observed when...

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A solution of $\mathrm{Fe}_2\left(\mathrm{SO}_4\right)_3$ is electrolyzed for ' x ' min with a current of 1.5 A to deposit 0.3482...

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A diatomic gas $(\gamma=1.4)$ does 400 J of work when it is expanded isobarically. The heat given to the gas...

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If the system of linear equations $...

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Five numbers $x_1, x_2, x_3, x_4, x_5$ are randomly selected from the numbers $1,2,3, \ldots \ldots, 18$ and are arranged...

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A small spherical ball of radius 0.1 mm and density $10^4 \mathrm{~kg} \mathrm{~m}^{-3}$ falls freely under gravity through a a...

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A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of...

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Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}=2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}$. Then the number of vectors $\overrightarrow{\mathrm{b}}$ such that $\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{a}}$ and $...

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The area enclosed by $y^2=8 x$ and $y=\sqrt{2} x$ that lies outside the triangle formed by $...

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If two straight lines whose direction cosines are given by the relations $I+m-n=0,3 I^2+m^2+c n l=0$ are parallel, then the...

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A mass of 10 kg is suspended vertically by a rope of length 5m from the roof. A force of...

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The vernier constant of Vernier callipers is 0.1 mm and it has zero error of (–0.05) cm. While measuring diameter...

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At 345 K, the half life for the decomposition of a sample of a gaseous compound initially at 55.5 kPa...

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Let the eccentricity of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ be $\frac{1}{4}$. If this ellipse passes through the point $...

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If the tangents drawn at the point $\mathrm{O}(0,0)$ and $\mathrm{P}(1+\sqrt{5}, 2)$ on the circle $x^2+y^2-2 x-4 y=0$ intersect at the...

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Let $S=(0,2 \pi)-\left\{\frac{\pi}{2}, \frac{3 \pi}{4}, \frac{3 \pi}{2}, \frac{7 \pi}{4}\right\}$. Let $y=y(x), x \in S$, be the solution curve of the...

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We do not transmit low frequency signal to long distances because (a) The size of the antenna should be comparable...

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A rigid nitrogen tank stored inside a laboratory has a pressure of 30 atm at 06:00 am when the temperature...

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A person can throw a ball upto a maximum range of 100 m. How high above the ground he can...

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Let $\vec{a}=\alpha \hat{i}+3 \hat{j}-\hat{k}, \vec{b}=3 \hat{i}-\beta \hat{j}+4 \hat{k}$ and $\vec{c}=\hat{i}+2 \hat{j}-2 \hat{k}$ where $\alpha, \beta \in R$, be three vectors....

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A protein ‘A’ contains 0.30% of glycine (molecular weight 75). The minimum molar mass of the protein ‘A’ is________ ×...

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Let the eccentricity of the hyperbola $H: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be $\sqrt{\frac{5}{2}}$ and length of its latus rectum be $6 \sqrt{2}$, If...

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Let $\mathrm{A}=\sum_{i=1}^{10} \sum_{j=1}^{10} \min \{\mathrm{i}, \mathrm{j}\}$ and $\mathrm{B}=\sum_{i=1}^{10} \sum_{j=1}^{10} \max \{\mathrm{i}, \beta\}$. Then $\mathrm{A}+\mathrm{B}$ is equal to $\_\_\_\_$ .

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The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external...

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An antiseptic dettol is a mixture of two compounds ' A ' and ' B ' where A has $...

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For a transistor to act as a switch, it must be operated in

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Let $f: R \rightarrow R$ be a function defined by: $...

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Which of the following ketone will NOT give enamine on treatment with secondary amines? [where $t-\mathrm{Bu}$ is $\left.-\mathrm{C}\left(\mathrm{CH}_3\right)_3\right]$

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If the electric potential at any point (x, y, z)m in space is given by $V=3 x^2$ volt. The electric...

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The value of the integral $\frac{48}{\pi^4} \int_0^\pi\left(\frac{3 \pi x^2}{2}-x^3\right) \frac{\sin x}{1+\cos ^2 x} d x$ is equal to

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Given below are two statements: Statement I : In hydrogen atom, the frequency of radiation emitted when an electron jumps...

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The major product formed in the following reaction, is

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Let $y=y(x)$ be the solution of the differential equation $x\left(1-x^2\right) \frac{d y}{d x}+\left(3 x^2 y-y-4 x^3\right)=0, x>1$, with $y(2)=-2$. Then...

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A block of mass M placed inside a box descends vertically with acceleration 'a'. The block exerts a force equal...

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Let $A=\{n \in N:$ H.C.F. $(n, 45)=1\}$ and Let $B=\{2 k: k \in\{1,2, \ldots, 100\}\}$. Then the sum of all...

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In the given figure, the block of mass m is dropped from the point 'A'. The expression for kinetic energy...

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If $\sin ^2\left(10^{\circ}\right) \sin \left(20^{\circ}\right) \sin \left(40^{\circ}\right) \sin \left(50^{\circ}\right) \sin \left(70^{\circ}\right)=\alpha-\frac{1}{16} \sin \left(10^{\circ}\right)$, then $16+\alpha^{-1}$ is equal to $\_\_\_\_$

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If the mirror image of the point (2, 4, 7) in the plane 3x – y + 4z = 2...

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A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an...

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Let the solution curve $y=y(x)$ of the differential equation, $\left[\frac{x}{\sqrt{x^2-y^2}}+e^{\frac{y}{x}}\right] x \frac{d y}{d x}=x+\left[\frac{x}{\sqrt{x^2-y^2}}+e^{\frac{y}{x}}\right] y$ pass through the points $(1,0)$...

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In the given reaction

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Let the solution curve $y=y(x)$ of the differential equation $\left(4+x^2\right) d y-2 x\left(x^2+3 y+4\right) d x=0$ pass through the origin....

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Amongst the following, the major product of the given chemical reaction is

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If a wave gets refracted into a denser medium, then which of the following is true?

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The area of the region $S=\left\{(x, y): y^2 \leq 8 x, y \geq \sqrt{2} x, x \geq 1\right\}$ is

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During halogen test, sodium fusion extract is boiled with concentrated HNO3 to

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Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as $$ f(x)=\left[\begin{array}{ll} {\left[e^x\right],} & x

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Let $f(x)=\max \{|x+1|,|x+2|, \ldots,|x+5|\}$. Then $\int_{-6}^0 f(x) d x$ is equal to $\_\_\_\_$ .

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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion...

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Let the solution curve of the differential equation $x \frac{d y}{d x}-y=\sqrt{y^2+16 x^2}, y(1)=3$ be $y=y(x)$. Then $y(2)$ is equal...

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A convex lens has power P. It is cut into two halves along its principal axis. Further one piece (out...

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In an isosceles triangle $A B C$, the vertex $A$ is $(6,1)$ and the equation of the base $B C$...

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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion...

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The probability that a randomly chosen 2 × 2 matrix with all the entries from the set of first 10...

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Let $[t]$ denote the greatest integer less than or equal to $t$. Then, the value of the integral $...

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The metal ion (in gaseous state) with lowest spin only magnetic moment value is

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Let the common tangents to the curves $4\left(x^2+y^2\right)=9$ and $y^2=4 x$ intersect at the point $Q$. Let an ellipse, centered...

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Given below are two statements : Statement I: The electric force changes the speed of the charged particle and hence...

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The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength $6630 \AA$ is 0.42 V ....

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Let $A_1, A_2, A_3, \ldots \ldots$ be an increasing geometric progression of positive real numbers. If $A_1 A_3 A_5 A_7=\frac{1}{1296}$...

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If $\frac{d y}{d x}+\frac{2^{x-y}\left(2^y-1\right)}{2^x-1}=0, x, y>0, y(1)=1$, then $y(2)$ is equal to :

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$\mathrm{PCl}_5$ is well known. but $\mathrm{NCl}_5$ is not. Because.

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The number of bridged oxygen atoms present in compound B formed from the following reactions is $\mathrm{Pb}\left(\mathrm{NO}_3\right)_2 \xrightarrow{673} \mathrm{~A}+\mathrm{PbO}+\mathrm{O}_2$ $...

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A vessel contains 16g of hydrogen and 128 g of oxygen at standard temperature and pressure. The volume of the...

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The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which...

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The correct order of reduction potentials of the following pairs is

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There are ten boys $\mathrm{B}_1, \mathrm{~B}_2, \ldots ., \mathrm{B}_{10}$ and five girls $\mathrm{G}_1, \mathrm{G}_2, \ldots ., \mathrm{G}_5$ in a class....

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Let $A$ be a matrix of order $3 \times 3$ and $\operatorname{det}(A)=2$. Then $\operatorname{det}\left(\operatorname{det}(A)\right.$ adj $\left(5 \operatorname{adj}\left(A^3\right)\right)$ ) is equal...

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Given below are two statements: Statement I : A time varying electric field is a source of changing magnetic field...

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The motion of a simple pendulum excuting S.H.M. is represented by following equation. Y = A sin $(\pi \mathrm{t}+\phi)$, where...

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Given below are two statements one is labelled as Assertion A and the other is labelled as Reason R: Assertion...

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Which one of the following compounds is used as a chemical in certain type of fire extinguishers?

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If the system of linear equations where $\lambda \in \mathbb{R}$, has no solution, then

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The sum of the cubes of all the roots of the equation $x^4-3 x^3-2 x^2+3 x+1=10$ is $\_\_\_\_$ .

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The TV transmission tower at a particular station has a height of 125 m. For dubling the coverage of its...

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Given below are two statements. Statement I: During electrolytic refining, blister copper deposits precious metals Statement II: In the process...

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If L, C and R are the self inductance, capacitance and resistance respectively, which of the following does not have...

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Let a function $f: \mathbb{N} \rightarrow \mathbb{N}$ be defined by $...

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In the industrial production of which of the following, molecular hydrogen is obtained as a byproduct?

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The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of...

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The correct order of electron gain enthalpies of Cl, F, Te and Po is

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Let $\Delta, \nabla \in\{\wedge, \vee\}$ be such that $p \nabla q \Rightarrow((p \nabla q) \nabla r)$ is a tautology. Then...

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The value of the integral $\int_{-2}^2 \frac{\left|x^3+x\right|}{\left(e^{x|x|}+1\right)} d x$ is equal to:

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If $\sum_{k=1}^{31}\left({ }^{31} C_k\right)\left({ }^{31} C_{k-1}\right)-\sum_{k=1}^{30}\left({ }^{30} C_k\right)\left({ }^{30} C_{k-1}\right)=\frac{\alpha(60!)}{(30!)(31!)}$, Where $\alpha \in R$, then the value of $16 \alpha$...

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Match List I with List II. Choose the correct answer from the options given below:

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Two long parallel conductors $\mathrm{S}_1$ and $\mathrm{S}_2$ are separated by a distance 10 cm and carrying currents of 4A and...

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Which of the following chemical reactions represents Hall-Heroult Process?

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$\int \frac{\left(x^2+1\right) e^x}{(x+1)^2} d x=f(x) e^x+C$, Where $C$ is a constant, then $\frac{d^3 f}{d x^3}$ at $x=1$ is equal to...

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Let $f(x)=2 \cos ^{-1} x+4 \cot ^{-1} x-3 x^2-2 x+10, x \in[-1,1]$. If $[a, b]$ is the range of the...

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The $\mathrm{K}_{\mathrm{sp}}$ for bismuth sulphide $\left(\mathrm{Bi}_2 \mathrm{~S}_3\right)$ is $1.08 \times 10^{-73}$. The solubility of $\mathrm{Bi}_2 \mathrm{~S}_3$ in $\mathrm{mol} \mathrm{L}^{-1}$ at...

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Two long current carrying conductors are placed parallel to each other at a distance of 8 cm between them. The...

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A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in...

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If $\cos ^{-1}\left(\frac{y}{2}\right)=\log _e\left(\frac{x}{5}\right)^5,|y|

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Solute A associates in water. When 0.7 g of solute A is dissolved in 42.0 g of water, it depresses...

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Three identical charged balls each of charge 2C are suspended from a common point P by silk threads of 2m...

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Metals generally melt at very high temperature. Amongst the following, the metal with the highest melting point will be

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At $25^{\circ} \mathrm{C}$ and 1 atm pressure, the enthalpy of combustion of benzene (1) and acetylene (g) are $...

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The mean of the numbers $a, b, 8,5,10$ is 6 and their variance is 6.8 . If $M$ is the...

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The lengths of the sides of a triangle are $10+x^2, 10+x^2$ and $20-2 x^2$. If for $x=k$, the area of...

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The minimum energy that must be possessed by photons in order to produce the photoelectric effect with platinum metal is:...

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For a first order reaction, the time required for completion of $90 \%$ reaction is ' $x$ ' times the...

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The number of distinct real roots of $x^4-4 x+1=0$ is :

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If a charge q is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through...

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Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability...

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A capacitor is discharging through a resistor R. Consider in time t1, the energy stored in the capacitor reduces to...

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Let a be an integer such that $\lim _{x \rightarrow 7} \frac{18-[1-x]}{[x-3 a]}$ exists, where $[t]$ is greatest integer $...

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In an experiment of CE configuration of n-p-n transistor, the transfer characteristics are observed as given in figure. If the...

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| Substance | $\mathrm{H}_2$ | C(graphite) | $\mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})$ | | :--- | :--- | :--- | :--- | |...

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The electric field at the point associated with a light wave is given by E = 200 $...

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The greatest integer less than or equal to the sum of first 100 terms of the sequence $...

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Let $\frac{d y}{d x}=\frac{a x-b y+a}{b x+c y+a}$, where $a, b, c$ are constants, represent a circle passing through the...

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In a series LCR circuit, the inductance, capacitance and resistance are L = 100mH,$C=100 \mu \mathrm{~F}$ and $\mathrm{R}=10 \Omega$ respectively....

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If $\vec{a} \cdot \vec{b}=1, \vec{b} \cdot \vec{c}=2$ and $\vec{c} \cdot \vec{a}=3$, then the value of $...

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The equation of a particle executing simple harmonic motion is given by $x=\sin \pi\left(t+\frac{1}{3}\right) m$ At t = 1s, the...

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Let A be a 3 × 3 matrix having entries from the set {–1, 0, 1}. The number of all...

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A small bulb is placed at the bottom of a tank containing water to a depth of $\sqrt{7} \mathrm{~m}$. The...

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In the following nuclear rection, Mass number of D is 182 and atomic number is 74 . Mass number and...

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The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the...

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If $x=\sum_{n=0}^{\infty} a^n, y=\sum_{n=0}^{\infty} b^n, z=\sum_{n=0}^{\infty} c^n$, where $a, b, c$ are in A.P. and $|a|

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Let the lines intersect at the point $S$. If a plane $a x+$ by $-z+d=0$ passes through $S$ and is...

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The correct order of bond orders of $\mathrm{C}_2^{2-}, \mathrm{N}_2^{2-}$ and $\mathrm{O}_2^{2-}$ is, respeptively.

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27 identical drops are charged at 22V each. They combine to form a bigger drop. The potential of the bigger...

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Let the plane $2 x+3 y+z+20=0$ be rotated through a right angle about its line of intersection with the plane...

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A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to...

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The speed of light in media ' $A$ ' and ' $B$ ' are $2.0 \times 10^{10} \mathrm{~cm} / \mathrm{s}$...

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Let $f: R \rightarrow R$ be a function defined by $f(x)=\left(2\left(1-\frac{x^{25}}{2}\right)\left(2+x^{25}\right)\right)^{\frac{1}{50}}$. If the function $g(x)=f(f(f(x)))+f(f(x))$, the greatest integer less than...

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When a gas filled in a closed vessel is heated by raising the temperature by 1°C, its pressure increase by...

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Two 10 cm long, straight wires, each carrying a current of 5 A are kept parallel to each other. If...

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Two satellites $S_1$ and $S_2$ are revolving in circular orbits around a planet with radius $R_1=3200 \mathrm{~km}$ and $R_2=800 \mathrm{~km}$...

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Let the system of linear equations $x+2 y+z=2, \alpha x+3 y-z=\alpha,-\alpha x+y+2 z=-\alpha$ be inconsistent. Then $\alpha$ is equal to...

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Two point charges Q each are placed at a distance d apart. A third point charge q is placed at...

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For a natural number n , let $\mathrm{a}_{\mathrm{n}}=19^{\mathrm{n}}-12^{\mathrm{n}}$. Then, the value of $\frac{31 \alpha_9-\alpha_{10}}{57 \alpha_8}$ is

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The energy of one mole of photons of radiation of wavelength 300 nm is (Given : $...

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According to kinetic theory of gases, A. The motion of the gas molecules freezes at 0ºC B. The mean free...

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Moment of Inertia (M.I.) of four bodies having same mass ‘M’ and radius ‘2R’ are as follows: I1= M.I. of...

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If the two lines $\ell_1: \frac{x-2}{3}=\frac{y+1}{-2}, z=2$ and $\ell_2: \frac{x-1}{1}=\frac{2 y+3}{\alpha}=\frac{z+5}{2}$ perpendicular, then an angle between the lines $l_2$ and...

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At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a...

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The number of values of $x$ in the interval $\left(\frac{\pi}{4}, \frac{7 \pi}{4}\right)$ for which $...

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A block of mass 200 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force...

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For a perfect gas, two pressures P1 and P2 are shown in figure. The graph shows:

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120 of an organic compound that contains only carbon and hydrogen gives 330 g of $\mathrm{CO}_2$ and 270 g of...

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A curved in a level road has a radius 75m. The maximum speed of a car turning this curved road...

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A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats...

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A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of...

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Let the normal at the point P on the parabola $\mathrm{y}^2=6 \mathrm{x}$ pass through the point $(5,-8)$. If the tangent...

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For $Z=a^2 x^3 y^{\overline{2}}$, where ' $a$ ' is a constant. If percentage error in measurement of ' $x$ '...

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Four spheres each of mass m form a square of side d (as shown in figure). A fifth sphere of...

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A heat engine operates with the cold reservoir at temperature 324 K. The minimum temperature of the hot reservoir, if...

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If n represents the actual number of deflections in a converted galvanometer of resistance G and shunt resistance S. Then...

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A geyser heats water flowing at a rate of 2.0 kg per minute from $30^{\circ} \mathrm{C}$ to $70^{\circ} \mathrm{C}$. If...

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In an experment ot verify Newton's law of cooling, a graph is plotted between, the temperature difference ( $\Delta T$...

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Let $C$ be a circle passing through the points $A(2,-1)$ and $B(3,4)$. The line segment $A B$ is not a...

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A stone tide to a string of length L is whirled in a vertical circle with the other end of...

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Let the abscissae of the two points $P$ and $Q$ be the roots of $2 x^2-r x+p=0$ and the ordinates...

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A monoatomic gas performs a work of $\frac{Q}{4}$ where $Q$ is the heat supplied to it. The molar heat capacity...

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A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is...

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The area of the polygon, whose vertices are the non-real roots of the equation $\bar{z}=i z^2$ is:

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One end of a massless spring of spring constant k and natural length $\mathrm{I}_0$ is fixed while the other end...

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Let $\theta$ be the angle between the vectors $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$ where $|\overrightarrow{\mathrm{a}}|=4,|\overrightarrow{\mathrm{~b}}|=3 \theta \in\left(\frac{\pi}{4}, \frac{\pi}{3}\right)$. Then

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A circular coil of 1000 turns each with area $1 \mathrm{~m}^2$ is rotated about its vertical diameter at the rate...

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A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its...

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Identify the logic operation performed by the given circuit :

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Let $R$ be the point $(3,7)$ and let $P$ and $Q$ be two points on the line $x+y=5$ such that...

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A ray of light is incident at an angle of incidence $60^{\circ}$ on the glass slab of refractive index $\sqrt{3}$....

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The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is ______.

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When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the...

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A sample contains $10^{-2} \mathrm{~kg}$ each of two substances $A$ and $B$ with half lives 4 s and 8 s...

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A ball is projected vertically upward with an initial velocity of $50 \mathrm{~ms}^{-1}$ at $t=0 \mathrm{~s}$. At $t=2 \mathrm{~s}$. another...

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Which of the following figure represents the variation of $\ln \left(\frac{R}{R_0}\right)$ with $\ln A$ (If $R=$ radius of a nucleus...

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In the given circuit- the value of current $\mathrm{I}_{\mathrm{L}}$ will be ______ mA. (When $\mathrm{R}_{\mathrm{L}}=\mathrm{lk} \Omega$

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A sinusoidal wave $y(t)=40 \sin \left(10 \times 10^6 \pi t\right)$ is amplitude modulated by another sinusoidal wave $...

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The area bounded by the curve $y=\left|x^2-9\right|$ and the line $y=3$ is :

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The distance of the Sun from earth is $1.5 \times 10^{11}$ m and its angular diameter is (2000) s when...

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If the shortest distance between the line $\vec{r}=(-\hat{i}+3 \hat{k})+\lambda(\hat{i}-a \hat{j})$ and $\vec{r}=(-\hat{j}+2 \hat{k})+\mu(\hat{i}-\hat{j}+\hat{k})$ is $\sqrt{\frac{2}{3}}$ then the integral value of...

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The positive feedback is required by an amplifier to act an oscillator. The feedback here means :

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Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce...

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A light whose electric field vectors are completely removed by using a good Polaroid, allowed to incident on the surface...

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A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is...

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The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be

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Let $S$ be the set of all the natural numbers, for which the line $\frac{x}{a}+\frac{y}{b}=2$ is a tangent to the...

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A potentiometer wire of length 10 m and resistance $20 \Omega$ is connected in series with a 25 V battery...

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Let $S$ be the region bounded by the curves $y=x^3$ and $y^2=x$. The curve $y=2|x|$ divides $S$ into two regions...

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A metal surface is illuminated by a radiation of wavelength 4500 Å. the ejected photo-electron enters a constant magnetic field...

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The interference pattern is obtained with two coherent light sources of intensity ratio 4 :1. And the ratio $...

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For a specific wavelength 670 nm of light coming from a galaxy moving with velocity v, the observed wavelength is...

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If two tangents drawn from a point ( $\alpha, \beta$ ) lying on the ellipse $25 x^2+4 y^2=1$ to the...

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An antenna is placed in a dielectric medium of dielectric constant 6.25. If the maximum size of that antenna is...

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A body is projected from the ground at an angle of $45^{\circ}$ with the horizontal. Its velocity after 2 s...

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Which is the correct ascending order of wavelength?

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The sum of the absolute minimum and the absolute maximum values of the function $f(x)=\left|3 x-x^2+2\right|-x$ in the interval $[-1,2]$...

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A metallic conductor of length 1 m rotates in a vertical plane parallel to east-west direction about one of its...

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Let $C_r$ denote the binomial coefficient of $x^r$ in the expansion of $(1+x)^{10}$. If $...

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Two coils of self inductance $L_1$ and $L_2$ are connected in series combination having mutual inductance of the coils as...

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A bar magnet having a magnetic moment of $2.0 \times 10^5 \mathrm{JT}^{-1}$, is placed along the direction of uniform magnetic...

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The equivalent resistance between points A and B in the given network is :

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Sixty four conducting drops each of radius 0.02 m and each carrying a charge of $5 \mu \mathrm{C}$ are combined...

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Let a circle C in complex plane pass although the points $z_1=3+4 i, z_2=4+3 i$ and $z_3=5 i$. If $...

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A parallel plate capacitor with plate area $A$ and plate separation $d=2 m$ has a capacitance of $4 \mu F$....

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Let $\operatorname{Max}_{0 \leq x \leq 2}\left\{\frac{9-x^2}{5-x}\right\}=\alpha$ and $\operatorname{Max}_{0 \leq x \leq 2}\left\{\frac{9-x^2}{5-x}\right\}=\beta$ If $...

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Let $x=2 t, y=\frac{t^2}{3}$ be a conic. Let $S$ be the focus and $B$ be the point on the axis...

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In the estimation of bromine, 0.5 g of an organic compound gave 0.40 g of silver bromide. The percentage of...

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The charge on capacitor of capacitance 15 F in the figure given below is :

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The number of carbon atoms present in the product B is __________.

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Number of complexes which will exhibit synergic bonding amongst, $\left[\mathrm{Cr}(\mathrm{CO})_6\right],\left[\mathrm{Mn}(\mathrm{CO})_5\right]$ and $\left[\mathrm{Mn}_2(\mathrm{CO})_{10}\right]$ is $\_\_\_\_$ .

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If the solution curve $y=y(x)$ of the differential equation $y^2 d x+\left(x^2-x y+y^2\right) d y=0$, which passes through the point...

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Let $f(\theta)=\sin \theta+\int_{-\pi / 2}^{\pi / 2}(\sin \theta+t \cos \theta) f(t) d t$. Then the value of $...

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The major product ' A ' of the following given reaction has $\_\_\_\_$ $\mathrm{sp}^2$ hybridized carbon atoms. 2,7 - Dimethyl1...

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Observe structures of the following compounds The total number of structures/compounds which possess asymmetric carbon atoms is __________.

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For a first order reaction $A \rightarrow B$, the rate constant, $\mathrm{k}=5.5 \times 10^{-14} \mathrm{~s}^{-1}$ . The time required for...

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Number of electrophilic centre in the given compound is ____

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A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept...

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Let $Q$ be the mirror image of the point $P(1,0,1)$ with respect to the plane $S: x+y+z=5$. If a line...

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Kjeldahl's method was used for the estimation of nitrogen in an organic compound. The ammonia evolved from 0.55 g of...

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The electromagnetic waves travel in a medium at a speed of $2.0 \times 10^8 \mathrm{~m} / \mathrm{s}$. The relative permeability...

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A 0.166 g sample of an organic compound was digested with cone. $\mathrm{H}_2 \mathrm{SO}_4$ and then distilled with NaOH ....

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If $\rho$ is the density and $\eta$ is coefficient of viscosity of fluid which flows with a speed $v$ in...

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If $y=m_1 x+c_1$ and $y=m_2 x+c_2, m_1 \neq m_2$ are two common tangents of circle $x^2+y^2=2$ and parabola $y^2=x$, then...

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A sinusoidal voltage $V(t)=210 \sin 3000 t$ volt is applied to a series LCR circuit in which $...

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Let a line having direction ratios $1,-4,2$ intersect the lines $\frac{x-7}{3}=\frac{y-1}{-1}=\frac{z+2}{1}$ and $\frac{x}{2}=\frac{y-7}{3}=\frac{z}{1}$ at the point $A$ and $B$. Then...

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The quantity of electricity in Faraday needed to reduce 1 mol of $\mathrm{Cr}_2 \mathrm{O}_7^{2-}$ to $\mathrm{Cr}^{3+}$ is $\_\_\_\_$ .

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An acidified manganate solution undergoes disproportionation reaction. The spin-only magnetic moment value of the product having manganese in higher oxidation...

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In Bohr's atomic model of hydrogen, let K. P and E are the kinetic energy, potential energy and total energy...

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Given below are two statements : One is labeled as Assertion A and the other is labelled as Reason R....

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A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and...

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Let $A\left(\frac{3}{\sqrt{a}}, \sqrt{a}\right) a>0$ be a fixed point in the $x y$-plane. The image of $A$ in $y$-axis be $B$...

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In the cobalt-carbonyl complex: $\left[\mathrm{Co}_2(\mathrm{CO})_4\right]$, number of Co -Co bonds is " X " and terminal CO ligands is "...

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Let $y=y(x)$ be the solution of the differential equation $(x+1) y^{\prime}-y=e^{3 x}(x+1)^2$, with $y(0)=\frac{1}{3}$. Then, the point $x =-\frac{4}{3}$ for...

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The number of terminal oxygen atoms present in the product B obtained from the following reaction is ________. $...

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$\lim _{x \rightarrow \frac{1}{\sqrt{2}}} \frac{\sin \left(\cos ^{-1} x\right)-x}{1-\tan \left(\cos ^{-1} x\right)}$ is equal to :

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The solubility product of a sparingly soluble salt $\mathrm{A}_2 \mathrm{X}_3$ is $1.1 \times 10^{-23}$. If specific conductance of the solution...

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Given below are two statements: Statement – I : Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature....

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In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct There...

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The difference in oxidation state of chromium in chromate and dichromate salts is _______.

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Let $\vec{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k} \quad a_i>0, i=1,2,3$ be a vector which makes equal angles with the coordinates axes OX,...

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The number of one-one function $f:\{a, b, c, d\} \rightarrow\left\{0,1,2_{\text {sui. }} .10\right\}$ such that $2 f(a) . f(b)+3 f(c)+f(d)=0$...

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Two light beams of intensities in the ratio of 9 : 4 are allowed to interfere. The ratio of the...

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Solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational...

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The activation energy of one of the reactions in a biochemical process is 532611 J $\mathrm{mol}^{-1}$. When the temperature falls...

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The remainder when $(2021)^{2023}$ is divided by 7 is :

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The rate constants for decomposition of acetaldehyde have been measured over the temperature range 700 1000 K . The data...

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The number of choices of $\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$, such that $...

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The light of two different frequencies whose photons have energies 3.8 eV and 1.4 eV respectively, illuminate a metallic surface...

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Arrange the four graphs in descending order of total work done; where W1, W2, W3 and W4 are the work...

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4.0 L of an ideal gas is allowed to expand isothermally into vacuum until the total volume is 20 L....

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Let $\mathrm{S}\left\{\theta \in[-\pi, \pi]-\left\{ \pm \frac{\pi}{2}\right\}: \sin \theta \tan \theta+\tan \theta=\sin 2 \theta\right\}$ If $T=\sum_{\theta \in S} \cos 2 \theta$,...

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The cell potential for the following cell $\mid$ $$ \mathrm{Pt}\left|\mathrm{H}_2(\mathrm{~g})\right| \mathrm{H}^{+}(\mathrm{ag})| | \mathrm{Cu}^{2+}(0.01 \mathrm{M}) \mid \mathrm{Cu}(\mathrm{~s}) $$ is 0.576 V...

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Let $\mathrm{g}:(0, \infty) \rightarrow \mathrm{R}$ be a differentiable function such that $\int\left(\frac{x(\cos x-\sin x)}{e^x+1}+\frac{g(x)\left(e^x+1-x e^x\right)}{\left(e^x+1\right)^2}\right) d x=\frac{x g(x)}{e^x+1}+c$, for all...

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A dilute solution of sulphuric acid is electrolyzed using a current of 0.10 A for 2 hours to produce hydrogen...

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The domain of the function $f(x)=\frac{\cos ^{-1}\left(\frac{x^2-5 x+6}{x^2-9}\right)}{\log _e\left(x^2-3 x+2\right)}$ is

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In the arrangement shown in figure $a_1 a_2, a_3$ and $a_4$ are the accelerations of masses $m_1 m_2 m_3$ and...

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The ordered pair ( $a, b$ ), for which the system of linear equations $$ \begin{aligned} & 3 x-2 y+z=b...

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The hybridization of P exhibited in $\mathrm{PF}_5$ is $\mathrm{sp}^x \mathrm{~d}^y$. The value of y is __________.

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Two metallic plates form a parallel plate capacitor. The distance between the plates is ‘d’. A metal sheet of thickness...

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An electric bulb is rated as 200 W. What will be the peak magnetic field at 4 m distance produced...

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The dimension of mutual inductance is :

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A long cylindrical volume contains a uniformly distributed charge of density $\rho$. The radius of cylindrical volume is R. A...

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If the work function of a metal is $6.63 \times 10^{-19} \mathrm{~J}$, the maximum wavelength of the photon required to...

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1.2 mL of acetic acid is dissolved in water to make 2.0 L of solution. The depression in reezing point...

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For a particle in uniform circular motion, the acceleration $\vec{a}$ at any point $P(R, \theta)$ on the circular path of...

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Let $A$ be a $3 \times 3$ invertible matrix. If $|\operatorname{adj}(24 A)|=|\operatorname{adj}(3 \operatorname{adj}(2 A))|$, then $|A|^2$ is equal to :

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If the charge on a capacitor is increased by 2 C, the energy stored in it increases by 44%. The...

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The ratio of specific heats $\left(\frac{C_p}{C_v}\right)$ in terms of degree of freedom (f) is given by:

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If a random variable $X$ follows the Binomial distribution $B(33, p)$ such that $3 P(X=0)=P(X=1)$, then the value of $\frac{P(X=15)}{P(X=18)}-\frac{P(X=16)}{P(X=17)}$...

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A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of $60 \mathrm{~ms}^{-1}$....

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A 2.0 g sample containing $\mathrm{MnO}_2$ is treated with HCl liberating $\mathrm{Cl}_2$. The $\mathrm{Cl}_2$.gas is passed into a solution of...

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Total number of possible stereoisomers of dimethyl cyclopentane is ___________

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The osmotic pressure of blood is 7.47 bar at 300 K . To inject glucose to a patient intravenously, it...

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17.0 g of $\mathrm{NH}_3$ completely vapourises at – $33.42^{\circ} \mathrm{C}$ and 1 bar pressure and the enthalpy change in the...

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A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated...

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Two elements A and B which form 0.15 moles of A2B and AB3 type compounds. If both A2B and AB3...

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An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding...

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$$ 2 \mathrm{O}_3(\mathrm{~g}) \rightleftharpoons 3 \mathrm{O}_2(\mathrm{~g}) $$ At 300 K , ozone is fifty percent dissociated. The standard free energy...

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Acidified potassium permanganate solution oxidises oxalic acid. The spin-only magnetic moment of the manganese product formed from the above reaction...

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Let $A=\left[\begin{array}{cc}0 & -2 \\ 2 & 0\end{array}\right]$. If $M$ and $N$ are two matrices given by $M=\sum_{k=1}^{10} A^{2 k}$...

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The formula of the purple colour formed in Laissaigne’s test for sulphur using sodium nitroprusside is

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The number of statement(s) correct from the following for copper (at no. 29) is/are ______

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Let: $A=\left\{z \in C:\left|\frac{z+1}{z-1}

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A solid metallic cube having total surface area $24 \mathrm{~m}^2$ is uniformly heated. If its temperature is increased by $...

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Potential energy as a function of r is given by $U=\frac{A}{r^{10}}-\frac{B}{r^5}$, where r is the interatomic distance, A and B...

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Atoms of element $X$ form hcp lattice and those of element $Y$ occupy $\frac{2}{3}$ of its tetrahedral voids. The percentage...

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Let $\hat{a}, \hat{b}$ be unit vectors. If $\vec{c}$ be a vector such that the angle between $\hat{a}$ and $\hat{c}$ is...

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Let $E_1$ and $E_2$ be two events such that the conditional probabilities $P\left(E_1 \mid E_2\right)=\frac{1}{2}, P\left(E_2 \mid E_1\right)=\frac{3}{4}$ and $...

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The rate constant for a first order reaction is given by the following equation: $\ln \mathrm{k}=33.24-\frac{2.0 \times 10^4 \mathrm{~K}}{\mathrm{~T}}$ The...

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Given below are two statements : Statement-I : The reactance of an ac circuit is zero. It is possible that...

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The limiting molar conductivities of $\mathrm{Nal}^{\circ} \mathrm{NaNO}_3$ and $\mathrm{AgNO}_3$ are $12.7,12.0$ and $13.3 \mathrm{mS} \mathrm{m}^2 \mathrm{~mol}^{-1}$, respectively (all at $...

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Let $\lambda x-2 y=\mu$ be a tangent to the hyperbola $a^2 x^2-y^2=b^2$. Then $\left(\frac{\lambda}{a}\right)^2-\left(\frac{\mu}{b}\right)^2$ is equal to:

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Given below are two statements. Statement I : Phenols are weakly acidic Statement II : Therefore they are freely soluble...

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A proton, a deuteron and an $\alpha-$particle with same kinetic energy enter into a uniform magnetic field at right angle...

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$2 \mathrm{NOCl}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_2(\mathrm{~g})$ In an experiment, 2.0 moles of NOCl was placed in a one-litre flask and the...

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Let $f(x)$ be a polynomial function such that $f(x)+f^{\prime}(x)+f^{\prime \prime}(x)=x^5+64$. Then, the value of $\lim _{x \rightarrow 1} \frac{f(x)}{x-1}$

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During the qualitative analysis of salt with cation $y^{2+}$ addition of a reagent $(X)$ to alkaline solution of the salt...

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2 g of a non-volatile non-electrolyte solute is dissolved in 200 g of two different solvents A and B whose...

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Which one of the following is NOT a copolymer ?

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The soft-iron is a suitable material for making an electromagnet. This is because soft-iron has :

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Two buses $P$ and $Q$ start from a point at the same time and move in a straight line and...

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If the uncertainty in velocity and position of a minute particle in space are, $2.4 \times 10^{-26}\left(\mathrm{~ms}^{-1}\right)$ and $10^{-7}(\mathrm{~m})$ respectively....

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What will be the most suitable combination of three resistors $\mathrm{A}=2 \Omega, \mathrm{~B}=4 \Omega, \mathrm{C}=6 \Omega$ so that $\left(\frac{22}{3}\right) \Omega$...

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Which of the following is not a broad spectrum antibiotic?

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A primary aliphatic amine on reaction with nitrous acid in cold (273 K) and there after raising temperature of reaction...

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Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. Assertion...

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Which of the following compound does not contain sulphur atom ?

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Metal deficiency defect is shown by $\mathrm{Fe}_{e 0.93} \mathrm{O}$. In the crystal, some $\mathrm{Fe}^{2+}$ cations are missing and loss of...

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Two massless springs with spring constants 2 k and 2 k, carry 50 g and 100 g masses at their...

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If $\frac{1}{2 \cdot 3^{10}}+\frac{1}{2^2 \cdot 3^9}+\ldots \cdot \frac{1}{2^{10} \cdot 3}=\frac{\mathrm{K}}{2^{10} \cdot 3^{10}}$, then the remainder when K is divided by...

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A polysaccharide ' X ' on boiling with dil $\mathrm{H}_2 \mathrm{SO}_4$ at 393 K under 2-3 atm pressure yields '...

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Sugar moiety in DNA and RNA molecules respectively are

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Identify the major product formed in the following sequence of reactions :

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Match List-I with List-II

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Consider the following two propositions: If the proposition $p \rightarrow((\sim p) \vee q)$ is evaluated as FALSE, then:

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A Carnot engine take 5000 kcal of heat from a reservoir at $727^{\circ} \mathrm{C}$ and gives heat to a sink...

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The polymer, which can be stretched and retains its original status on releasing the force is

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The number of oxygens present in a nucleotide formed from a base, that is present only in RNA is ________.

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Two identical charged particles each having a mass 10 g and charge $2.0 \times 10^{-7} \mathrm{C}$ area placed on a...

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Consider the above reaction, the product A and product B respectively are

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Which one of the following compounds is inactive towards $\mathrm{S}_{\mathrm{N}} 1$ reaction?

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Let: $f(x)=\frac{x-1}{x+1}, x \in R-\{0,-1,1\}$. If $f^{n+1}(x)=f\left(f^n(x)\right)$ for all $x \in N$, then $f^6(6)+f^7(7)$ is equal to:

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Compound 'P' on nitration with dil. HNO3 yields two isomers (A) and (B). These isomers can be separated by steam...

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A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed....

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On complete combustion 0.30 g of an organic compound gave 0.20 g of carbon dioxide and 0.10 g of water....

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The correct structure of product ‘A’ formed in the following reaction.

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The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes...

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Given below are two statements : Statement I : The esterification of carboxylic acid with an alcohol is a nucleophilic...

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Match List-I with List-II Choose the correct answer from the options given below:

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The spin-only magnetic moment value of an octahedral complex among $\mathrm{CoCl}_3 .4 \mathrm{NH}_3, \mathrm{NiCl}_2 .6 \mathrm{H}_2 \mathrm{O}$ and $...

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In the given conversion the compound A is:

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The spin–only magnetic moment value of the most basic oxide of vanadium among $\mathrm{V}_2 \mathrm{O}_3, \mathrm{~V}_2 \mathrm{O}_4$ and $\mathrm{V}_2 \mathrm{O}_5$...

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Given below are two statements: Statements-I : In Hofmann degradation reaction, the migration of only an alkyl group takes place...

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The major product (P) in the reaction

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2.0 g of H2 gas is adsorbed on 2.5 g of platinum powder at 300 K and 1 bar pressure....

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Identify the pair of physical quantities that have same dimensions :

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A flask is filled with equal moles of A and B. The half lives of A and B are 100...

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Which of the following reactions will yield benzaldehyde as a product?

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Two isomers 'A' and 'B' with molecular formula $\mathrm{C}_4 \mathrm{H}_8$ give different products on oxidation with $\mathrm{KMnO}_4$ in acidic medium....

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Number of grams of bromine that will completely react with 5.0g of pent-1-ene is ______ $\times 10^{-2} \mathrm{~g}$.(Atomic mass of...

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50 mL of $0.1 \mathrm{M} \mathrm{CH}_3 \mathrm{COOH}$ is being titrated against 0.1 M NaOH . When 25 mL of NaOH...

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Which of the following structures are aromatic in nature?

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If $\left[\mathrm{Cu}\left(\mathrm{H}_2 \mathrm{O}\right)_4\right]^{2+}$ absorbs a light of wavelength 600 nm for d–d transition, then the value of octahedral crystal field...

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The acid that is believed to be mainly responsible for the damage of Taj Mahal is

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The major product of the following reaction is:

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A 0.5 percent solution of potassium chloride was found to freeze at –0.24°C. If the percentage dissociation of potassium chloride...

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' A ' and ' B ' respectively are: $...

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The oxoacid of phosphorus that is easily obtained from a reaction of alkali and white phosphorus and has two P-H...

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For a given chemical reaction $\gamma_1 A+\gamma_2 B \rightarrow \gamma_3 C+\gamma_4 D$ Concentration of C changes from 10 mmol $\mathrm{dm}^{-3}$...

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For complete combustion of methanol $\mathrm{CH}_3 \mathrm{OH}(1)+\frac{3}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(1)$ the amount of heat produced as measured by...

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Which of the following is structure of a separating funnel?

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Given below are two statements: Statement I: Classical smog occurs in cool humid climate. It is a reducing mixture of...

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Which of the following will have maximum stabilization due to crystal field?

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Heating white phosphorus with conc. NaOH solution gives mainly

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Match List-I with List-II Choose the correct answer from the options given below:

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$\mathrm{BeCl}_2$ reacts with $\mathrm{LiAlH}_4$ to give

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If $x=x(y)$ is the solution of the differential equation $y \frac{d x}{d y}=2 x+y^3(y+1) e^y, x(1)=0$; then $x(e)$ is equal...

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If $\left\{a_i\right\}_{i=1}^n$ where $n$ is an even integer, is an arithmetic progression with common difference 1 , and $\sum_{i=1}^n a_i=192$,...

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The sum of absolute maximum and absolute minimum values of the function $f(x)=\left|2 x^2+3 x-2\right|+\sin x \cos x$ in the...

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$f(x)=4 \log _e(x-1)-2 x^2+4 x+5, x>1$, which one of the following is NOT correct?

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Let $A$ be $a \times 3$ real matrix such that $...

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Match the List-I with List- II. Choose the most appropriate answer from the option given below:

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Let $f: N \rightarrow R$ be a function such that $f(x+y)=2 f(x) f(y)$ for natural numbers $x$ and $y$. If...

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Let $S=\{\sqrt{n}: 1 \leq n \leq 50$ and $n$ is odd $\}$ Let $a \in S$ and $...

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Let $a, b$ and $c$ be the length of sides of a triangle $A B C$ such that $\frac{a+b}{7}=\frac{b+c}{8}=\frac{c+a}{9}$. If...

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Match the List-I with List- II. Choose the most appropriate answer from the options given below:

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For the network shown below, the value $V_B-V_A$ is V.

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The set of all values of $k$ for which $\left(\tan ^{-1} x\right)^3+\left(\cot ^{-1} x\right)^3=k \pi^3, x \in R$, is the...

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Which one of the following reactions indicates the reducing ability of hydrogen peroxide in basic medium ?

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The value of $\int_0^\pi \frac{e^{\cos x} \sin x}{\left(1+\cos ^2 x\right)\left(e^{\cos x}+e^{-\cos x}\right)} d x$ is equal to

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If the sum of the squares of the reciprocals of the roots $a$ and $b$ of the equation $...

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Let a circle $C$ touch the lines $L_1: 4 x-3 y+K_1=0$ and $L_2: 4 x-3 y+K_2=0, K_1, K_2 \in R$....

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A chemical which stimulates the secretion of pepsin is :

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The electronic configuration of Pt (atomic number 78) is:

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A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive...

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The number of values of a for which the system of equations : $...

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Which of the following sets are correct regarding polymer ? (A) Copolymer : Buna–S (B) Condensation polymer : Nylon–6,6 (C)...

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Let $x^2+y^2+A x+B y+C=0$ be a circle passing through $(0,6)$ and touching the parabola $y=x^2$ at $(2,4)$. Then $\mathrm{A}+\mathrm{C}$ is...

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Which of the following is a correct statement ?

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A transistor is used in an amplifier circuit in common emitter mode. If the base current changes by $...

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The solubility of AgCl will be maximum in which of the following ?

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Among the following structures, which will show the most stable enamine formation ? (Where Me is $-\mathrm{CH}_3$ )

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Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and...

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The surface area of a balloon of spherical shape being in flated, increases at a constant rate. If initially, the...

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Arrange the following in the decreasing order of their covalent character : (A) LiCl (B) NaCl (C) KCl (D) CsCl...

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The remainder when $3^{2022}$ is divided by 5 is

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In a cell, the following reactions take place $...

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Let $A=\{z \in C: 1 \leq|z-(1+i)| \leq 2\}$ and $B=\{z \in A:|z-(1-i)|=1\}$. Then, $B:$

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Which of the following statements are correct ? (A) The electronic configuration of Cr is $[\mathrm{Ar}] 3 \mathrm{~d}^5 4 \mathrm{~s}^1$....

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The standard free energy change ( $\Delta \mathrm{G}^{\circ}$ ) for $50 \%$ dissociation of $\mathrm{N}_2 \mathrm{O}_4$ into $\mathrm{NO}_2$ at $...

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$\sqrt{d_1}$ and $\sqrt{d_2}$ are the impact parameters corresponding to scattering angles $60^{\circ}$ and $90^{\circ}$ respectively, when an $\alpha$ particle is...

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Given below are two statements : Statement I : $[\mathrm{Ni}(\mathrm{CN}) 4]^2$ is square planar and diamagnetic complex. with $\mathrm{dsp}^2$ hybridization...

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1 L aqueous solution of $\mathrm{H}_2 \mathrm{SO}_4$ contains $0.02 \mathrm{~m} \mathrm{~mol} \mathrm{H}_2 \mathrm{SO}_4 .50 \%$ of this solution is diluted...

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300 cal . of heat is given to a heat engine and it rejects 225 cal . of heat. If...

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The standard entropy change for the reaction $4 \mathrm{Fe}(\mathrm{s})+3 \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{Fe}_2 \mathrm{O}_3(\mathrm{~s})$ is $-550 \mathrm{JK}^{-1}$ at 298 K....

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The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire...

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Which of the following is an example of polyester?

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Which one of the lanthanoids given below is the most stable in divalent form?

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The major product of the above reaction is

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The longest wavelength of light that can be used for the ionisation of lithium atom (Li) in its ground state...

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Given below are two statements : Statement -I :The pentavalent oxide of group- 15 element. $\mathrm{E}_2 \mathrm{O}_5$.. is less acidic...

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Which of the following is an example of conjugated diketone?

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Addition of $\mathrm{H}_2 \mathrm{SO}_4$ to $\mathrm{BaO}_2$ produces:

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A body is performing simple harmonic with an amplitude of 10 cm . The velocity of the body was tripled...

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Two statements are given below : Statement I: The melting point of monocarboxylic acid with even number of carbon atoms...

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Nitrogen gas is obtained by thermal decomposition of

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As per the given figure, two plates $A$ and $B$ of thermal conductivity $K$ and $2 K$ are joined together...

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A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75...

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Match List – I with List – II Choose the most appropriate answer from the options given below:

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Dihydrogen reacts with CuO to give

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In the given reactions sequence, the major product ‘C’ is :

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The area of cross-section of a large tank is $0.5 \mathrm{~m}^2$. It has a narrow opening near the bottom having...

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The intensity of the light from a bulb incident on a surface is $0.22 \mathrm{~W} / \mathrm{m}^2$. The amplitude of...

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Match List-I with List-II Choose the correct answer from the options given below.

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Given are two statements one is labelled as Assertion A and other is labelled as Reason R. Assertion A :Magnesium...

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The distance between $\mathrm{Na}^{+}$and $\mathrm{Cl}^{-}$ions in 'solid NaCl of density $43.1 \mathrm{~g} \mathrm{~cm}^{-3}$ is $\_\_\_\_$ $\times 10^{-10} \mathrm{~m}$. (Nearest Integer)...

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The number of N atoms is 681 g of $\mathrm{C}_7 \mathrm{H}_5 \mathrm{~N}_3 \mathrm{O}_6$ is $\mathrm{x} \times 10^{21}$. The value of...

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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason(R) Assertion (A):...

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Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to...

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Which one of the following is an example of artificial sweetner ?

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A capacitor of capacitance 50 pF is charged by 100 V source. It is then connected to another uncharged identical...

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Using very little soap while washing clothes, does not serve the purpose of cleaning of clothes because

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The current density in a cylindrical wire of radius 4 mm is 4 $\times 10^6 \mathrm{Am}^{-2}$. The current through the...

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Which one of the following elemental forms is not present in the enamel of the teeth?

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Element "E" belongs to the period 4 and group 16 of the periodic table. The valence shell electron configuration of...

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The reaction of with bromine and KOH gives $\mathrm{RNH}_2$ as the end product. Which one of the following is the...

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Only $2 \%$ of the optical source frequency is the available channel bandwidth for an optical communicating system operating at...

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Match List-I with List-II Choose the correct answer from the options given below:

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A cell, shunted by a 8 $\Omega$ resistance, is balanced across a potentiometer wire of length 3m. The balancing length...

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The most stable trihalide of nitrogen is:

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Match List-I with List-II Choose the correct answer from the options given below:

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Which will have the highest enol content ?

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The Zeta potential is related to which property of colloids”

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A beam of monochromatic light is used to excite the electron in Li++ from the first orbit to the third...

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In the following reaction : The compounds A and B respectively are :-

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Consider the above reaction sequence and identify the product B.

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Using Young's double slit experiment, a monochromatic light of wavelength 5000 Å produces fringes of fringe width 0.5 mm ....

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Identify the correct statement for B2H6 from those given below. Choose the most appropriate answer from the options given below...

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Based upon VSEPR theory, match the shape (geometry) of the molecules in List-I with the molecules in List-II and select...

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In Young’s double slit experiment the two slits are 0.6 mm distance apart. Interference pattern is observed on a screen...

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The incorrect statement about the imperfections in solids is :

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$$ \left(\mathrm{C}_7 \mathrm{H}_5 \mathrm{O}_2\right)_2 \xrightarrow{\mathrm{hv}}[\mathrm{X}]+2 \dot{\mathrm{C}}_6 \mathrm{H}_5+2 \mathrm{CO}_2 $$ Consider the above reaction and identify the intermediate ' $X$ '

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A 220 V, 50 Hz AC source is connected to a 25 V, 5 W lamp and an additional resistance...

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The intermediate X, in the reaction is?

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Given below are two statements : Statement I : In 'Lassaigne's Test, when both nitrogen and sulphur are present in...

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In a carnot engine, the temperature of reservoir is $527^{\circ} \mathrm{C}$ and that of sink is 200 K. If the...

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A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength $...

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The major product in the reaction

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Polar stratospheric clouds facilitate the formation of :

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Given below are the oxides: $\mathrm{Na}_2 \mathrm{O}, \mathrm{As}_2 \mathrm{O}_3, \mathrm{~N}_2 \mathrm{O}, \mathrm{NO}$ and $\mathrm{Cl}_2 \mathrm{O}_7$ Number of amphoteric oxides is:

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The highest industrial consumption of molecular hydrogen is to produce compounds of element:

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Consider the following reaction : A + alkali → B (Major Product) If B is an oxoacid of phosphorus with...

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The IUPAC name of ethylidene chloride is :

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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R) Assertion...

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A mixture of hydrogen and oxygen has volume 2000 $\mathrm{cm}^3$, temperature 300 K, pressure 100 kPa and mass 0.76 g...

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Which of the following statements are correct ? Choose the most appropriate answer from the options given below:

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A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged....

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The products formed in the following reaction.

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The correct order of melting points of hydrides of group 16 elements is :

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In the following structures, which one is having staggered conformation with maximum dihedral angle?

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The correct order of melting point is :

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A longitudinal wave is represented by $x=10 \sin 2 \pi\left(n t-\frac{x}{\lambda}\right) \mathrm{cm}$. The maximum particle velocity will be four times...

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Identify the correct Logic Gate for the following output (Y) of two inputs A and B.

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Phenol on reaction with dilute nitric acid, gives two products. Which method will be most effective for large scale separation?

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An ideal fluid of density 800 $\mathrm{kgm}^{-3}$, flows smoothly through a bent pipe (as shown in figure) that tapers in...

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Consider the following reaction: $2 \mathrm{HSO}_4^{-}(\mathrm{aq}) \xrightarrow[\text { (2)Hydrolysis }]{\text { (1) Electrolysis }} 2 \mathrm{HSO}_4^{-}+2 \mathrm{H}^{+}+\mathrm{A}$ The dihedral angle...

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A hydrogen atom in is ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen...

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Given below are two statements: Statement I : According to the Ellingham diagram, any metal oxide with higher $\Delta \mathrm{G}^{\circ}$...

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The eutrophication of water body results in :

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At a certain place the angle of dip is $30^{\circ}$ and the horizontal component of earth's magnetic field is 0.5...

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A 110 V, 50 Hz, AC source is connected in the circuit (as shown in figure). The current through the...

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The escape velocity of a body on a planet ' A ' is $12 \mathrm{kms}^{-1}$. The escape velocity of the...

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Choose the correct stability order of group 13 elements in their +1 oxidation state.

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Consider a light ray travelling in air is incident into a medium of refractive index $\sqrt{2 \mathrm{n}}$ . The incident...

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Two vectors $\vec{A}$ and $\vec{B}$ have equal magnitudes. If-magnitude of $\vec{A}+\vec{B}$ is equal to two times the magnitude of $\vec{A}-\vec{B}$,...

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Among the following, which is the strongest oxidizing agent ?

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A telegraph line of length loo km has a capacity of $0.01 \mu \mathrm{~F} / \mathrm{km}$ and it carries an...

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An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound....

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Consider the ions/molecule For increasing bond order the correct option is :

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A singly ionized magnesium atom (A24) ion is accelerated to kinetic energy 5 keV and is projected perpendicularly into a...

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Cerium (IV) has a noble gas configuration. Which of the following is correct statement about it?

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In Vander Waals equation $\left[P+\frac{a}{V^2}\right][V-b]=R T ; P$ is pressure, $V$ is volume, $R$ is universal gas constant and $T$...

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As per the given circuit, the value of current through the battery will be ........... A.

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The total internal energy of two mole monoatomic ideal gas at temperature $\mathrm{T}=300 \mathrm{~K}$ will be J . (Given $...

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It the radius of the 3rd Bohr’s orbit of hydrogen atom is r3 and the radius of 4th Bohr’s orbit...

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White precipitate of AgCl dissolves in aqueous ammonia solution due to formation of :

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In a vernier callipers, each cm on the main scale is divided into 20 equal parts. If tenth vernier scale...

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Which one of the following alkaline earth metal ions has the highest ionic mobility in its aqueous solution?

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A hanging mass $M$ is connected to a four times bigger mass by using a string-pulley arrangement. as shown in...

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An evacuated glass vessel weights 40.0 g when empty, 135.0 g when filled with a liquid of density $...

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A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck...

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Given below are two statements : Statement I : Emulsions of oil in water are unstable and sometimes they separate...

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The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its...

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Number of electron deficient molecules among the following $\mathrm{PH}_3, \mathrm{~B}_2 \mathrm{H}_6, \mathrm{CCl}_4, \mathrm{NH}_3$, LiH and $\mathrm{BCl}_3$ is

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A light ray is incident, at an incident angle $\theta_1$, on the system of two plane mirrors $\mathrm{M}_1$ and $\mathrm{M}_2$...

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A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass...

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A commercially sold conc. HCl is 35% HCl by mass. If the density of this commercial acid is 1.46 g/mL,...

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Leaching of gold with dilute aqueous solution of NaCN in presence of oxygen gives complex [A], which on reaction with...

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A force of 10N acts on a charged particle placed between two plates of a charged capacitor. If one plate...

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For a series LCR circuit, I vs $\omega$ curve is shown : $\mid$ (a) To the left of $\omega r_r$,...

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The position vector of 1 kg object is $\vec{r}=(3 \hat{i}-\hat{j}) \mathrm{m}$ and its velocity $\vec{v}=(3 \hat{j}+k) \mathrm{ms}^{-1}$. The magnitude of...

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For a reaction at equilibrium $$ \mathrm{A}(\mathrm{~g}) \rightleftharpoons \mathrm{B}(\mathrm{~g})+\frac{1}{2} \mathrm{C}(\mathrm{~g}) $$ the relation between dissociation constant (K), degree of dissociation...

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The pair, in which ions are isoelectronic with $\mathrm{Al}^{3+}$ is :-

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An AC source is connected to an inductance of 100 mH , a capacitance of $100 \mu \mathrm{~F}$ and a...

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A $10 \Omega$, 20 mH coil carrying constant current is connected to a battery of 20 V through a switch...

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Incorrect statement for Tyndall effect is :-

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Bonding in which of the following diatomic molecules(s) become(s) stronger, on the basis of MO Theory, by removal of an...

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Match List – I with List – II

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An $\alpha$ particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelength $...

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The elongation of a wire on the surface of the earth is $10^{-4}$ m. The same wire of same dimensions...

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Current measured by the ammeter (A) in the reported circuit when no current flows through $10 \Omega$ resistance. will be...

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A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g...

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Consider the following pairs of electrons (A) (a) $\mathrm{n}=3, \ell=1, \mathrm{~m}_1=1, \mathrm{~m}_{\mathrm{s}}=+\frac{1}{2}$ (b) $\mathrm{n}=3, \ell=2, \mathrm{~m}_1=1, \mathrm{~m}_{\mathrm{s}}=+\frac{1}{2}$ (B) (a) $...

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Mach List-I with List – II : Choose the correct answer from the options given below :

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A charged particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the...

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In a potentiometer arrangement, a cell gives a balancing point at 75 cm length of wire. This cell is now...

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A meter bridge setup is shown in the figure. It is used to determine an unknown resistance R using a...

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The elastic behaviour of material for linear streass and linear strain, is shown in the figure. The energy density for...

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A ball of mass 100 g is dropped from a height h = 10 cm on a platform fixed at...

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A pendulum is suspended by a string of length 250 cm . The mass of the bob of the pendulum...

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A particle of mass 500 gm is moving in a straight line with velocity $v=b x^{5 / 2}$. The work...

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From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A...

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If a rocket runs on a fuel ( $\mathrm{C}_{15} \mathrm{H}_{30}$ ) and liquid oxygen, the weight of oxygen required and...

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A ball of mass 0.5 kg is dropped from the height of 10m. The height, at which the magnitude of...

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The current flowing through an ac circuit is given by $I=5 \sin (120 \pi t) A$ How long will the...

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The velocity of sound in a gas. in which two wavelengths 4.08 m and 4.16 m produce 40 beats in...

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When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted election...

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A fighter jet is flying horizontally at a certain altitude with a speed of 200 $\mathrm{ms}^{-1}$. When it passes directly...

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Sodium light of wavelengths 650 nm and 655 nm is used to study diffraction at a single slit of aperture...

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Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R....

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Match List-I with List-II Choose the correct answer from the options given below :

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A force on an object of mass 100 g is $(10 \hat{\mathrm{i}}+5 \hat{\mathrm{j}}) \mathrm{N}$. The position of that object at...

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As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220...

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The current in a coil of self inductance 2.0 H is increasing according to $\mathrm{I}=2 \sin \left(\mathrm{t}^2\right) \mathrm{A}$. The amount...

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The susceptibility of a paramagnetic material is 99. The permeability of the material in Wb/A-m is : [Permeability of free...

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Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R....

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Choose the correct statement for amplitude modulation:

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A transistor is used in common-emitter mode in an amplifier circuit. When a signal of 10 mV is added to...

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The total current supplied to the circuit as shown in figure by the 5V battery is __________A

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For using a multimeter to identify diode from electrical components. choose the correct statement out of the following about the...

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Two identical thin biconvex lenses of focal length 15 cm and refractive index 1.5 are in contact with each other....

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The velocity of a small ball of mass ‘m’ and density d1, when dropped in a container filled with glycerine,...

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A resistor develops 300 J of thermal energy in 15s, when a current of 2A is passed through it. If...

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The I-V characteristics of a p-n junction diode in forward bias is shown in the figure. The ratio of dynamic...

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0.056 kg of Nitrogen is enclosed in a vessel at a temperature of $127^{\circ} \mathrm{C}$. The amount of heat required...

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The equivalent capacitance between points A and B in below shown figure will be _____μF.

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What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary...

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Two metallic blocks $\mathrm{M}_1$ and $\mathrm{M}_2$ of same area of cross-section are connected to each other (as shown in figure)....

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The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe....

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The magnetic field at the centre of a circular coil of radius r, due to current I flowing through it,...

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How many alpha and beta particles are emitted when Uranium ${ }_{92} \mathrm{U}^{238}$ decays to lead $82 \mathrm{~Pb}^{206}$?

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In the following circuit, the correct relation between output (Y) and inputs A and B will be :

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A wire of length $L$ is hanging from a fixed support. The length changes to $L_1$ and $L_2$ when masses...

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A steam engine intakes 50 g of steam at $100^{\circ} \mathrm{C}$ per minute and cools it down to $20^{\circ} \mathrm{C}$....

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A parallel plate capacitor is formed by two plates each of area $30 \pi \mathrm{~cm}^2$ separated by 1 mm. A...

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The velocity of upper layer of water in a river is $36 \mathrm{kmh}^{-1}$. Shearing stress between horizontal layers of water...

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Given below are two statements : Statement I : The law of gravitation holds good for any pair of bodies...

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An electron with speed v and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy...

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A 0.5 kg block moving at a speed of $12 \mathrm{~ms}^{-1}$ compresses a spring through a distance 30 cm when...

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A Carnot engine whose heat sinks at $27^{\circ} \mathrm{C}$, has an efficiency of $25 \%$. By how many degrees should...

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A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat...

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A uniform chain of 6 m length is placed on a table such that a part of its length is...

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A baseband signal of 3.5 MHz frequency is modulated with a carrier signal of 3.5 GHz frequency using amplitude modulation...

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A teacher in his physics laboratory allotted an experiment to determine the resistance (G) of a galvanometer. Students took the...

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In free space, an electromagnetic wave of 3 GHz of 3 GHz frequency strikes over the edge of an object...

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Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two...

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A 72 $\Omega$ galvanometer is shunted by a resistance of 8 $\Omega$. The percentage of the total current which passes...

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The de Brogue wavelengths for an electron and a photon are $\lambda_{\mathrm{e}}$ and $\lambda_{\mathrm{p}}$ respectively. For the same kinetic energy...

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The difference of speed of light in the two media $A$ and $B\left(v_A-v_B\right)$ is $2.6 \times 10^7 \mathrm{~m} / \mathrm{s}$....

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Choose the correct option from the following options given below :

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The aperture of the objective is 24.4 cm. The resolving power of this telescope. If a light of wavelength 2440...

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If electric field intensity of a uniform plane electro magnetic wave is given as $$ E=-301.6 \sin (k z-\omega t)...

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A plane electromagnetic wave travels in a medium of relative permeability 1.61 and relative permittivity 6.44. If magnitude of magnetic...

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A signal of 100 THz frequency can be transmitted with maximum efficiency by :

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Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0, 0)...

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The photodiode is used to detect the optical signals. These diodes are preferably operated in reverse biased mode because.

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The refracting angle of a prism is A and refractive index of the material of the prism is cot (A/2)....

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The equations of two waves are given by : $...

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The ratio for the speed of the electron in the 3rd orbit of He+ to the speed of the electron...

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A proton and an alpha particle of the same enter in a uniform magnetic field which is acting perpendicular to...

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The activity of a radioactive material is $2.56 \times 10^{-3} \mathrm{Ci}$. If the half life of the material is 5...

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A radar sends an electromagnetic signal of electric field $\left(\mathrm{E}_0\right)=2.25 \mathrm{~V} / \mathrm{m}$ and magnetic field $\left(\mathrm{B}_0\right)=1.5 \times 10^{-8} \mathrm{~T}$...

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Given below are two statements Statement I : Davisson-Germer experiment establishes the wave nature of electrons. Statement II : If...

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A resistance of 40 $\Omega$ is connected to a source of alternating current rated 220 V, 50 Hz. Find the...

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An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface. Choose the correct representation...

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An aluminium wire is stretched to make its length, 04% larger. Then percentage change in resistance is:

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A light wave travelling linearly in a medium of dielectric constant 4, incident on the horizontal interface separating medium with...

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The approximate height from the surface of earth at which the weight of the body becomes $\frac{1}{3}$ of its weight...

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The three charges q / 2, q and q / 2 are placed at the corners $A, B$ and $C$...

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The magnetic flux through a coil perpendicular to its plane is varying according to the relation $\phi=\left(5 t^3+4 t+2 t-5\right)$...

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A system of two blocks of masses m = 2 kg and M = 8 kg is placed on a...

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A particle experiences a variable force $\vec{F}=\left(4 x \hat{i}+3 y^2 \hat{j}\right)$ in a horizontal $x-y$ plane. Assume distance in meters...

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A body of mass $M$ at rest explodes into three pieces, in the ratio of masses $1: 1: \mid 2$....

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Given below are two statements : Statement-I : A point charge is brought in an electric field. The value of...

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Assertion (A) : Non-polar amterials do not have my permanent dipole moment. Reason (R) : When an non-polar material is...

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A sliver wire has mass $(0.6 \pm 0.006) \mathrm{g}$, radius $(0.5 \pm 0.005)$ mm and length $(4 \pm 0.04)$ cm....

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Given below are two statement: Statement -I : What $\mu$ amount of an ideal gas undergoes adiabatic change from state...

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The two light beams having intensities I and 91 interfere to produce a fringe pattern on a screen. The phase...

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Two balls $A$ and $B$ are placed at the top of 180 m tall tower. Ball $A$ is released from...

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The electric field in an electromagnetic wave is given by $\mathrm{E}=56.5 \sin \omega(\mathrm{t}-\mathrm{x} / \mathrm{c}) \mathrm{NC}^{-1}$. Find the intensity of...

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Two capacitors having capacitance $\mathrm{C}_1$ and $\mathrm{C}_2$ respectively are connected as shown in figure. Initially, capacitor C1 is charged to...

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A girl standing on road holds her umbrella at $45^{\circ}$ with the vertical to keep the rain away. If she...

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If wattless current flows in the AC circuit, then the circuit is

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A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is...

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A projectile is launched at an angle‘ $\alpha$ ’ with the horizontal with a velocity 20 $\mathrm{ms}^{-1}$. After 10 s,...

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Time period of a simple pendulum in a stationary lift is 'T'. If the lift accelerates with $\frac{g}{6}$, vertically upwards...

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The efficiency of a Carnot's engine, working between steam point and ice point, will be :

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A water drop of diameter cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m....

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A long straight wire with a circular crosssection having radius R , is carrying a steady current I . The...

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The variation of acceleration due to gravity (g) with distance (r) from the center of the earth is correctly represented...

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A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 $\mathrm{rads}^{-1}$ in...

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Two planets A and B of equal mass are having their period of revolutions $T_A$ and $T_B$ such that $...

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Match List-I with List-II Choose the correct answer from the options given below :-

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A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio...

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In the figure, a very large plane sheet of positive charge is shown. $P_1$ and $P_2$ are two points at...

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A vertical electric field of magnitude $4.9 \times 10^5 \mathrm{~N} / \mathrm{C}$ just prevents a water droplet of a mass...

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The relation between root mean square speed $\left(v_{\mathrm{rms}}\right)$ and most probable speed $\left(v_p\right)$ for the molar mass $M$ of oxygen...

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A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls...

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An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero ?

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Motion of a particle in x-y plane is described by a set of following equations $...

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The terminal velocity $\left(V_t\right)$ of the spherical rain drop depends on the radius (r) of the spherical rain drop as:-

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A block of mass 10 kg starts sliding on a surface with an initial velocity of $9.8 \mathrm{~ms}^{-1}$. The coefficient...

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A particle of mass m is moving in a circular path of constant radius $r$ such that its centripetal acceleration...

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A projectile is projected with velocity of 25 m/s at an angle $\theta$ with the horizontal. After t seconds its...

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A person is standing in an elevator. In which situation, he experiences weight loss ?

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The height of any point P above the surface of earth is equal to diameter of earth. The value of...

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Given below are two statements: One is labeled as Assertion A and the other is labelled as Reason R. Assertion...

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If force $\vec{F}=3 \hat{i}+4 \hat{j}-2 \hat{k}$ acts on a particle having position vector $2 \hat{i}+\hat{j}+2 \hat{k}$ then, the torque about...

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Identify the pair of physical quantities which have different dimensions :

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An expression for a dimensionless quantity P is given by $P=\frac{\alpha}{\beta} \log _e\left(\frac{k t}{\beta x}\right)$ ; where $\alpha$ and $\beta$...

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Which of the following relations is true for two unit vectors $\hat{A}$ and $\hat{B}$ making an angle $\theta$ to each...

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Two identical cells each of emf 1.5 V are connected in parallel across a parallel combination of two resistors each...

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Given below are two statements : One is labeled as Assertion (A) and the other is labelled as Reason (R)....

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If $Z=\frac{A^2 B^3}{C^4}$, then the relative error in $Z$ will be

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The bulk modulus of a liquid is $3 \times 10^{10} \mathrm{Nm}^{-2}$ The pressure required to reduce the volume of liquid...

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