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Three isomers A. B and C (mol. formula $\mathrm{C}_2 \mathrm{H}_7, \mathrm{~N}$ ) give the following results

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The mass of gas adsorbed, $x$, per unit mass of absorbate, $m$, was measured at various pressures, p. A graph...

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The number of chiral carbons present in the molecule given below is ______.

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If the variance of the terms in an increasing A.P., $b_1, b_2, b_3, \ldots, b_{11}$ is 90 , then the...

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The Gibbs energy change (in J ) for the given reaction at $[\mathrm{Cu} 2+]=[\mathrm{Sn} 2+]=1 \mathrm{M}$ and 298 K is:...

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For a positive integer $n,\left(1+\frac{1}{x}\right)^n$ is expanded in increasing powers of $x$. If three consecutive coefficients in this expansion are...

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The oxidation states of iron atoms in compounds (A), (B) and (C), respectively, are $x, y$ and $z$. The sum...

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Let $[t]$ denote the greatest integer less than or equal to $t$. Then the value of $...

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The internal energy change (in J ) when 90 g of water undergoes complete evaporation at $100^{\circ} \mathrm{C}$ is $\_\_\_\_$...

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The metal mainly used in devising photoelectric cells is

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If $y=\sum_{k=1}^6 k \cos ^{-1}\left\{\frac{3}{5} \cos k x-\frac{4}{5} \sin k x\right\}$, then $\frac{d y}{d x}$ at $x=0$ is

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The increasing order of the following compounds towards HCN addition is

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The area (in sq. units) of an equilateral triangle inscribed in the parabola $y^2=8 x$, with one of its vertices...

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In general the property (magnitudes only) that show an opposite trend in comparison to other properties across a period is

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The major aromatic product C in the following reaction sequence will be

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If a curve $\mathrm{y}=f(\mathrm{x})$, passing through the point $(1,2)$, is the solution of the differential equation, $...

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Which of the following is used for the preparation of colloids?

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If the equation $\cos ^4 \theta+\sin ^4 \theta+\lambda=0$ has real solutions for $\theta$, then $\lambda$ lies in the interval

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The integral $\int_0^2 \| x-1|-x| d x$ is equal to $\_\_\_\_$ .

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Let $f:(-1, \infty) \longrightarrow R$ be defined by $f(0)=1$ and $f(x)=\frac{1}{x} \log _e(1+x), x \neq 0$. Then the function $f$...

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If $\lim _{x \rightarrow 1} \frac{x+x^2+x^3+\ldots .+x^n-n}{x-1}=820,(n \in N)$ then the value of $n$ is equal to $\_\_\_\_$

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$\lim _{x \rightarrow 0}\left(\tan \left(\frac{\pi}{4}+x\right)\right)^{\frac{1}{x}}$ is equal to :

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Let $f: \mathrm{R} \rightarrow \mathrm{R}$ be a function which satisfies $f(\mathrm{x}+\mathrm{y})=f(\mathrm{x})+f(\mathrm{y}) \forall \mathrm{x}, \mathrm{y} \in \mathrm{R}$. If $f(1)=2$ and $...

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A plane passing through the point $(3,1,1)$ contains two lines whose direction ratios are $1,-2,2$ and $2,3,-1$ respectively. If this...

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The statement that is not true about ozone is

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While titrating dilute HCl solution with aqueous NaOH, which of the following will not be required?

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Let $E^C$ denote the complement of an event $E$. Let $E_1, E_2$ and $E_3$ be any pairwise independent events with...

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The IUPAC name for the following compound is

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Let $S$ be the sum of the first 9 terms of the series : $\{x+k a\}+\left\{x^2+(k+2) a\right\}+\left\{x^3+(k+4) a\right\}+\left\{x^4+(k+6) a\right\}+\ldots$ where...

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If the letters of the word ‘MOTHER’ be permuted and all the words so formed (with or without meaning) be...

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Which of the following compunds will show retention in configuration on nucleophic substitution by OH– ion?

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The number of integral values of $k$ for which the line, $3 x+4 y=k$ intersects the circle, $...

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Let $n>2$ be an integer. Suppose that there are $n$ Metro stations in a city located along a circular path....

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Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three unit vectors such that $|\vec{a}-\vec{b}|^2+|\vec{a}-\vec{c}|^2=8$. Then $|\vec{a}+2 \vec{b}|^2+|\vec{a}+2 \vec{c}|^2$ is equal to

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Consider that a $\mathrm{d}^6$ metal ion $\left(\mathrm{M}^{2+}\right)$ forms a complex with aqua ligands, and the spin only magnetic moment of...

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Consider a region $\mathrm{R}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathrm{R}^2 \cdot \mathrm{x}^2 \leq \mathrm{y} \leq 2 \mathrm{x}\right\}$. if a line $\mathrm{y}=\alpha$ divides the...

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Let $\alpha>0, \beta>0$ be such that $\alpha^3+\beta^2=4$. If the maximum value of the term independent of $x$ in the binomial...

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For octahedral Mn(II) and tetrahedral Ni(II) complexes, consider the following statements: (I) both the complexes can be high spin. (II)...

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Area (in sq. units) of the region outside $\frac{|x|}{2}+\frac{|y|}{3}=1$ and inside the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ is :

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Which one of the following graphs is not correct for ideal gas? d = Density, P = Pressure, T =...

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Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If one of the roots of f(x)...

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Consider the following rections: (i) Glucose $+\mathrm{ROH} \xrightarrow{\text { dry } \mathrm{HCl}}$ Acetal $\xrightarrow[\left(\mathrm{CH}_3 \mathrm{cO}\right)_2 \mathrm{O}]{\text { xeq. of }}$...

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If the sum of first 11 terms of an A.P., $\mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3, \ldots$ is $0\left(\mathbf{a}_1 \neq 0\right)$, then the...

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The sum of the first three terms of a G.P. is S and their product is 27. Then all such...

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An open beaker of water in equilibrium with water vapour is in a sealed container. When a few grams of...

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The major product in the following reaction is

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The plane passing through the points (1, 2, 1), (2, 1, 2) and parallel to the line, 2x = 3y,...

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For the following Assertion and Reason, the correct option is Assertion (A): When Cu (II) and sulphide ions are mixed,...

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Let $A$ be a $2 \times 2$ real matrix with entries from $\{0,1\}$ and $|A| \neq 0$. Consider the following...

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The set of all possible values of  in the interval (0, ) for which the points (1, 2) and...

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If $\mathrm{AB}_4$ molecule is a polar molecule, a possible geometry of $A B_4$ is

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If $R=\left\{(x, y) ; x, y \in Z, x^2+3 y^2 \leq 8\right\}$ is a relation on the set of integers...

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The figure that is not a direct manifestation of the quantum nature of atoms is

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For some $\theta \in\left(0, \frac{\pi}{2}\right)$, if the eccentricity of the hyperbola, $x^2-y^2 \sec ^2 \theta=10$ is $\sqrt{5}$ times the eccentricity...

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On heating compound (A) gives a gas (B) which is a constituent of air. This gas when treated with H2...

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Let $A=\left\{X=(x, y, z)^{\top}: P X=0\right.$ and $\left.x^2+y^2+z^2=1\right\}$, where $...

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Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A...

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In Carius method of estimation of halogen, 0.172 g of an organic compound showed presence of 0.08 g of bromine....

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The imaginary part of $(3+2 \sqrt{-54})^{1 / 2}-(3-2 \sqrt{-54})^{1 / 2}$ can be :

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A circular coil of radius 10 cm is placed in a uniform magnetic field of $3.0 \times 10^{-5} \mathrm{~T}$ with...

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A 5 F capacitor is charged fully by a 220 V supply. It is then disconnected from the supply and...

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Let $a, b, c \in R$ be all non-zero and satisfy $a^3+b^3+c^3=2$. If the matrix $$ A=\left(\begin{array}{lll} a & b...

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When radiation of wavelength $\lambda$ is used to illuminate a metallic surface, the stopping potential is V . When the...

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A line parallel to the straight line $2 x-y=0$ is tangent to the hyperbola $\frac{x^2}{4}-\frac{y^2}{2}=1$ at the point $\left(x_1, y_1\right)$....

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A small block starts slipping down from a point B on an inclined plane AB, which is making an angle...

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The ratio of the mass percentages of ‘C & H’ and ‘C & O’ of a saturated acyclic organic compound...

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An engine takes in 5 moles of air at $20^{\circ} \mathrm{C}$ and 1 atm , and compresses it adiabatically to...

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For the disproportionation reaction $2 \mathrm{Cu}^{+}(\mathrm{ag}) \rightleftharpoons \mathrm{Cu}(\mathrm{s})+\mathrm{Cu}^{2+}(\mathrm{ag})$ at $298 \mathrm{~K} . \mathrm{In} \mathrm{K}$ (where K is the equilibrium constant)...

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A beam of protons with speed $4 \times 10^5 \mathrm{~ms}^{-1}$ enters a uniform magnetic field of 0.3 T at an...

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In a reactor, 2 kg of ${ }_{92} \mathrm{U}^{235}$ fuel is fully used up in 30 days. The energy released...

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The heat of combustion of ethanol into carbon dioxide and water is -327 kcal at constant pressure. The heat evolved...

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A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is positioned...

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The work function of sodium metal is $4.41 \times 10^{-19} \mathrm{~J}$. If photons of wavelength 300 nm are incident on...

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The oxidation states of transition metal atoms in $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7, \mathrm{KMnO}_4$ and $\mathrm{K}_2 \mathrm{FeO}_4$, respectively, are $\mathrm{x}, \mathrm{y}$ and...

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The correct observation in the following reactions is :

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The major product of the following reaction is:

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An organic compound ' A ' $\left(\mathrm{C}_9 \mathrm{H}_{10} \mathrm{O}\right)$ when treated with conc. HI undergoes cleavage to yield compounds '...

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The shape / structure of $\left[\mathrm{XeF}_5\right]^{-}$and $\mathrm{XeO}_3 \mathrm{~F}_2$, respectively, are

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If a function f(x) defined by be continuous for some $a, b, c \in R$ and $f^{\prime}(0)+f^{\prime}(2)=e$, then the value...

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Two compounds $A$ and $B$ with same molecular formula $\left(\mathrm{C}_3 \mathrm{H}_6 \mathrm{O}\right)$ undergo Grignard's reaction with methylmagnesium bromide to give...

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A particle of mass $m$ with an initial velocity $u \hat{i}$ collides perfectly elastically with a mass 3 m at...

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Let $y=y(x)$ be the solution of the differential equation, $\frac{2+\sin x}{y+1} \cdot \frac{d y}{d x}-\cos x, y>0, y(0)=1$. If $...

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Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity $\rho \mathrm{c}$,

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Amongst the following statements regarding adsorption, those that are valid are (a) $\Delta \mathrm{H}$ becomes less negative as adsorption proceeds...

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A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases...

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The value of $\left(\frac{1+\sin \frac{2 \pi}{9}+i \cos \frac{2 \pi}{9}}{1+\sin \frac{2 \pi}{9}-i \cos \frac{2 \pi}{9}}\right)$ is :

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Train $A$ and train $B$ are running on parallel tracks in the opposite directions with speeds of $...

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The molecular geometry of SF6 is octahedral. What is the geometry of SF4 (including lone pair(s) of electrons, if any)?

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An amplitude modulated wave is represented by the expression $\mathrm{v}_{\mathrm{m}}=5(1+0.6 \cos 6280 \mathrm{t}) \sin (211 \times 10^4 \mathrm{t}$ ) volts...

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The results given in the below table were obtained during kinetic studies of the following reaction $2 A+B \rightarrow C+D$...

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Magnetic materials used for making permanent magnets (P) and magnets in a transformer (T) have different properties of the following,...

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The domain of the function $f(x)=\sin ^{-1}\left(\frac{|x|+5}{x^2+1}\right)$ is $(-\infty,-a] \cup[a, \infty)$. Then a is equal to:

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The mass density of a spherical galaxy varies as $\frac{\mathrm{K}}{\mathrm{r}}$ over a large distance ' r ' from its centre....

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The one that is not expected to show isomerism is

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If speed V, area A and force F are chosen as fundamental units, then the dimension of Young’s modulus will...

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Let S be the set of all $\lambda \in \mathrm{R}$ for which the system of linear equations has no solution....

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Match the type of interaction in column A with the distance dependence of their interaction energy in column B

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The least count of the main scale of a vernier callipers is 1 mm . Its vernier scale is divided...

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A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a...

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If $|x|

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The size of a raw mango shrinks to a much smaller size when kept in a concentrated salt solution. Which...

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Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings...

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If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and...

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Simplified absorption spectra of three complexes ((i), (ii) and (iii)) of $\mathrm{M}^{n^{+}}$ion are provided below; their $\lambda_{\max }$ values are...

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A bead of mass $m$ stays at point $P(a, b)$ on a wire bent in the shape of a parabola...

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Let $X=\{x \in N: 1 \leq x \leq 17\}$ and $Y\{a x+b: x \in X$ and $...

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If you spill a chemical toilet cleaning liquid on your hand, your first aid would be

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Two identical strings $X$ and $Z$ made of same material have tension $\mathrm{T}_{\mathrm{x}}$ and $\mathrm{T}_{\mathrm{z}}$ in them. If their fundamental...

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The number of subshells associated with n = 4 and m = –2 quantum numbers is

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Let $\alpha$ and $\beta$ be the roots of the equation, $5 x^2+6 x- 2=0$. If $S_n=\alpha^n+\beta^n, n=1,2,3, \ldots$, then :

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A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as...

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Arrange the following labelled hydrogens in decreasing order of acidity

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Interference fringes are observed on a screen by illuminating two thin slits 1 mm apart with a light source (...

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Three elements X, Y and Z are in the 3rd period of the periodic table. The oxides of X, Y...

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A plane electromagnetic wave, has frequency of $2.0 \times 1010 \mathrm{~Hz}$ and its energy density is $...

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Cast iron is used for the manufacture of

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A charged particle (mass $m$ and charge $q$ ) moves along X -axis with velocity V 0 . When it...

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The major product obtained from $\mathrm{E}_2$ - elimination of 3-bromo-2-fluoropentane is

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Two elements A and B have similar chemical properties. They don’t form solid hydrogencarbonates, but react with nitrogen to form...

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Consider the reaction sequence given below: Which of the following statements is true?

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A light ray enters a solid glass sphere of refractive index $\mu=\sqrt{3}$ at an angle of incidence $60^{\circ}$. The ray...

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An ideal cell of emf 10 V is connected in circuit shown in figure. Each resistance is $2 \Omega$. The...

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If for $x \geq 0, y=y(x)$ is the solution of the differential equation, $(x+1) d y=\left((x+1)^2+y-3\right) d x, y(2)=0$, then...

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A particle of mass $m$ is moving along the $x$-axis with initial velocity $u \hat{i}$. It collides elastically with a...

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The number of distinct solutions of the equation, $\log _{\frac{1}{2}}|\sin x|=2-\log _{\frac{1}{2}}|\cos x|$ in the interval $[0,2 \pi]$, is $\_\_\_\_$...

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If the vectors, $\vec{p}=(a+1) \hat{i}+a \hat{j}+a \hat{k}$, $\overrightarrow{\mathrm{q}}=\mathrm{a} \hat{\mathrm{i}}+(\mathrm{a}+1) \hat{\mathrm{j}}+\mathrm{a} \hat{\mathrm{k}}$, and $\vec{r}=a \hat{i}+a \hat{j}+(a+1) \hat{k}(a \in R)$ are coplanar...

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A wire of density $9 \times 10^{-3} \mathrm{~kg} \mathrm{~cm}^{-3}$ is stretched between two clamps 1 m apart. The resulting strain...

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The coefficient of $x^4$ in the expansion of $\left(1+x+x^2\right)^{10}$ is. $\_\_\_\_$

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A square shaped hole of side $I=\frac{a}{2}$ is carved out at a distance $d=\frac{a}{2}$ from the centre ' $O$ '...

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The projection of the line segment joining the point (1, –1, 3) and (2, –4, 11) on the line joining...

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A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness that melts...

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A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide...

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If $f(x)= \begin{cases}\frac{\sin (a+2) x+\sin x}{x} & ; x0\end{cases}$ is continuous at $x=0$, then $a+2 b$ is equal to

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If the number of five digit numbers with distinct digits and 2 at the $10^{\text {th }}$ place is 336...

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In the following digital circuit, what will be the output at ‘Z’, when the input (A, B) are (1, 0),...

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The value of $\cos ^3\left(\frac{\pi}{8}\right) \cdot \cos \left(\frac{3 \pi}{8}\right)+\sin ^3\left(\frac{\pi}{8}\right) \cdot \sin \left(\frac{3 \pi}{8}\right)$ is

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A charge $Q$ is distributed over two concentric conducting thin spherical shells radii $r$ and $R(R>r)$. If the surface charge...

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Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The...

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If for all real triplets $(a, b, c), f(x)=a+b x+c x^2$; then $\int_0^1 f(x) d x$ is equal to

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Let the observations $x_i(1 \leq i \leq 10)$ satisfy the equations, $\sum_{\mathrm{i}=1}^{10}\left(\mathrm{x}_{\mathrm{i}}-5\right)=10$ and $\sum_{\mathrm{i}=1}^{10}\left(\mathrm{x}_{\mathrm{i}}-5\right)^2=40$. If $\mu$ and $\lambda$ are the...

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A potentiometer wire $P Q$ of $1 m$ length is connected to a standard cell $E_1$. Another cell $E_2$ of...

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Negation of the statement : ' $\sqrt{5}$ is an integer of 5 is irrational is

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the height ‘h’ at which the weight of a body will be the same as that at the same depth...

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The product $2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}}$. to $\infty$ is equal to

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The value of $\int_0^{2 \pi} \frac{x \sin ^8 x}{\sin ^8 x+\cos ^8 x} d x$ is equal to

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A small point mass carrying some positive charge on it, is released from the edge of a table. There is...

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I the matrices $...

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A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle...

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A $10 \mu \mathrm{~F}$ capacitor is fully charged to a potential difference of 50 V . After removing the source...

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A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular...

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An inductance coil has a reactance of $100 \Omega$. When an AC signal of frequency 1000 Hz is applied to...

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The integral $\int \frac{d x}{(x+4)^{\frac{8}{7}}(x-3)^{\frac{6}{7}}}$ is equal to (where C is a constant of integration)

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The figure shows a region of length ' l ' with a uniform magnetic field of 0.3 T in it...

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Let C be the centroid of the triangle with vertices (3, –1), (1, 3) and (2, 4). Let P be...

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If $e_1$ and $e_2$ are the eccentricitis of the ellipse, $\frac{x^2}{18}+\frac{y^2}{4}=1 \quad$ and the hyperbola, $\quad \frac{x^2}{9}-\frac{y^2}{4}=1$ respectively and (...

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The displacement time graph of a particle executing S.H.M is given in figure (sketch is schematic and not to scale)...

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The number of real roots of the equation, $e^{4 x}+e^{3 x}-4 e^{2 x}+e^x+1=0$ is

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If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for...

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In a hydrogen atom the electron makes a transition from ( $n+1 \alpha_{\sim \sim}^{\text {th }}$ level to the $...

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A heat engine is involved with exchange of heat of 1915 J, – 40J, + 125 J and –Q J,...

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An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are...

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When the temperature of a metal wire is increased from 0°C to 10°C, its length increases by 0.02%. The percentage...

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In a Young’s double slit experiment, 16 fringes are observed in a certain segment of the screen when light of...

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In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by $\hat{\mathrm{k}}$ and $...

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Let $f(x)=x \cdot\left[\frac{x}{2}\right]$ for $-10

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The number of words, with or without meaning, that can be formed by taking 4 letters at a time from...

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The natural number m , for which the coefficient of $x$ in the binomial expansion of $\left(x^m+\frac{1}{x^2}\right)^{22}$ is 1540 ,...

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If the line, $2 x-y+3=0$ is at a distance $\frac{1}{\sqrt{5}}$ and $\frac{2}{\sqrt{5}}$ from the lines $4 x-2 y+\alpha=0$ and $...

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Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up...

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If the volume of a parallelopiped, whose coterminus edges are given by the vectors $\vec{a}=\hat{i}+\hat{j}+n \hat{k}, \vec{b}=2 \hat{i}+4 \hat{j}-n \hat{k}$...

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If the point $P$ on the curve, $4 x^2+5 y^2=20$ is farthest from the point $\mathrm{Q}(0,-4)$, then $\mathrm{PQ}^2$ is equal...

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The product of the roots of the equation $9 x^2-18 |x|+5=0$, is :

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If $2^{10}+2^9 \cdot 3^1+2^8 \cdot 3^2+\ldots .+2 \cdot 3^9+3^{10}=S-2^{11}$, then $S$ is equal to:

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A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x...

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If the minimum and the maximum values of the function $f: f:\left[\frac{\pi}{4}, \frac{\pi}{2}\right] \rightarrow R$, defined by $$ f(\theta)=\left|\begin{array}{ccc} -\sin...

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If $\alpha$ is the positive root of the equation, $p(x)=x^2-x -2=0$, then $\lim _{x \rightarrow \alpha^{+}} \frac{\sqrt{1-\cos (p(x))}}{x+\alpha-4}$ is equal...

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If the four complex numbers $z, \bar{z}, \bar{z}-2 \operatorname{Re}(\bar{z})$ and $z-2 \operatorname{Re}(z)$ represent the vertices of a square of side...

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The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12,...

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If $3^{2 \sin 2 \alpha-1}, 14$ and $3^{4-2 \sin 2 \alpha}$ are the first three terms of an A.P. for...

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If $(a, b, c)$ is the image of the point $(1,2,-3)$ in the line, $\frac{x+1}{2}=\frac{y-2}{-2}=\frac{z}{-1}$, then $a+b+c$ is equal to...

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If S is the sum of the first 10 terms of the series $\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{13}\right)+\tan ^{-1}\left(\frac{1}{21}\right)+\ldots \ldots$ then...

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The value of $\int_{-\pi / 2}^{\pi / 2} \frac{1}{1+\mathrm{e}^{\sin x}} \mathrm{dx}$ is:

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Let $A D$ and $B C$ be two vertical poles at $A$ and $B$ respectively on a horizontal ground. If...

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If $y=y(x)$ is the solution of the differential equation $\frac{5+\mathrm{e}^{\mathrm{x}}}{2+\mathrm{y}} \cdot \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{e}^{\mathrm{x}}=0$ satisfying $\mathrm{y}(0)=1$, then a value of $...

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If $\vec{a}$ and $\vec{b}$ are unit vectors, then the greatest value of $\sqrt{3}|\vec{a}+\vec{b}|+|\vec{a}-\vec{b}|$ is

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The angle of elevation of the top of a hill from a point on the horizontal plane passing through the...

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Set A has m elements and Set B has n elements. If the total number of subsets of A is...

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If $\alpha$ and $\beta$ be two roots of the equation $x^2-64 x+256=0$. Then the value of $...

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Let $a, b, c, d$ and $p$ be any non zero distinct real numbers such that $...

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If $\sum_{i=1}^n\left(x_i-a\right)=n$ and $\sum_{i=1}^n\left(x_i-a\right)^2=n a,(n, a>1)$ then the standard deviation of $n$ observations $x_1, x_2, \ldots, x_n$ is :

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The position of a moving car at time $t$ is given by $f(t)=a t^2+b t+c, t>0$, where $a, b$ and...

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Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the...

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Consider the data on $x$ taking the values $0,2,4,8$, $\ldots, 2^n$ with frequencies $...

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If the common tangent to the parabolas, $y^2=4 x$ and $x^2=4 y$ also touches the circle, $x^2+y^2=c^2$, then c is...

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The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER”...

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If the co-ordinates of two points $A$ and $B$ are $(\sqrt{7}, 0)$ and $(-\sqrt{7}, 0)$ respectively and $P$ is any...

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The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to:

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The sum of distinct values of λ for which the system of equations (λ – 1)x + (3λ + 1)y...

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The area (in sq. units) of the region $A=\left\{(x, y)\right.$ : $\left.|x|+|y| \leq 1,2 y^2 \geq|x|\right\}$ is :

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If the function $f(x)\left\{\begin{array}{ll}k_1(x-\pi)^2-1, & x \leq \pi \\ k_2 \cos x, & x>\pi\end{array}\right.$ is twice differentiable, then the ordered...

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The values of $\lambda$ and $\mu$ for which the system of linear equations $$ \begin{aligned} & x+y+z=2 \\ & x+2...

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Let $\lambda \in \mathrm{R}$. The system of linear equations $$ \begin{aligned} & 2 x_1-4 x_2+\lambda x_3=1 \\ & x_1-6 x_2+x_3=2...

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Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the...

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If $\quad \int\left(e^{2 x}+2 e^x-e^{-x}-1\right) e^{\left(e^x+e^{-x}\right)} d x=g(x) e^{\left(e^x+e^{-x}\right)}+c$ where c is a constant of integration, then $\mathrm{g}(0)$ is equal...

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A plane P meets the coordinate axes at A, B and C respectively. The centroid of ΔABC is given to...

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A soft drink was bottled with a partial pressure of $\mathrm{CO}_2$ of 3 bar over the liquid at room temperature....

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The area (in sq. units) of the region enclosed by the curves $y=x^2-1$ and $y=1-x^2$ is equal to :

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An oxidation-reduction reaction in which 3 electrons are transferred has a $\Delta \mathrm{G}^0$ of $17.37 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at $25^{\circ} \mathrm{C}$....

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If $I_1=\int_0^1\left(1-x^{50}\right)^{100} d x$ and $I_2=\int_0^1\left(1-x^{50}\right)^{101} d x$ such that $I_2=\alpha I_1$ then $\alpha$ equals to:

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The number of chiral carbon(s) present in peptide, Ile-Arg-Pro, is

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Let $z=x+$ iy be a non-zero complex number such that $z^2=i|z|^2$, where $i=\sqrt{-1}$, then $z$ lies on the

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The region represented by $\{z=x+i y \in C:|z|-\operatorname{Re}(z) \leq 1\}$ is also given by the inequality :

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For a suitably chosen real constant a , let a function, $\mathrm{f}: \mathrm{R}-\{-\mathrm{a}\} \rightarrow \mathrm{R}$ be defined by $f(x)=\frac{a-x}{a+x}$. Further...

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$$ \text { The integral } \int_1^2 e^x \cdot x^x\left(2+\log _e x\right) d x \text { equals : } $$

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If $\{p\}$ denotes the fractional part of the number $p$, then $\left\{\frac{3^{200}}{8}\right\}$, is equal to:

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The total number of coordination sites in ethylenediaminetetraacetate (EDTA ${ }^{4-}$ ) is

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The minimum number of moles of $\mathrm{O}_2$ required for complete combustion of 1 mole of propane and 2 moles of...

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The difference between radii of $3^{\text {rd }}$ and $4^{\text {th }}$ orbits of $\mathrm{Li}^{2+}$ is $\Delta \mathrm{R}_1$. The difference...

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For all twice differentiable functions f : R → R, with f(0) = f(1) = f′(0) = 0,

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A diatomic molecule $X_2$ has a body-centred cubic (bcc) structure with a cell edge of 300 pm . The density...

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A ray of light coming from the point $(2,2 \sqrt{3})$ is incident at an angle $30^{\circ}$ on the line $x=1$...

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Consider the following reaction : $\mathrm{N}_2 \mathrm{O}_4(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_2(\mathrm{~g}) ; \Delta \mathrm{H}^0=+58 \mathrm{~kJ}$ For each of the following cases...

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Consider the statement: "For an integer n , if $\mathrm{n}^3-1$ is even, then n is odd." The contrapositive statement of...

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The general solution of the differential equation $\sqrt{1+x^2+y^2+x^2 y^2}+x y \frac{d y}{d x}=0$ is : (where C is a constant...

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In the following reaction sequence the major products A and B are:

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The shortest distance between the lines $\frac{x-1}{0}=\frac{y+1}{-1}=\frac{z}{1}$ and $x+y+z+1=0,2 x-y+z+3=0$ is :

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A flask contains a mixture of compounds A and B. Both compounds decompose by first-order kinetics. The half-lives for A...

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Let $f: R \rightarrow R$ be a function defined by $f(x)=\max \left\{x, x^2\right\}$. Let $S$ denote the set of all...

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The negation of the Boolean expression $p \vee(\sim p \wedge q)$ is equivalent to

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Identify the correct molecular picture showing what happens at the critical micellar concentration (CMC) of an aqueous solution of a...

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If the constant term in the binomial expansion of $\left(\sqrt{x}-\frac{k}{x^2}\right)^{10}$ is 405 , then $|k|$ equals :

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The increasing order of basicity of the following compounds is

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If $f(x+y)=f(x) f(y)$ and $\sum_{x=1}^{\infty} f(x)=2 x, y \in N$, where $N$ is the set of all natural numbers, then...

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The potential energy curve for the $\mathrm{H}_2$ molecule as a function of internuclear distance is

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The angle of elevation of the summit of a mountain from a point on the ground is 45°. After climbing...

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Which of the following derivatives of alcohols is unstable in an aqueous base?

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Let $L_1$ be a tangent to the parabola $y^2=4(x+1)$ and $L_2$ be a tangent to the parabola $y^2=8(x+2)$ such that...

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The increasing order of the acidity of the $\alpha$ hydrogen of the following compounds is

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The common difference of the A.P. $b_1, b_2, \ldots, b_m$ is 2 more than the common difference of A.P. $...

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The structure of PCl5 in the solid state is

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Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they...

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Let $\theta=\frac{\pi}{5}$ and $\mathrm{A}=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]$. If $\mathrm{B}=\mathrm{A}+\mathrm{A}^4$, then $\operatorname{det}(\mathrm{B})$ :

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The most appropriate reagent for conversion of $\mathrm{C}_2 \mathrm{H}_5 \mathrm{CN}$ into $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{NH}_2$ is

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The correct electronic configuration and spinonly magnetic moment (BM) of $\mathrm{Gd}^{3+}(\mathrm{Z}=64)$, respectively, are

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If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor...

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A spherical balloon of radius 3 cm containing helium gas has a pressure of $48 \times 10^{-3}$ bar. At the...

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Which of the following is not an essential amino acid?

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If α and β are the roots of the equation 2x(2x + 1) = 1, then β is equal to...

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An Ellingham diagram provides information about

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If a person is suffering from the deficiency of nor-adrenaline, what kind of drug can be suggested?

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The probabilities of three events $\mathrm{A}, \mathrm{B}$ and C are given by $\mathrm{P}(\mathrm{A})=0.6, \mathrm{P}(\mathrm{B})=0.4$ and $\mathrm{P}(\mathrm{C})=0.5$. If $...

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The number of Cl = O bonds in perchloric acid is

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The condition that indicates a polluted environment is

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The equation that represents the water-gas shift reaction is

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The values of the crystal field stabilization energies for a high spin $d^6$ metal ion in octahedral and tetrahedral fields,...

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The centre of the circle passing through the point $(0,1)$ and touching the parabola $\mathrm{y}=\mathrm{x}^2$ at the point $(2,4)$ is...

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The elevation of boiling point of 0.10 m aqueous $\mathrm{CrCl}_3 . \mathrm{xNH}_3$ solution is two times that of 0.05 m...

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In the sixth period, the orbitals that are filled are

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Potassium chlorate is prepared by the electrolysis of KCl in basic solution. $$ 6 \mathrm{OH}^{-}+\mathrm{Cl}^{-} \rightarrow \mathrm{ClO}^{-}{ }_3+3 \mathrm{H}_2 \mathrm{O}+6...

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A beam of electrons of energy $E$ scatters from a target having atomic spacing of $1 \AA$. The first maximum...

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A compound microscope consists of an objective lens of focal length 1 cm and an eyepiece of focal length 5...

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In a Young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength $\lambda=500 \mathrm{~nm}$ is incident...

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A particle of mass $200 \mathrm{MeV} / \mathrm{c}^2$ collides with a hydrogen atom at rest. Soon after the collision the...

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Two concentric circular coils, $C_1$ and $C_2$ are placed in the XY plane. $\mathrm{C}_1$ has 500 turns, and a radius...

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In an estimation of bromine by Carius method, 1.6 g of an organic compound gave 1.88 g of AgBr. The...

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The set that contains atomic numbers of only transition elements, is

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The rate of a reaction decreased by 3.555 times when the temperature was changed from $40^{\circ} \mathrm{C}$ to $30^{\circ} \mathrm{C}$....

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A force $\vec{F}=(\hat{i}+2 \hat{j}+3 \hat{k}) \mathrm{N}$ acts at a point $(4 \hat{i}+3 \hat{j}+\hat{k}) \mathrm{m}$. Then the magnitude of torque about...

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Consider the Assertion and Reason given below. Assertion (A) : Ethene polymerized in the presence of Ziegler Natta Catalyst at...

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A square loop of side 2a, and carrying current I, is kept in XZ plane with its centre at origin....

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The atomic number of Unnilunium is _______.

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Number of molecules in a volume of $4 \mathrm{~cm}^3$ of a perfect monoatomic gas at some temperature T and at...

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If the solubility product of $\mathrm{AB}_2$ is $3.20 \times 10^{-11} \mathrm{M}^3$, then the solubility of $A B_2$ in pure water...

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For Freundlich adsorption isotherm, a plot of log (x/m) (y-axis) and $\log p$ (x-axis) gives a straight line. The intercept...

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The correct statement with respect to dinitrogen is

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A balloon is moving up in air vertically above a point A on the ground. When it is at a...

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A galvanometer of resistance G is converted into a voltmeter of range 0 – 1 V by connecting a resistance...

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A solution of phenol in chloroform when treated with aqueous NaOH gives compound P as a major product. The mass...

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In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from...

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The major product obtained from the following reaction is

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Dihydrogen of high purity (> 99.95%) is obtained through

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For a $\mathrm{d}^4$ metal ion in an octahedral field, the correct electronic configuration is

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For a concave lens of focal length f, the relation between object and image distances u and v, respectively, from...

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The value of the acceleration due to gravity is $\mathrm{g}_1$ at a height $h=\frac{R}{2}$ ( $R=$ radius of the earth)...

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The increasing order of the boiling points of the major products A, B and C of the following reactions will...

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A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small...

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Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V diagram. The...

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The element that can be refined by distillation is

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The presence of soluble fluoride ion upto 1 ppm concentration in drinking water, is

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The coef ficient of $x^4$ in the expansion of $\left(1+x+x^2+x^3\right)^6$ in powers of $x$, is $\_\_\_\_$ ...

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Match the following :

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A physical quantity $z$ depends on four observables $a, b, c$ and $d$, as $z=\frac{a^2 b^{\frac{2}{3}}}{\sqrt{c d^3}}$. The percentages of...

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Among the sulphates of alkaline earth metals, the solubilities of $\mathrm{BeSO}_4$ and $\mathrm{MgSO}_4$ in water, respectively, are

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With increasing biasing voltage of a photodiode, the photocurrent magnitude

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Let the vectors $\vec{a}, \vec{b}, \vec{c}$, be such that $|\vec{a}|=2,|\vec{b}|=4$ and $|\vec{c}|=4$ and $|\vec{c}|=4$. If the projection of $\vec{b}$ on...

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In a bombing attack, there is 50% chance that a bomb will hit the target. Atleast two independent hits are...

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The lanthanoid that does NOT show +4 oxidation state is

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If the lines $x+y=a$ and $x-y=b$ touch the curve $y=x^2-3 x+2$ at the points where the curve intersects the $x$-axis,...

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A set of solutions is prepared using 180 g of water as a solvent and 10 g of different nonvolatile...

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Let $A=\{a, b, c\}$ and $B=\{1,2,3,4\}$. Then the number of elements in the set $...

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For the given cell; $$ \mathrm{Cu}(\mathrm{~s})\left|\mathrm{Cu}^{2+}\left(\mathrm{C}_1 \mathrm{M}\right) \| \mathrm{Cu}^{2+}\left(\mathrm{C}_2 \mathrm{M}\right)\right| \mathrm{Cu}(\mathrm{~s}) $$ change in Gibbs energy ( $\Delta \mathrm{G}$ )...

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The area (in sq. units) of the region $...

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Which of the following compounds shows geometrical isomerism?

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Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respectively. These are then connected...

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For a reaction, $$ 4 \mathrm{M}(\mathrm{~s})+\mathrm{nO}_2(\mathrm{~g}) \rightarrow 2 \mathrm{M}_2 \mathrm{O}_{\mathrm{n}}(\mathrm{~s}) $$ the free energy change is plotted as a function...

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The derivative of $\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$ with respect to $\tan ^{-1}\left(\frac{2 x \sqrt{1-x^2}}{1-2 x^2}\right)$ at $x=\frac{1}{2}$ is :

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The major product of the following reaction is

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If $\int \frac{\cos \theta}{5+7 \sin \theta-2 \cos ^2 \theta} d \theta=A \log _e|B(\theta)|+C$, where $C$ is a constant of integration,...

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The correct match between Item-I (starting material) and Item-II (reagent) for the preparation of benzaldehyde is

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If the line $y=m x+c$ is a common tangent to the hyperbola $\frac{x^2}{100}-\frac{y^2}{64}=1$ and the circle $x^2+y^2=36$, then which one...

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The major products of the following reaction are

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A crystal is made up of metal ions $M_1$ and $M_2$ and oxide ions. Oxide ions form a ccp lattice...

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If $L=\sin ^2\left(\frac{\pi}{16}\right)-\sin ^2\left(\frac{\pi}{8}\right)$ and $M=\cos ^2\left(\frac{\pi}{16}\right)-\sin ^2\left(\frac{\pi}{8}\right)$, then

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The average molar mass of chlorine is 35.5 g $\mathrm{mol}^{-1}$. The ratio of ${ }^{35} \mathrm{Cl}$ to ${ }^{37} \mathrm{Cl}$...

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If the system of linear equations $...

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Mischmetal is an alloy consisting mainly of

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The numer of all $3 \times 3$ matrices A , with enteries from the set $\{-1,0,1)$ such that the sum...

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Reaction of an inorganic sulphite X with dilute $\mathrm{H}_2 \mathrm{SO}_4$ generates compound Y . Reaction of Y with NaOH gives...

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The least positive value of ' $a$ ' for which the equation, $2 x^2+(a-10) x+\frac{33}{2}=2 a$ has real roots is...

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The sum $\sum_{k=1}^{20}(1+2+3+\ldots . .+k)$ is $\_\_\_\_$ .

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Let the normal at a point $P$ on the curve $y^2-3 x^2+y+10=0$ intersect the $y$-axis at $\left(0, \frac{3}{2}\right)$. If $m$...

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An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which...

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Let the line $y=m x$ and the ellipse $2 x^2+y^2=1$ intersect at a point $P$ in the first quadrant. If...

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If $\int \frac{\cos x d x}{\sin ^3 x\left(1+\sin ^6 x\right)^{2 / 3}}=f(x)\left(1+\sin ^6 x\right)^{1 / 2}+c$ where $c$ is a...

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For $a>0$, let the curves $C_1: y^2=a x$ and $C_2: x^2=$ ay intersect at origin $O$ and a point $P$....

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The locus of a point which divides the line segment joining the point $(0,-1)$ and a point on the parabola,...

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If the equation, $x^2+b x+45=0(b \in R)$ has conjuate complex roots and they satisfy $|z+1|=2 \sqrt{10}$, then

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The shortest distance between the lines $\frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1}$ and $\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{2}$ is

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The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations...

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If $a, b$ and $c$ are the greatest values of ${ }^{19} \mathrm{C}_{\mathrm{p}},{ }^{20} \mathrm{C}_{\mathrm{q}}$ and ${ }^{21} \mathrm{C}_{\mathrm{r}}$ respectively,...

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Which one of the following is a tautology?

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For which of the following ordered pairs $(\mu, \delta)$, the system of linear equations $...

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Let the volume of a parallelopiped whose coterminous edges are given by $\overrightarrow{\mathrm{u}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}, \quad \overrightarrow{\mathrm{v}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{w}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$...

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Let $f: R \rightarrow R$ be such that for all $x \in R\left(2^{1+x}+2^{1-x}\right), f(x)$ and $\left(3^x+3^{-x}\right)$ are in A.P., then...

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Arrange the following solutions in the decreasing order of pOH

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Kraft temperature is the temperature

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The incorrect statement is

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A solution of two components containing $n_1$ moles of the $1^{\text {st }}$ component and $n_2$ moles of the $...

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The increasing order of $\mathrm{pK}_{\mathrm{b}}$ values of the following compounds is

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The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in...

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Suppose that intensity of a laser is $\left(\frac{315}{\pi}\right) \mathrm{W} / \mathrm{m}^2$. The rms electric field, in units of $...

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The IUPAC name of the following compound is

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Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They...

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The correct match between Item - I and Item – II is

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Initially a gas of diatomic molecules is contained in a cylinder of volume $\mathrm{V}_1$ at a pressure $\mathrm{P}_1$ and temperature...

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Match the following compounds (Column-I) with their uses (Column-II)

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A sound source S is moving along a straight track with speed v , and is emitting sound of frequency...

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Which one of the following statements is not true?

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You are given that Mass of ${ }_3^{\prime} \mathrm{Li}=7.0160 \mathrm{u}$, Mass of ${ }_2^4 \mathrm{He}=4.0026 \mathrm{u}$ and Mass of $...

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$$ \text { The reaction of } \mathrm{NO} \text { with } \mathrm{N}_2 \mathrm{O}_4 \text { at } 250 \mathrm{~K}...

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Let $f$ be any function continuous on $[a, b]$ and twice differentiable on $(a, b)$. If for all $...

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In a box, there are 20 cards, out of which 10 are labelled as A and the remaining 10 are...

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A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the...

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Charges $Q_1$ and $Q_2$ are at points $A$ and $B$ of a right angle triangle $O A B$ (see figure)....

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If for some $\alpha$ and $\beta$ in R , the intersection of the following three planes $...

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Let $f(x)=x \cos ^{-1}(-\sin |x|), x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$, then which of the following is true?

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The output characteristics of a transistor is shown in the figure. When $\mathrm{V}_{\mathrm{CE}}$ is 10 V and $\mathrm{I}_{\mathrm{C}}=4.0 \mathrm{~mA}$, then...

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Let $z$ be a complex number such that $\left|\frac{z-i}{z+2 i}\right|=1$ and $|z|=\frac{5}{2}$. Then the value of $|z+3 i|$ is

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$\lim _{x \rightarrow 0}\left(\frac{3 x^2+2}{7 x^2+2}\right)^{\frac{1}{x^2}}$ is equal to

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In a series LR circuit, power of 400 W is dissipated from a source of $250 \mathrm{~V}, 50 \mathrm{~Hz}$. The...

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An AC circuit has $\mathrm{R}=100 \Omega, \mathrm{C}=2 \mu \mathrm{~F}$ and $\mathrm{L}=80 \mathrm{mH}$, connected in series. The quality factor of the...

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An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of...

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In the figure below, P and Q are two equally intense coherent sources emitting radiation of wavelength 20 m ....

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An electron, a doubly ionized helium ion ( $\mathrm{He}^{++}$) and a proton are having the same kinetic energy. The relation...

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A Young's double-slit experiment is performed using monochromatic light of wavelength $\lambda$. The intensity of light at a point on...

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The mass percentage of nitrogen in histamine is _____.

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The centre of mass of a solid hemisphere of radius 8 cm is x cm from the centre of the...

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108 g of silver (molar mass $108 \mathrm{~g} \mathrm{~mol}^{-1}$ ) is deposited at cathode from $\mathrm{AgNO}_3(\mathrm{aq})$ solution by a certain...

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The hardness of a water sample containing $10^{-3} \mathrm{M} \mathrm{MgSO}_4$ expressed as $\mathrm{CaCO}_3$ equivalents (in ppm) is $\_\_\_\_$ . (molar...

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The molarity of $\mathrm{HNO}_3$ in a sample which has density $1.4 \mathrm{~g} / \mathrm{mL}$ and mass percentage of $63 \%$...

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How much amount of NaCl should be added to 600 g of water ( $\rho=1.00 \mathrm{~g} / \mathrm{mL}$ ) to...

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The correct order of heat of combustion for following alkadienes is

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Consider the force F on a charge ‘q’ due to a uniformly charged spherical shell of radius R carrying charge...

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For following reactions $...

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B has a smaller first ionization enthalpy than Be. Consider the following statements. (I) It is easier to remove 2p...

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A double convex lens has power P and same radii of curvature R of both the surfaces. The radius of...

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‘X’ melts at low temperature and is a bad conductor of electricity in both liquid and solid state. X is

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The linear mass density of a thin rod $A B$ of length $L$ varies from $A$ to $B$ as $$...

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The compound that cannot act both as oxidising and reducing agent is

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For the given input voltage waveform $\bigvee_{\text {in }}(t)$, the output voltage waveform $\bigvee_0(t)$, across the capacitor is correctly depicted...

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Which of these will produce the highest yield in Friedel Crafts reaction?

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For a plane electromagnetic wave, the magnetic field at a point x and time t is

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An electron is moving along $+x$ direction with a velocity of $6 \times 10^6 \mathrm{~ms}^{-1}$. It enters a region of...

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The acidic, basic and amphoteric oxides, respectively, are

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According to the following diagram, A reduces $\mathrm{BO}_2$ when the temperature is

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A point like object is placed at a distance of 1 m in front of a convex lens of focal...

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The increasing order of basicity for the following intermediates is (from weak to strong)

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When a particle of mass $m$ is attached to a vertical spring of spring constant $k$ and released, its motion...

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Let two points be $\mathrm{A}(1,-1)$ and $\mathrm{B}(0,2)$. If a point $\mathrm{P}\left(\mathrm{x}^{\prime}, \mathrm{y}^{\prime}\right)$ be such that the area of $\Delta \mathrm{PAB}=5$...

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If the magnetic moment of a dioxygen species is 1.73 B.M, it may be

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Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom....

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A chemist has 4 samples of artificial sweetener A, B, C and D. To identify these samples, he performed certain...

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Two planets have masses M and 16M and their radii are a and 2a, respectively. The separation between the centres...

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The inverse function of $f(x)=\frac{8^{2 x}-8^{-2 x}}{8^{2 x}+8^{-2 x}}, x \in(-1,1)$, is $\_\_\_\_$ .

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The major product (Y) in the following reaction is

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A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the...

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Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity $\mathrm{K}_1, \mathrm{~K}_2$ and $\mathrm{K}_3$,...

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Identify (A) in the following reaction sequence.

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Let $A$ and $B$ be two independent events such that $P(A)=\frac{1}{3}$ and $P(B)=\frac{1}{6}$. Then, which of the following is TRUE...

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Four point masses, each of mass m , are fixed at the corners of a square of side $\ell$. The...

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The de Broglie wavelength of an electron in the $4^{\text {th }}$ Bohr orbit

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Assuming the nitrogen molecule is moving with r.m.s. velocity at 400 K , the de-Broglie wavelength of nitrogen molecule is...

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In the figure shown, the current in the 10 V battery is close to

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Two identical electric point dipoles have dipole moments $\overline{\mathrm{p}_1}=\mathrm{p} \hat{\mathrm{i}}$ and $\overline{\mathrm{p}_2}=\mathrm{p} \hat{\mathrm{i}}$ and are held on the $x$ axis...

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A particle of charge $q$ and mass $m$ is moving with a velocity $-v \hat{i}(v \neq 0)$ towards a large...

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The electronic configurations of bivalent europium and trivalent cerium are (atomic number : Xe = 54, Ce = 58, Eu...

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If the length of the chord of the circle, $x^2+y^2=r^2(r>0)$ along the line, $y-2 x=3$ is $r$, then $r^2$ is...

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An insect is at the bottom of a hemispherical ditch of radius 1 m . It crawls up the ditch...

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Complex $X$ of composition $\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_6 \mathrm{Cl}_n$ has a spin only magnetic moment of 3.83 BM . It reacts with...

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If $\alpha$ and $\beta$ are the roots of the equation, $7 x^2-3 x-2=0$, then the value of $\frac{\alpha}{1-\alpha^2}+\frac{\beta}{1-\beta^2}$ is equal...

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The major product Z obtained in the following reaction scheme is

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If $c$ is a point at which Rolle's theorem holds for the function, $f(x)=\log _e\left(\frac{x^2+\alpha}{7 x}\right)$ in interval $[3,4]$, where...

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A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch...

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A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the...

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If enthalpy of atomisation for $\mathrm{Br}_{2(I)}$ is $\times \mathrm{kJ} / \mathrm{mol}$ and bond enthalpy for $\mathrm{Br}_2$ is $...

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If for some $\alpha \in \mathrm{R}$, the lines $L_1: \frac{x+1}{2}=\frac{y-2}{-1}=\frac{z-1}{1}$ and $\mathrm{L}_2: \frac{\mathrm{x}+2}{\alpha}=\frac{\mathrm{y}+1}{5-\alpha}=\frac{\mathrm{z}+1}{1}$ are coplanar, then the line $L_2$ passes...

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Ferrous sulphate heptahydrate is used to fortify foods with iron. The amount (in grams) of the salt required to achieve...

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$[\mathrm{Pd}(\mathrm{F})(\mathrm{Cl})(\mathrm{Br})(\mathrm{I})]^{2-}$ has n number of geometrical isomers. Then, the spin-only magnetic moment and crystal field stabilisation energy [CFSE] of $...

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If $x=1$ is a critical point of the function $f(x)=\left(3 x^2+a x-2-a\right) e^x$, then :

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In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a molecule varies...

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What would be the electrode potential for the given half cell reaction at $\mathrm{pH}=5$ ? $\_\_\_\_$ . $...

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Shown in the figure is a hollow icecream cone (it open at the top). If its mass is M, radius...

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An object of mass m is suspended at the end of a massless wire of length L and area of...

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There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a...

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A body of mass $\mathrm{m}=10 \mathrm{~kg}$ is attached to one end of a wire of length 0.3 m . The...

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The number of chiral centres in penicillin is _____.

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If the mean and the standard deviation of the data 3, 5, 7, a, b are 5 and 2 respectively,...

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Both the diodes used in the circuit shown are assumed to be ideal and have negligible resistance when these are...

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A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite...

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The volume (in mL ) of $0.125 \mathrm{M} \mathrm{AgNO}_3$ required to quantitatively precipitate chloride ions in 0.3 g of $...

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One end of a straight uniform 1 m long bar is pivoted on horizontal table. It is released from rest...

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$\lim _{x \rightarrow 0} \frac{x\left(e^{\left(\sqrt{1+x^2+x^4}-1\right) / x}-1\right)}{\sqrt{1+x^2+x^4}-1}$

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If the potential energy between two molecules is given by $\mathrm{U}=\frac{\mathrm{A}}{\mathrm{r}^6}+\frac{\mathrm{B}}{\mathrm{r}^{12}}$, then at equilibrium, separation between molecules, and the potential...

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When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with...

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Let $y=y(x)$ be the solution of the differential equation $...

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In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes...

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The magnitude of work done by a gas that undergoes reversible expansion along the path ABC shown in the figure...

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The distance $x$ covered by a particle in one dimensional motion varies with time $t$ as $x^2=a t^2+$ 2bt +c...

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Which of the following points lies on the tangent to the curve $x^4 e^y+2 \sqrt{y+1}=3$ at the point (1, 0)?

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The number of bonds between sulphur and oxygen atoms in $\mathrm{S}_2 \mathrm{O}_8^{2-}$ and the number of bonds between sulphur and...

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Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure? where, $...

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Let $\{x\}$ and $[x]$ denote the fractional part of $x$ and the greatest integer $\leq x$ respectively of a real...

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Three harmonic waves having equal frequency $v$ and same intensity $\mathrm{I}_0$, have phase angles $0, \frac{\pi}{4}$ and $-\frac{\pi}{4}$ respectively. When...

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Given the masses of various atomic particles $\mathrm{m}_{\mathrm{p}}= 1.0072 \mathrm{u}, \mathrm{m}_{\mathrm{n}}=1.0087 \mathrm{u}, \mathrm{m}_{\mathrm{e}}=0.000548 \mathrm{u}$, $\mathrm{m}_{\mathrm{v}}^{-}=0, \quad \mathrm{~m}_{\mathrm{d}}=2.0141 \mathrm{u}$, where $...

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The major products A and B in the following reactions are

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The value of $\left(\frac{-1+i \sqrt{3}}{1-i}\right)^{30}$ is :

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A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The...

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A quantity $f$ is given by $f=\sqrt{\frac{h c^5}{G}}$ where $c$ is speed of light, $G$ universal gravitational constant and $h$...

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A flask contains a mixture of isohexane and 3-methylpentane. One of the liquids boils at 63°C while the other boils...

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If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum...

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An electric dipole of moment $\vec{p}-=(-\hat{i}-3 \hat{j}+2 \hat{k}) \times 10^{-29}$ C.m is at the origin $(0,0$, 0 ). The electric...

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If $\vec{a}=2 \hat{i}+\hat{j}+2 \hat{k}$, then the value of $|\hat{i} \times(\vec{a} \times \hat{i})|^2+|\hat{j} \times(\vec{a} \times \hat{j})|^2+|\hat{k} \times(\vec{a} \times \hat{k})|^2$ is equal...

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The major product of the following reaction is

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A square loop of side 2a and carrying current I is kept in xz plane with its centre at origin....

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Considering that $\Delta_0>\mathrm{P}$, the magnetic moment (in BM) of $\left[\mathrm{Ru}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$ would be $\_\_\_\_$ .

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A vessel of depth 2 h is half filled with a liquid of refractive index $2 \sqrt{2}$ and the upper...

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Let $P Q$ be a diameter of the circle $x^2+y^2=9$. If $\alpha$ and $\beta$ are the lengths of the perpendiculars...

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The number of chiral carbons present in sucrose is _____.

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Among the gases (a) - (e), the gases that cause greenhouse effect are

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A body $A$ of mass $m$ is moving in a circular orbit of radius $R$ about a planet. Another body...

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For a dimerization reaction $$ 2 \mathrm{~A}(\mathrm{~g}) \rightarrow \mathrm{A}_2(\mathrm{~g}) $$ at $298 \mathrm{~K}, \Delta \mathrm{U}^{\circ}=-20 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta \mathrm{~S}^{\circ}=-30$ $...

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The third ionization enthalphy is minimum for

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A long straight wire of radius a carries a current distributed uniformly over its crosssection. The ratio of the magnetic...

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The integral $$ \int_{\pi / 6}^{\pi / 3} \tan ^3 x \cdot \sin ^2 3 x\left(2 \sec ^2 x \cdot...

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The volume, in mL , of $0.02 \mathrm{M} \mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ solution required to react with 0.288 g of ferrous...

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Radiation, with wavelength 6561 Å falls on a metal surface to produce photoelectrons. The electrons are made to enter a...

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Which of the following statement is not true for glucose?

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Consider a sphere of radius $R$ which carries a uniform charge density $\rho$. If a sphere of radius $\frac{R}{2} \frac{R}{2}$...

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For a reaction $X+Y=2 Z, 1.0 \mathrm{~mol}$ of $X, 1.5 \mathrm{~mol}$ of $Y$ and 0.5 mol of $Z$ were taken...

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A circuit to verify Ohm’s law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In...

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The most suitable reagent for the given conversion is

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In a game two players A and B take turns in throwing a pair of fair dice starting with player...

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The one that is NOT suitable for the removal of permanent hardness of water is

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Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres...

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Lattice enthalpy and enthalpy of solution of NaCl are $788 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $4 \mathrm{~kJ} \mathrm{~mol}^{-1}$, respectively. The hydration enthalpy...

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The strength of an aqueous NaOH solution is most accurately determined by titrating

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The minimum value of $2^{\sin x}+2^{\cos x}$ is :

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The final major product of the following reaction is

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The aperture diameter of a telescope is 5 m . The separation between the moon and the earth is $...

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The rate of a certain biochemical reaction at physiological temperature (T) occurs 106 times faster with enzyme than without. The...

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If $\mathrm{C}_{\mathrm{r}} \equiv{ }^{25} \mathrm{C}_{\mathrm{r}}$ and $\mathrm{C}_0+5 . \mathrm{C}_1+9 . \mathrm{C}_2+\ldots . .+(101) . \mathrm{C}_{25}= 2^{25} \cdot \mathrm{k}$, then k...

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Boron and silicon of very high purity can be obtained through

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Arrange the following compounds in increasing order of C – OH bond length methanol, phenol, p-ethoxyphenol

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In the given circuit diagram, a wire is joining points B and D. The current in this wire is:

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The circle passing through the intersection of the circles, $x^2+y^2-6 x=0$ and $x^2+y^2-4 y=0$, having its centre on the line,...

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The major product formed in the following reaction is $\mathrm{CH}_3 \mathrm{CH}=\mathrm{CHCH}\left(\mathrm{CH}_3\right)_2 \xrightarrow{\mathrm{HBr}}$

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When gypsum is heated to 393 K, it forms

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If the curves, $x^2-6 x+y^2+8=0$ and $x^2-8 y+y^2+ 16-\mathrm{k}=0,(\mathrm{k}>0)$ touch each other at a point, then the largest value of...

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If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If...

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The rate constant (k) of a reaction is measured at different temperatures (T), and the data are plotted in the...

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Let $a_1, a_2, \ldots a_n$ be a given A.P. whose common difference is an integer and $S_n=a_1+a_2+\ldots+$ an. If $...

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A charged particle of mass ' $m$ ' and charge ' $q$ ' moving under the influence of uniform electric...

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The stoichiometry and solubility product of a salt with the solubility curve given below is, respectively

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Reaction of ammonia with excess Cl2 gives

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Consider two ideal diatomic gases A and B at some temperature $T$. Molecules of the gas $A$ are rigid, and...

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If the distance between the plane, $23 x-10 y-2 z+ 48=0$ and the plane containing the lines $$ \frac{x+1}{2}=\frac{y-3}{4}=\frac{z+1}{3} $$...

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If $a$ and $b$ are real numbers such that $(2+\alpha)^4=a+b \alpha$, where $\alpha=\frac{-1+i \sqrt{3}}{2}$, then $a+b$ is equal to

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Among the following compounds geometrical isomerism is exhibited by

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A graph of vapour pressure and temperature for three different liquids X, Y, and Z is shown below The following...

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Hydrogen peroxide, in the pure state, is

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The following molecule acts as an

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The predominant intermolecular forces present in ethyl acetate, a liquid, are

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The number of terms common to the two A.P.’s 3, 7, 11,.....,407 and 2, 9, 16,.....,709 is______.

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Let $x=4$ be a directrix to an ellipse whose centre is at the origin and its eccentricity is $\frac{1}{2}$. If...

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An element crystallises in a face-centred cubic (fcc) unit cell with cell edge a. The distance between the centres of...

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The first ionization energy (in kJ/mol) of Na, Mg, Al and Si respectively, are

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The increasing order of boiling points of the following compounds is

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For the Balmer series in the spectrum of H atom, $\bar{v}=\mathrm{R}_{\mathrm{H}}\left\{\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right\}$, the correct statements among (I) to (VI) are (I)...

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Let $\bigcup_{i=1}^{50} X_i=\bigcup_{i=1}^n Y_i=T$ where each $X_i$ contains 10 elements and each $Y_i$ contains 5 elements. If each element of...

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The variation of molar conductivity with concentration of an electrolyte (X) in aqueous solution is shown in the given figure....

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If $\int \frac{d \theta}{\cos ^2 \theta(\tan 2 \theta+\sec 2 \theta)}=\lambda \tan \theta+2 \log _e|f(\theta)|+C$ where C is a constant of...

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Contrapositive of the statement : ‘If a function f is differentiable at a, then it is also continuous at a’,...

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The decreasing order of reactivity towards dehydrohalogenation $\left(\mathrm{E}_1\right)$ reaction of the following compounds is

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Consider the complex ions, trans- $\left[\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2\right]_{\sim}^{+}(\mathrm{A})$ and cis- $\left[\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2\right]_{\sim}^{+}(\mathrm{B})$. The correct statement regarding them is

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The correct statement about probability density (except at infinite distance from nucleus) is

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As per Hardy-Schulze formulation, the flocculation values of the following for ferric hydroxide sol are in the order

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Adsorption of a gas follows Freundlich adsorption isotherm. If x is the mass of the gas adsorbed on mass m...

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If $A=\{x \in R:|x|

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The angle of elevation of a cloud $C$ from a point $P, 200 \mathrm{~m}$ above a still lake is $30^{\circ}$....

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The complex that can show fac-and mer-isomers is

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Assume that the displacement (s) of air is proportional to the pressure difference $(\Delta \mathrm{p})$ created by a sound wave....

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The compound that has the largest H – M – H bond angle (M = N, O, S, C) is

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A hollow spherical shell at outer radius $R$ floats just submerged under the water surface. The inner radius of the...

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A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature...

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Let $\lambda \neq 0$ be in R . If $\alpha$ and $\beta$ are the roots of the equation, $\mathrm{x}^2-\mathrm{x}+2 \lambda=0$...

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Let $[t]$ denote the greatest integer $\leq t$ and $\lim _{x \rightarrow 0} x\left[\frac{4}{x}\right]=A$. Then the function, $...

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A particle is moving along the $x$-axis with its coordinate with time ' $t$ ' given by $x(t)=10+8 t-3 t^2$....

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Which one of the following polymers is not obtained by condensation polymerisation?

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The major product of the following reaction is

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A body $A$, of mass $m=0.1 \mathrm{~kg}$ has an initial velocity of $3 \hat{i} \mathrm{~ms}^{-1}$. It collides elastically with another...

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Suppose the vectors $x_1, x_2$ and $x_3$ are the solutions of the system of linear equations, $A x=b$ when the...

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Let a function $f:[0,5] \rightarrow R$ be continuous, $f(1)=3$ and $F$ be defined as : $$ F(x)=\int_1^x t^2 g(t) d...

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A body of mass 2 kg is driven by an engine delivering a constant power of 1 J/s. The body...

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A one metre long (both ends open) organ pipe is kept in a gas that has double the density of...

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The surface of a metal is illuminated alternately with photons of energies $E_1=4 \mathrm{eV}$ and $E_2=2.5 \mathrm{eV}$ respectively. The ratio...

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Four resistances of $15 \Omega, 12 \Omega, 4 \Omega$ and $10 \Omega$ respectively in cyclic order to form Wheatstone's network....

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A prism of angle $\mathrm{A}=1^{\circ}$ has a refractive index $\mu=1.5$. A good estimate for the minimum angle of deviation (in...

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A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that...

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A leak proof cylinder of length 1 m, made of a metal which has very low coefficient of expansion is...

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A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped...

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Nitrogen gas is at $300^{\circ} \mathrm{C}$ temperature. The temperature (in K ) at which the rms speed of a $\mathrm{H}_2$...

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Consider a uniform rod of mass $M=4 m$ and length I pivoted about its centre. A mass $m$ moving with...

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In the circuit shown, charge on the 5 $\mu$F capacitor is

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The magnifying power of a telescope with tube length 60 cm is 5. What is the focal length of its...

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An infinitely long, straight wire carrying current I, one side opened rectangular loop and a conductor C with a sliding...

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In an experiment to verify Stokes law, a small spherical ball of radius $r$ and density $\rho$ falls under gravity...

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The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure....

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Activities of three radioactive substances $\mathrm{A}, \mathrm{B}$ and C are represented by the curves $\mathrm{A}, \mathrm{B}$ and C , in...

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Two coherent sources of sound, $S_1$ and $S_2$, produce sound waves of the same wavelength, $\lambda=1 \mathrm{~m}$, in phase. $S_1$...

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A wheel is rotating freely with an angular speed  on a shaft. The moment of inertia of the wheel...

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A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of...

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An electron is constrained to move along the $y$-axis with a speed of 0.1 c ( c is the speed...

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A bullet of mass 5 g , travelling with a speed of 210 $\mathrm{m} / \mathrm{s}$, strikes a fixed wooden...

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An electrical power line, having a total resistance of $2 \Omega$, delivers 1 kW at 220 V . The efficiency...

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If the equation of a plane P , passing through the intersection of the planes $x+4 y-z+7=0$ and $...

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$\left(2 x^2+3 x+4\right)^{10}=\sum_{r=10}^{20} a_r x^r$. Then $\frac{a_7}{a_{13}}$ is equal to $\_\_\_\_$ .

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Suppose a differentiable function $f(x)$ satisfies the identity $f(x+y)=f(x)+f(y)+x y^2+x^2 y$, for all real $x$ and $...

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If the system of equations $$ \begin{aligned} & x-2 y+3 z=9 \\ & 2 x+y+z=b \end{aligned} $$ $x-7 y+a z=24$,...

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The probability of a man hitting a target is $\frac{1}{10}$. The least number of shots required, so that the probability...

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Let $[\mathrm{t}]$ denote the greatest integer $\leq \mathrm{t}$. Then the equation in $x,[x]^2+2[x+2]-7=0$ has :

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If $(a+\sqrt{2} b \cos x)(a-\sqrt{2 b} \cos y)=a^2-b^2$, where $a >\mathrm{b}>0$, then $\frac{\mathrm{dx}}{\mathrm{dy}} \mathrm{at}\left(\frac{\pi}{4}, \frac{\pi}{4}\right)$ is :

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Let $u=\frac{2 z+i}{z-k i}, z=x+i y$ and $k>0$. If the curve represented by $\operatorname{Re}(\mathrm{u})+\operatorname{Im}(\mathrm{u})=1$ intersects the y axis at the...

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Let $f$ be a twice differentiable function on $(1,6)$. If $f(2)=8, f^{\prime}(2)=5, f^{\prime}(x) \geq 1$ and $f^{\prime \prime}(x) \geq 4$,...

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Let $a-2 b+c=1$. $f(x)=\left|\begin{array}{lll}x+a & x+2 & x+1 \\ x+b & x+3 & x+2\end{array}\right|$, then

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Let $y=y(x)$ be the solution of the differential equation, $x y^{\prime}-y=x^2(x \cos x+\sin x), x>0$. If $y(\pi)=\pi$, then $y^{\prime \prime}\left(\frac{\pi}{2}\right)+y\left(\frac{\pi}{2}\right)$...

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If one end of a focal chord AB of the parabola $\mathrm{y}^2= 8 x$ is at $A\left(\frac{1}{2},-2\right)$, then the equation...

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Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$ be a given ellipse, length of whose latus rectum is 10 . If its eccentricity is the maximum...

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Let $f(x)=\int \frac{\sqrt{x}}{(1+x)^2} d x(x \geq 0)$. Then $f(3)-f(1)$ is equal to:

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The length of the minor axis (along $y$-axis) of an ellipse in the standard form is $\frac{4}{\sqrt{3}}$. If this ellipse...

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If $1+\left(1-2^2 \cdot 1\right)+\left(1-4^2 \cdot 3\right)+\left(1-6^2 \cdot 5\right)+\ldots \ldots+ \left(1-20^2 \cdot 19\right)=\alpha-220 \beta$, then an ordered pair $(\alpha, \beta)$ is...

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Let $x_0$ be the point of local maxima of $f(x)=\vec{a} \cdot(\vec{b} \times \vec{c})$, where $...

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If z be a complex number satisfying |Re(z)| + |km(z)| = 4, then |z| cannot be

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The value of $\sum_{\mathrm{r}=0}^{20}{ }^{50-\mathrm{r}} \mathrm{C}_6$ is equal to:

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The function $f(x)=\left\{\begin{array}{l}\frac{\pi}{4}+\tan ^{-1} x,|x| \leq 1 \\ \frac{1}{2}(|x|-1),|x|>1\end{array}\right.$ is :

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Let $\mathrm{P}(3,3)$ be a point on the hyperbola, $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If the normal to it at P intersects the x axis...

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A random variable X has the following probability distribution X : 1 2 3 4 5 $...

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A triangle $A B C$ lying in the first quadrant has two vertices as $\mathrm{A}(1,2)$ and $\mathrm{B}(3,1)$. If $\angle \mathrm{BAC}=90^{\circ}$,...

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The area (in sq. units) of the largest rectangle $A B C D$ whose vertices $A$ and $B$ lie on...

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The critical angle of medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability $\frac{4}{3}$...

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Given the following two statements: $\left(\mathrm{S}_1\right):(\mathrm{q} \vee \mathrm{p}) \rightarrow(\mathrm{p} \leftrightarrow \sim \mathrm{q})$ is a tautology: $...

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The following system of linear equations 7x + 6y – 2z = 0 3x + 4y + 2z = 0...

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The distance of the point $(1,-2,3)$ from the plane $x-y+z=5$ measured parallel to the line $\frac{x}{2}=\frac{y}{3}=\frac{z}{-6}$ is :

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The acceleration due to gravity on the earth’s surface at the poles is g and angular velocity of the earth...

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At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed...

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$$ \text { If } A=\left[\begin{array}{cc} \cos \theta & i \sin \theta \\ i \sin \theta & \cos \theta \end{array}\right],\left(\theta=\frac{\pi}{24}\right)...

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A parallel plate capacitor has plate of length ‘$\ell$’, width ‘w’ and separation of plates is ‘d’. It is connected...

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Let $f:(0, \infty) \rightarrow(0, \infty)$ be a dif ferentiable function such that $f(1)=e$ and $...

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The integral $\int\left(\frac{x}{x \sin x+\cos x}\right)^2 d x$ is equal to (where C is a constant of integration):

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The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4 kg. (The...

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In an adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of...

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Let $f(\mathrm{x})=|\mathrm{x}-2|$ and $\mathrm{g}(\mathrm{x})=f(f(\mathrm{x})), \mathrm{x} \in[0,4]$. Then $\int^3(g(x)-f(x)) d x$ is equal to:

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In finding the electric field using Gauss law the formula $|\vec{E}|=\frac{q_{\text {enc }}}{\varepsilon_0|A|}$ is applicable. In the formula $\varepsilon_0$ is...

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The solution of the dif ferential equation $\frac{d y}{d x}-\frac{y+3 x}{\log _e(y+3 x)}+3=0$ is (where C is a constant of...

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SOLVE this

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Two vertical poles AB = 15 m and CD = 10 m are standing apart on a horizontal ground with...

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Three charged particles A, B and C with charges –4q, 2q and –2q are present on the circumference of a...

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$...

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The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7,...

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A radioactive nucleus decays by two different processes. The half life for the first process is 10 s and that...

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If for some positive integer $n$, the coefficients of three consecutive terms in the binomial expansion of $(1+x)^{n+5}$ are in...

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The graph which depicts the results of Rutherford gold foil experiment with $\alpha$-particle is $\theta$ : Scattering angle Y: Number...

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A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from...

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Let $\alpha$ and $\beta$ be the roots of $x^2-3 x+p=0$ and $\gamma$ and $\delta$ be the roots of $x^2-6 x+q=0$....

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The plot that depicts the behavior of the mean free time $\tau$ (time between two successive collisions) for the molecules...

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If the perpendicular bisector of the line segment joining the points P(1, 4) and Q(k, 3) has y-intercept equal to...

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Let $f$ and $g$ be differentiabel functions on $R$ such that fog is the identity function. If for some $...

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Two different wires having lengths $L_1$ and $L_2$, and respective temperature coefficient of linear expansion $\alpha_1$ and $\alpha_2$, are joined...

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Consider two solid spheres of radii $R_1=1 m, R_2=2 m$ and masses $M_1$ and $M_2$, respectively. The gravitational field due...

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Two Zener diodes (A and B) having breakdown voltages of 6 V and 4 V respectively, are connected as shown...

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A 20.0 mL solution containing 0.2 g impure $\mathrm{H}_2 \mathrm{O}_2$ reacts completely with 0.316 g of $\mathrm{KMnO}_4$ in acid solution....

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A thermodynamic cycle xyzx is shown on a V-T diagram The P-V diagram that best describes this cycle is :...

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The correct match between the entries in column I and column II are

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The mass of ammonia in grams produced when 2.8 kg of dinitrogen quantitatively reacts with 1 kg of dihydrogen is

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The dimension of stopping potential $V_0$ in photoelectric effect in units of Planck's constant ' $h$ ', speed of light...

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If $p \rightarrow(p \wedge \sim q)$ is false, then the truth values of $p$ and $q$ are respectively :

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Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges....

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The quantities $x=\frac{1}{\sqrt{\mu_0 \varepsilon_0}}, y=\frac{E}{B}$ and $z=\frac{I}{C R}$ are defined where $C$-capacitance, R-Resistance, I-length, E-Electric field, B-magnetic field and $...

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Proton with kinetic energy of 1 MeV moves from south to north. It gets an acceleration of $...

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The number of molecules with energy greater than the threshold energy for a reaction increases five fold by a rise...

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If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of...

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Consider a solid sphere of radius $R$ and mass density $\rho(r)=\rho_0\left(1-\frac{r^2}{R^2}\right), 0

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A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a...

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A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate $...

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Boolean relation at the output stage-Y for the following circuit is :

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If $\frac{d y}{d x}=\frac{x y}{x^2+y^2} ; y(1)=1 ; \quad$ then a value of $x$ satisfying $y(x)=e$ is :

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A particle of mass m is fixed to one end of a light spring having force constant k and unstretched...

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If the tangent to the curve, $y=e^x$ at a point $\left(c, e^c\right)$ and the normal to the parabola, $y^2=4 x$...

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Let $a, b \in R, a \neq 0$ be such that the equation, $a x^2- 2 \mathrm{bx}+5=0$ has a repeated...

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Effective capacitance of parallel combination of two capacitors $C_1$ and $C_2$ is $10 \mu F$. When these capacitors are individually...

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https://competishun.com/let-s-be-the-set-of-all-integer-solutions-x-y-z-of-the-system-of-equationsbr-beginaligned-x-2-y5-z0-2-x4-yz0-7-x14-y9-z0-endaligned-such-that-15-leq-x2y2z2-leq-150-then-the-number-of-elements-in-the-s/

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Let S be the set of all integer solutions, (x, y, z), of the system of equations $$ \begin{aligned} &...

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The length of a potentiometer wire is 1200 cm and it carries a current of 60 mA . For a...

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The total number of 3-digit numbers, whose sum of digits is 10, is ______.

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Let a plane P contain two lines $$ \overrightarrow{\mathrm{r}}=\hat{\mathrm{i}}+\lambda(\hat{\mathrm{i}}+\hat{\mathrm{j}}), \lambda \in \mathrm{R} \text { and } \overrightarrow{\mathrm{r}}=-\hat{\mathrm{i}}+\mu(\hat{\mathrm{j}}-\hat{\mathrm{k}}), \mu \in \mathrm{R}...

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When photon of energy 4.0 eV strikes the surface of a metal A , the ejected photoelectrons have maximum kinetic...

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The probability that a randomly chosen 5-digit number is made from exactly two digits is :

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If $x^3 d y+x y d x=x^2 d y+2 y d x ; x(2)=e$ and $x>1$, then $x(4)$ is equal...

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The sum, $\sum_{n=1}^7 \frac{n(n+1)(2 n+1)}{4}$ is equal toThe sum, $\sum_{n=1}^7 \frac{n(n+1)(2 n+1)}{4}$ is equal to

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$\lim _{x \rightarrow a} \frac{(a+2 x)^{\frac{1}{3}}-(3 x)^{\frac{1}{3}}}{(3 a+x)^{\frac{1}{3}}-(4 x)^{\frac{1}{3}}}(a \neq 0)$ is equal to : $(3 a+x)^{\frac{1}{3}}-(4 x)^{\frac{1}{3}}$

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Let a line y=m x(m>0) intersect the parabola, $y^2=x$ at a point $P$, other than the origin. Let the tangent...

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In the expansion of $\left(\frac{x}{\cos \theta}+\frac{1}{x \sin \theta}\right)^{16}$, if $l_1$ is the least value of the term independent of x...

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Let f(x) be a polynomial of degree 3 such that f(–1) = 10, f(1) = –6, f(x) has a critical...

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If the surface area of a cube is increasing at a rate of $3.6 \mathrm{~cm}^2 / \mathrm{sec}$, retaining its shape;...

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The plane which bisects the line joining, the points (4, –2, 3) and (2, 4, –1) at right angles also...

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The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the...

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If a $\Delta$ABC has vertices A(–1, 7), B(–7, 1) and C(5, –5), then its orthocentre has coordinates

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If $\frac{\sqrt{2} \sin \alpha}{\sqrt{1+\cos 2 \alpha}}=\frac{1}{7}$ and $\sqrt{\frac{1-\cos 2 \beta}{2}}=\frac{1}{\sqrt{10}}, \alpha, \beta, \in\left(0, \frac{\pi}{2}\right)$, then $\tan (\alpha+2 \beta)$ is equal...

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Let $f:(1,3) \rightarrow R$ be a function defined by $f(x)=\frac{x[x]}{1+x^2}$, where $[x]$ denotes the greatest integer $\leq x$. Then the...

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Let $x i(1 \leq i \leq 10)$ be ten observations of a random variable $X$. If $\sum_{i=1}^{10}\left(x_i-p\right)=3$ and $\sum_{i=1}^{10}\left(x_i-p\right)^2=9$ where...

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Let $\mathrm{a}_{\mathrm{n}}$ be the $\mathrm{n}^{\text {th }}$ term of a G.P. of positive terms. If $\sum_{n=1}^{100} a_{2 n+1}=200$ and $...

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Let A and B be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and...

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Let $\alpha=\frac{-1+\mathrm{i} \sqrt{3}}{2}$. If $\mathrm{a}=(1+\alpha) \sum_{\mathrm{k}=0}^{100} \alpha^{2 \mathrm{k}}$ and $\mathrm{b}=\sum_{\mathrm{k}=0}^{100} \alpha^{3 \mathrm{k}}$, then a and b are the roots of...

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If a line, y=m x+c is a tangent to the circle $\ldots(x-3)^2+y^2=1$ and it is perpendicular to a line $L_1$,...

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If $\alpha$ and $\beta$ be the coefficients of $x^4$ and $x^2$ respectively in the expansion of $\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6$, then

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The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found...

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Let S be the set of all real roots of the equation, $3^x\left(3^x-1\right)+2=\left|3^x-1\right|+\left|3^x-2\right|$. Then $S$

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If the $10^{\text {th }}$ term of an A.P. is $\frac{1}{20}$ and its $20^{\text {th }}$ term is $\frac{1}{10}$, then...

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$\lim _{x \rightarrow 0} \frac{\int_0^x t \sin (10 t) d t}{x}$ is equal to

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At 300 K, the vapour pressure of a solution containing 1 mole of n-hexane and 3 moles of n-heptane is...

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If 75% of a first order reaction was completed in 90 minutes, 60% of the same reaction would be completed...

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The number of chiral centres present in [B] is

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On heating, lead (II) nitrate gives a brown gas (A). The gas (A) on cooling changes to a colourless solid/liquid...

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Identify the incorrect statement from the option below for the above cell:

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The intermolecular potential energy for the molecules A, B, C and D given below suggests that :

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The pair in which both the species have the same magnetic moment (spin only) is

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$[\mathrm{P}]$ on treatment with $\mathrm{Br}_2 / \mathrm{FeBr}_3$ in $\mathrm{CCl}_4$ produced a single isomer $\mathrm{C}_8 \mathrm{H}_7 \mathrm{O}_2 \mathrm{Br}$ while heating $[\mathrm{P}]$...

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The number of isomers possible for $\left[\mathrm{Pt}(\mathrm{en})\left(\mathrm{NO}_2\right)_2\right]$ is

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When neopentyl alcohol is heated with an acid, it slowly converted into an 85 : 15 mixture of alkenes A...

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The ionic radii of $\mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{Na}^{+}$and $\mathrm{Mg}^{2+}$ are in the order

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The region in the electromagnetic spectrum where the Balmar series lines appear is

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On combustion of Li, Na and K in excess of air, the major oxides formed, respectively, are

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For the equilibrium $\mathrm{A} \rightleftharpoons \mathrm{B}$, the variation of the rate of the forward (a) and reverse (b) reaction with...

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The osmotic pressure of a solution of NaCl is 0.10 atm and that of a glucose solution is 0.20 atm...

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Consider the following equations : $$ 2 \mathrm{Fe}^{2+}+\mathrm{H}_2 \mathrm{O}_2 \rightarrow x A+y B $$ (in basic medium) $$ 2 \mathrm{MnO}_4^{-}+6...

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The number of chiral centres present in threonine is ________.

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The mechanism of action of “Terfenadine” (Seldane) is :

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Match the following

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If a hyperbola passes through the point $\mathrm{P}(10,16)$ and it has vertices at $( \pm 6,0)$, then the equation of...

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Which of the following compounds will form the precipitate with aq. $\mathrm{AgNO}_3$ solution most readily?

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If $z_1, z_2$ are complex numbers such that $\operatorname{Re}\left(z_1\right)=\left|z_1-1\right|, \operatorname{Re}\left(z_2\right)=\left|z_2-1\right|$, and $\arg \left(z_1-z_2\right)=\frac{\pi}{6}$, then $\operatorname{Im}\left(z_1+z_2\right)$ is equal to

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Among statements (a) - (d), the correct ones are (a) Lime stone is decomposed to CaO during the extraction of...

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A sample of red ink (a colloidal suspension) is prepared by mixing eosin dye, egg white, HCHO and water. The...

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If the sum of the series $20+19 \frac{3}{5}+19 \frac{1}{5}+18 \frac{4}{5}+\ldots .$. upto $n$th term is 488 and the $n$th term...

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A sample of milk splits after 60 min. at 300 K and after 40 min. at 400 K when the...

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The length of the perpendicular from the origin, on the normal to the curve, $x^2+2 x y-3 y^2=0$ at the...

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Two particles of equal mass $m$ have respective initial velocities $u \hat{i}$ and $u\left(\frac{\hat{i}+\hat{j}}{2}\right)$. They collide completely inelastically. The energy...

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The set of all real values of $\lambda$ for which the quadratic equations, $\left(\lambda^2+1\right) x^2-4 \lambda x+2=0$ always have exactly...

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The molecule in which hybrid MOs involve only one d-orbital of the central atom is

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Water flows in a horizontal tube (see figure). The pressure of water changes by $700 \mathrm{Nm}^{-2}$ between A and $B$...

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The system of linear equations $...

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If the term independent of $x$ in the expansion of $\left(\frac{3}{2} x^2-\frac{1}{3 x}\right)^9$ is $k$, then $18 k$ is equal...

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The sum of the total number of bonds between chromium and oxygen atoms in chromate and dichromate ions is ____________...

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The IUPAC name of the following compound is

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Let $e_1$ and $e_2$ be the eccentricities of the ellipse, $\frac{x^2}{25}+\frac{y^2}{b^2}=1(b

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The major product [C] of the following reaction sequence will be

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Which of the following statements is a tautology?

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The decreasing order of reactivity of the following organic molecules towards $\mathrm{AgNO}_3$ solution is

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10.30 mg of $\mathrm{O}_2$ is dissolved into a litre of sea water of density $1.03 \mathrm{~g} / \mathrm{mL}$. The concentration...

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The mirror image of the point $(1,2,3)$ in a plane is $\left(-\frac{7}{3},-\frac{4}{3},-\frac{1}{3}\right)$. Which of the following points lies on this...

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Suppose $f(x)$ is a polynomial of degree four, having critical points at $-1,0,1$. If $T=\{x \in R \mid f(x)=f(0)\}$, then...

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250 mL of a waste solution obtained from the workshop of a goldsmith contains $0.1 \mathrm{M} \mathrm{AgNO}_3$ and 0.1 M...

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The elements with atomic numbers 101 and 104 belong to, respectively,

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Consider the following reactions

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An organic compound (A) (molecular formula $\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_2$ ) was hydrolysed with dil. $\mathrm{H}_2 \mathrm{SO}_4$ to give a carboxylic...

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Five moles of an ideal gas at 1 bar and 298 K is expanded into vacuum to double the volume....

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For one mole of an ideal gas, which of these statements must be true? (a) U and H each depends...

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A cylinder containing an ideal gas $(0.1 \mathrm{~mol}$ of 1.0 $\mathrm{dm}^3$ ) is in thermal equilibrium with a large volume...

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What are the functional groups present in the structure of maltose?

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The shortest wavelength of H atom in the Lyman series is $\lambda_1$. The longest wavelength in the Balmar series of...

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Which of the following will react with $\mathrm{CHCl}_3+$ alc. KOH ?

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Among the statements (a)-(d), the correct ones are (a) Lithium has the highest hydration enthalpy among the alkali metals. (b)...

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The isomer(s) of $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right]$ that has/have a $\mathrm{Cl}-\mathrm{Co}-\mathrm{Cl}$ angle of $90^{\circ}$, is/are

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An alkaline earth metal ‘M’ readily forms water soluble sulphate and water insoluble hydroxide. Its oxide MO is very stable...

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The electric fields of two plane electromagnetic plane waves in vacuum are given by $...

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A, B and C are three biomolecules. The results of the tests performed on them are given below

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Consider a force $\vec{F}=-x \hat{i}+y \hat{j}$. The work done by this force in moving a particle from point $\mathrm{A}(1,0)$ to...

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The reaction in which the hybridisation of the underlined atom is affected is

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A particle moving with kinetic energy E has de Broglie wavelength $\lambda$. If energy $\Delta \mathrm{E}$ is added to its...

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The first and second ionisation enthalpies of a metal are 496 and $4560 \mathrm{~kJ} \mathrm{~mol}^{-1}$, respectively. How many moles of...

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If the equilibrium constant for $\mathrm{A} \rightleftharpoons \mathrm{B}+\mathrm{Cis}_{\mathrm{eq}}^{(1)}$ and that of $\mathrm{B}+\mathrm{C} \rightleftharpoons \mathrm{P}$ is $\mathrm{K}_{\mathrm{eq}}^{(2)}$, the equilibrium constant for...

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Which of the following reactions will not produce a racemic product?

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In the following reaction sequence, [C] is

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Let $S$ be the set of points where the function, $f(x)=|2-|x-3| \|, x \in R$, is not differentiable. Then $...

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The correct order of the spin-only magnetic moments of the following complexes is : (I) $\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Br}_2$ (II) $\mathrm{Na}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]$...

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In the line spectra of hydrogen atom, difference between the largest and the shortest wavelengths of the Lyman series is...

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If the sum of the coefficients of all even powers of x in the product $\left(1+x+x^2+\ldots \ldots+x^{2 n}\right)\left(1-x+x^2-x^3+\ldots .+x^{2 n}\right)$...

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The Crystal Field Stabilization Energy $(\mathrm{CFSE})$ of $\left[\mathrm{CoF}_3\left(\mathrm{H}_2 \mathrm{O}\right)_3\right]\left(\Delta_0

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If the variance of the first n natural numbers is 10 and the variance of the first m even natural...

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A circular disc of mass $M$ and radius $R$ is rotating about its axis with angular speed $\omega_1$. If another...

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A closed vessel contains 0.1 mole of a monatomic ideal gas at 200 K. If 0.05 mole of the same...

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The one that can exhibit highest paramagnetic behaviour among the following is gly = glycinato; bpy = 2, 2'-bipyridine

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In the figure shown below reactant A (represented by square) is in equilibrium with product B (represented by circle). The...

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$\lim _{x \rightarrow 2} \frac{3^x+3^{3-x}-12}{3^{-x / 2}-3^{1-x}}$ is equal to $\_\_\_\_$ .

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ABC is a plane lamina of the shape of an equilateral triangle. $\mathrm{D}, \mathrm{E}$ are mid points of $\mathrm{AB}, \mathrm{AC}$...

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Let $\mathrm{A}(1,0), \mathrm{B}(6,2)$ and $\mathrm{C}\left(\frac{3}{2}, 6\right)$ be the vertices of a triangle $A B C$. If $P$ is a point...

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If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then...

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Biochemical Oxygen Demand (BOD) is the amount of oxygen required (in ppm)

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The process that is NOT endothermic in nature is

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In a compound microscope, the magnified virtual image is formed at a distance of 25 cm from the eye-piece. The...

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Given figure shows few data points in a photo electric effect experiment for a certain metal. The minimum energy for...

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The decreasing order of basicity of the following amines is

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The incorrect statement(s) among (a) - (c) is (are) (a) W(VI) is more stable than Cr(VI). (b) In the presence...

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If $y(\alpha)=\sqrt{2\left(\frac{\tan \alpha+\cot \alpha}{1+\tan ^2 \alpha}\right)+\frac{1}{\sin ^2 \alpha}}, \alpha \in\left(\frac{3 \pi}{4}, \pi\right)$ then $\frac{\mathrm{dy}}{\mathrm{d} \alpha}$ at $\alpha=\frac{5 \pi}{6}$ is

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A air bubble of radius 1 cm in water has an upward acceleration $9.8 \mathrm{~cm} \mathrm{~s}^{-2}$. The density of water...

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Take the breakdown voltage of the zener diode used in the given circuit as 6 V. For the input voltage...

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The true statement amongst the following is

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Let the function, $\mathrm{f}:[-7,0] \rightarrow \mathrm{R}$ be continuous on $[- 7,0]$ and differentiable on $(-7,0)$. If $f(-7)=-3$ and $...

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A battery of 3.0 V is connected to a resistor dissipating 0.5 W of power. If the terminal voltage of...

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The processes of calcination and roasting in metallurgical industries, respectively, can Iead to

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A small bar magnet placed with its axis at 30° with an external field of 0.06 T experiences a torque...

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Particle $A$ of mass $m_A=\frac{m}{2}$ moving along the $x-$ axis with velocity $\mathrm{v}_0$ collides elastically with another particle $B$ at...

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5 g of zinc is treated separately with an excess of (a) Dilute hydrochloric acid and (b) Aqueous sodium hydroxide....

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Match the $\mathrm{C}_{\mathrm{p}} / \mathrm{C}_{\mathrm{v}}$ ratio for ideal gases with different type of molecules

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On the x -axis and at a distance x from the origin, the gravitational field due to a mass distribution...

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The solubility product of $\mathrm{Cr}(\mathrm{OH})_3$ at 298 K is $6.0 \times 10^{-31}$. The concentration of hydroxide ions in a saturated...

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Let S be the set of all functions f : [0, 1]  R, which are continuous on [0, 1]...

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Which of the following has the shortest C – Cl bond?

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Let $\vec{a}=\hat{i}-2 \hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$ be two vectors. If $\vec{c}$ is a vector such that $\vec{b} \times \vec{c}=\vec{b} \times \vec{a}$...

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The reaction of $\mathrm{H}_3 \mathrm{~N}_3 \mathrm{~B}_3 \mathrm{Cl}_3$ (A) with $\mathrm{LiBH}_4$ in tetrahydrofuran gives inorganic benzene (B). Further, the reaction of...

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Amongst the following, the form of water with the lowest ionic conductance at 298 K is

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The area (in sq. units) of the region $\left\{(x, y) \in \mathbb{R}^2: x^2 \leq y \leq 3-2 x\right\}$, is

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Let $a, b c \in R$ be such that $a^2+b^2+c^2=1$. If $a \cos \theta=b \cos \left(\theta+\frac{2 \pi}{3}\right)=c \cos \left(\theta+\frac{4 \pi}{3}\right)$,...

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The differential equation of the family of curves, $x^2=4 b(y+b), b \in R$, is

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Let the latus ractum of the parabola $y^2=4 x$ be the common chord to the circles $C_1$ and $C_2$ each...

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Let $p, q, r$ be three statements such that the truth value of $(p \wedge q) \rightarrow(\sim q \vee r)$...

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If $\mathrm{A}=\left(\begin{array}{ll}2 & 2 \\ 9 & 4\end{array}\right)$ and $\mathrm{I}=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$, then $10 \mathrm{~A}^{-1}$ is...

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Which polymer has ‘chiral’ monomer(s)?

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Let $R_1$ and $R_2$ be two relation defined as follows : $\mathrm{R}_1=\left\{(\mathrm{a}, \mathrm{b}) \in \mathrm{R}^2: \mathrm{a}^2+\mathrm{b}^2 \in \mathrm{Q}\right\}$ and $...

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Complexes (ML5) of metals Ni and Fe have ideal square pyramidal and trigonal bipyramidal geometries, respectively. The sum of the...

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The change in the magnitude of the volume of an ideal gas when a small additional pressure $\Delta \mathrm{P}$ is...

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Choose the correct option relating wavelengths of different parts of electromagnetic wave spectrum

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In the following sequence of reactions the maximum number of atoms present in molecule ‘C’ in one plane is __________....

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If the value of the integral $\int_0^{1 / 2} \frac{x^2}{\left(1-x^2\right)^{3 / 2}} d x$ is $\frac{k}{6}$, then $k$ is equal...

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A two point charges $4 q$ and $-q$ are fixed on the xaxis at $x=-\frac{d}{2}$ and $x=\frac{d}{2}$, respectively. If a...

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$\mathrm{NaClO}_3$ is used, even in spacecrafts, to produce $\mathrm{O}_2$. The daily consumption of pure $\mathrm{O}_2$ by a person is 492...

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In the following reaction A is

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Four resistances $40 \Omega, 60 \Omega, 90 \Omega$ and $110 \Omega$ make the arms of a quadrilateral ABCD. Across AC...

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Starting from the origin at time $t=0$, with initial velocity $5 \hat{j} \mathrm{~ms}^{-1}$, a particle moves in the $x-y$ plane...

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If $250 \mathrm{~cm}^3$ of an aqueous solution containing 0.73 g of a protein A is isotonic with one litre of...

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For an electrochemical cell, $\mathrm{Sn}(\mathrm{s})\left|\mathrm{Sn}^{2+}(\mathrm{aq}, 1 \mathrm{M}) \| \mathrm{Pb}^{2+}(\mathrm{aq}, 1 \mathrm{M})\right| \mathrm{Pb}(\mathrm{s})$ the ratio $\frac{\left[\mathrm{Sn}^{2+}\right]}{\left[\mathrm{Pb}^{2+}\right]}$ when this cell attains equilibrium...

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The volume (in mL) of 0.1 N NaOH required to neutralise 10 mL of 0.1 N phosphinic acid is ____.

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A small bar magnet is moved through a coil at constant speed from one end to the other. Which of...

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At constant volume, 4 mol of an ideal gas when heated from 300 K to 500 K changes its internal...

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An acidic solution of dichromate is electrolyzed for 8 minutes using 2 A current. As per the following equation $...

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An unsaturated hydrocarbon $X$ absorbs two hydrogen molecules on catalytic hydrogenation, and also gives following reaction $...

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A beam of plane polarised light of large crosssectional area and uniform intensity of 3.3 $\mathrm{Wm}^{-2}$ falls normally on a...

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$6.023 \times 10^{22}$ molecules are present in 10 g of a substance ' x '. The molarity of a solution...

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Dimensional formula for thermal conductivity is (here K deontes the temperature)

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The distance between an object and a screen is 100 cm . A lens can produce real image of the...

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For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m, while the...

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Among (a) - (d), the complexes that can display geometrical isomerism are (a) $\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_3 \mathrm{Cl}\right]^{+}$ (b) $\left[\mathrm{Pt}\left(\mathrm{NH}_3\right) \mathrm{Cl}_5\right]^{-}$ (c) $...

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The number of $\mathrm{sp}^2$ hybrid orbitals in a molecule of benzene is

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Complex A has a composition of $\mathrm{H}_{12} \mathrm{O}_6 \mathrm{Cl}_3 \mathrm{Cr}$. If the complex on treatment with conc. $\mathrm{H}_2 \mathrm{SO}_4$ loses...

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The speed versus time graph for a particle is shown in the figure. The distance travelled (in m ) by...

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Consider the following reaction : The product ‘P’ gives positive ceric ammonium nitrate test. This is because of the presence...

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Kjeldahl’s method cannot be used to estimate nitrogen for which of the following compounds?

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An electric field $\stackrel{m \mathrm{E}}{\mathrm{E}}=4 x \hat{\mathrm{i}}-\left(\mathrm{y}^2+1\right) \hat{\mathrm{j}} \mathrm{N} / \mathrm{C}$ passes through the box shown in figure. The flux...

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Two monomers in maltose are

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The compound A in the following reactions is

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Orange light of wavelength $6000 \times 10^{-10} \mathrm{~m}$ illuminates a single slit of width $0.6 \times 10^{-4} \mathrm{~m}$. The maximum...

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White phosphorus on reaction with concentrated NaOH solution in an inert atmosphere of CO2 gives phosphine and compound (X). (X)...

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A mixture of one mole each of $\mathrm{H}_2, \mathrm{He}$ and $\mathrm{O}_2$ each are enclosed in a cylinder of volume $V$...

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Blocks of masses m, 2m, 4m and 8m are arranged in a line on a frictionless floor. Another block of...

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Arrange the following bonds according to their average bond energies in descending order C – Cl, C – Br, C...

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The major product in the following reaction is

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In a meter bridge experiment S is a standard resistance. R is a resistance wire. It is found that balancing...

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A tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and...

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For the following Assertion and Reason, the correct option is Assertion : For hydrogenation reactions, the catalytic activity increases from...

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The d-electron configuration of $\left[\mathrm{Ru}(\mathrm{en})_3\right] \mathrm{Cl}_2$ and $\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_2$ , respectively are

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The value of current i1 flowing from A to C in the circuit diagram is

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Consider the following plots of rate constant versus $\frac{1}{\top}$ for four different reactions. Which of the following orders is correct...

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A wire A, bent in the shape of an arc of a circle, carrying a current of 2 A and...

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An ionic micelle is formed on the addition of

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The circuit shown below is working as a 8 V dc regulated voltage source. When 12 V is used as...

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The specific heat of water $=4200 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$ and the latent heat of ice $...

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A body is moving in a low circular orbit about a planet of mass M and radius R. The radius...

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The five successive ionization enthalpies of an element are 800, 2427, 3658, 25024 and 32824 kJ mol–1. The number of...

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Two charged thin infinite plane sheets of uniform surface charge density $\sigma_{+}$and $\sigma_{-}$, where $\left|\sigma_{+}\right|>\left|\sigma_{-}\right|$, intersect at right angle. Which...

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The strengths of 5.6 volume hydrogen peroxide (of density 1 g/mL) in terms of mass percentage and molarity (M), respectively,...

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In a Young's double slit experiment 15 fringes are observed on a small portion of the screen when light of...

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A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a...

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A metal (A) on heating in nitrogen gas gives compound B. B on treatment with $\mathrm{H}_2 \mathrm{O}$ gives a colourless...

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Starting at temperature 300 K , one mole of an ideal diatomic gas ( $\gamma=1.4$ ) is first compressed adiabatically...

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Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density $d$. The area...

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Consider the following molecules and statements related to them

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A series L-R circuit is connected to a battery of emf $V$. If the circuit is switched on at $t=0$,...

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Match the following drugs with their therapeutic actions

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A particle of mass $m$ is projected with a speed $u$ from the ground at an angle $\theta=\pi / 3$...

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100 mL of 0.1 M HCl is taken in a beaker and to it 100 mL of 0.1 M NaOH...

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Among the statements (I – IV), the correct ones are (I) Be has smaller atomic radius compared to Mg. (II)...

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In a photoelectric effect experiment, the graph of stopping potential V versus reciprocal of wavelength obtained is shown in the...

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There is a small source of light at some depth below the surface of water (refractive index $=4 / 3$...

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The increasing order of the reactivity of the following compounds in nucleophilic addition reaction is Propanal, Benzaldehyde, Propanone, Butanone

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A capacitor $C$ is fully charged with voltage $V_0$. After disconnecting the voltage source, it is connected in parallel with...

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The incorrect statement(s) among (a) – (d) regarding acid rain is (are) (a) It can corrode water pipes. (b) It...

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A small spherical droplet of density d is floating exactly half immersed in a liquid of density $\rho$ and surface...

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The decreasing order of reactivity of the following compounds towards nucleophilic substitution $\left(\mathrm{S}_{\mathrm{N}} 2\right)$ is

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Consider two uniform discs of the same thickness and different radii $R_1=R$ and $R_2=\alpha R$ made of the same material....

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Consider the hypothetical situation where the azimuthal quantum number,l, takes value 0, 1, 2, ... n + 1, where n...

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In LC circuit the inductance L $=40 \mathrm{mH}$ and capacitance $\mathrm{C}=100 \mu \mathrm{~F}$. If a voltage $\mathrm{V}(\mathrm{t})=10 \sin (314 \mathrm{t})$...

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A cube of metal is subjected to a hydrostatic pressure of 4 GPa . The percentage change in the length...

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The incorrect statement is

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When an object is kept at a distance of 30 cm from a concave mirror, the image is formed at...

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If minimum possible work is done by a refrigerator in converting 100 grams of water at 0°C to ice, how...

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The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from 420...

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A galvanometer coil has 500 turns and each turn has an average area of $3 \times 10^{-4} \mathrm{~m}^2$. If a...

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Identify the operation performed by the circuit given below

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A spring mass system (mass $m$, spring constant $k$ and natural length I) rests in equilibrium on a horizontal disc....

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A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its centre of...

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A paramagnetic sample shows a net magnetisation of $6 \mathrm{~A} / \mathrm{m}$ when it is placed in an external magnetic...

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A particle starts from the origin at $t=0$ with an initial velocity of $3.0 \hat{i} \mathrm{~m} / \mathrm{s}$ and moves...

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A particle of charge $q$ and mass $m$ is subjected to an electric field $E=E_0\left(1-a x^2\right)$ in the $x$-direction, where...

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Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear,...

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If $\operatorname{Re}\left(\frac{z-1}{2 z+i}\right)=1$, where $z=x+i y$, then the point $(x, y)$ lies on a

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If $y=y(x)$ is the solution of the differential equation, $e^y\left(\frac{d y}{d x}-1\right)=e^x$ such that $y(0)=0$, then $y(1)$ is equal to

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A quantity x is given by (IFv²/ $\mathrm{WL}^4$ ) in terms of moment of inertia I , force F ,...

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Find the binding energy per nucleon for ${ }_{50}^{120} \mathrm{Sn}$. Mass of proton $m_p=1.00783 \mathrm{U}$, mass of neutron $m_n=1.00867 \mathrm{U}$...

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An massless equilateral triangle EFG of side 'a' (As shown in figure) has three particles of mass $m$ situated at...

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The electric field of a plane electromagnetic wave is given by $\overrightarrow{\mathrm{E}}=\mathrm{E}_0(\hat{\mathrm{x}}+\hat{\mathrm{y}}) \sin (\mathrm{kz}-\omega \mathrm{t})$ Its magnetic field will be...

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For the following Assertion and Reason, the correct option is Assertion : The pH of water increases with increase in...

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The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the Wavelength...

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An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive...

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The major product in the following reaction is

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If $y=m x+4$ is a tangent to both the parabolas, $y^2 =4 x$ and $x^2=2 b y$, then $b$ is...

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A block starts moving up an inclined plane of inclination $30^{\circ}$ with an initial velocity of $v_0$. It comes back...

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Hydrogen has three isotopes (A), (B) and (C). If the number of neutron(s) in (A), (B) and (C) respectively, are...

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Five number are in A.P., whose sum is 25 and product is 2520 . If one of these five numbers...

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A block of mass 1.9 kg is at rest at the edge of a table, of height 1m. A bullet...

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A circular coil has moment of inertia $0.8 \mathrm{~kg} \mathrm{~m}^2$ around any diameter and is carrying current to produce a...

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The major product [B] in the following sequence of reactions is

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A vector $\vec{a}=\alpha \hat{i}+2 \hat{j}+\beta \hat{k}(\alpha, \beta \in R)$ lies in the plane of the vectors, $\vec{b}=\hat{i}+\hat{j}$ and $\vec{c}=\hat{i}-\hat{j}+4 \hat{k}$....

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A uniform rod of length ' $l$ ' is pivoted at one of its ends on a vertical shaft of...

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The correct order of the calculated spin-only magnetic moments of complexes (A) to (D) is (A) $\mathrm{Ni}(\mathrm{CO})_4$ (B) $...

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Let $\alpha$ and $\beta$ be two real roots of the equation $(\mathrm{k}+1) \tan ^2 \mathrm{x}-\sqrt{2} \cdot \lambda \tan \mathrm{x}=(1-\mathrm{k})$, where...

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If a semiconductor photodiode can detect a photon with a maximum wavelength of 400 nm, then its band gap energy...

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The radius of the second Bohr orbit, in terms of the Bohr radius, $\mathbf{a}_0$, in $\mathrm{Li}^{2+}$ is

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Let $x^k+y^k=a^k,(a, k>0)$ and $\frac{d y}{d x}+\left(\frac{y}{x}\right)^{\frac{1}{3}}=0$, then k is :

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A small ball of mass $m$ is thrown upward with velocity $u$ from the ground. The ball experiences a resistive...

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A rod of length $L$ has non-uniform linear mass density given by $$ \rho(\mathrm{x})=\mathrm{a}+\mathrm{b}\left(\frac{\mathrm{x}}{\mathrm{~L}}\right)^2 $$ , where a and b...

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If $g(x)=x^2+x-1$ and $(g \circ f)(x)=4 x^2-10 x+5$, then $\mathrm{f}\left(\frac{5}{4}\right)$ is equal to:

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The increasing order of the atomic radii of the following elements is (a) C (b) O (c) F (d) CI...

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A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The...

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Let $\alpha$ be a root of the equation $x^2+x+1=0$ and the matrix $...

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Two light waves having the same wavelength $\lambda$ in vacuum are in phase initially. Then the first wave travels a...

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Among the reactions (a) - (d), the reaction(s) that does/do not occur in the blast furnace during the extraction of...

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Planet $A$ has mass $M$ and radius $R$. Planet $B$ has half the mass and half the radius of Planet...

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Let P be a plane through the points (2, 1, 0), (4, 1, 1) and (5, 0, 1) and R...

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The radius $R$ of a nucleus of mass number $A$ can be estimated by the formula $...

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Which of the following compounds is likely to show both Frenkel and Schottky defects in its crystalline form ?

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Two identical capacitors A and B , charged to the same potential 5 V are connected in two different circuits...

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The area of the region, enclosed by the circle $x^2+ y^2=2$ which is not common to the region bounded by...

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A calorimeter of water equivalent 20 g contains 180 g of water at $25^{\circ} \mathrm{C}$. ' m ' grams of...

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Among the compounds $A$ and $B$ with molecular formula $\mathrm{C}_9 \mathrm{H}_{18} \mathrm{O}_3, A$ is having higher boiling point the $B$....

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A uniform magnetic field $B$ exists in a direction perpendicular to the plane of a square loop made of a...

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For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to...

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If the system of linear equations 2x + 2ay + az = 0 2x + 3by + bz = 0...

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A ball is dropped from the to of a 100 m high tower on a planet. In the last $...

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The greatest positive integer k , for which $49^{\mathrm{k}}+1$ is a factor of the sum $49^{125}+49^{124}+\ldots \ldots+49^2+49+1$, is

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Two resistors $400 \Omega$ and $800 \Omega$ are connected in series across a 6 V battery. The potential difference measured...

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An electron of mass m and magnitude of charge |e| initially at rest gets accelerated by a constant electric field...

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The logical statement $(p \Rightarrow q) \wedge(q \Rightarrow \sim p)$ is equivalent to

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The first member of the Balmer series of hydrogen atom has a wavelength of 6561 Å. The wavelength of the...

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Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their...

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Amount of solar energy received on the earth’s surface per unit area per unit time is defined a solar constant....

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Chlorine reacts with hot and concentrated NaOH and produces compounds (X) and (Y). Compound (X) gives white precipitate with silver...

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The series combination of two batteries, both of the same emf 10 V , but different internal resistance of $...

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For the reaction $\mathrm{A}(\mathrm{l}) \rightarrow 2 \mathrm{~B}(\mathrm{~g})$ $\Delta \mathrm{U}=2.1 \mathrm{kcal}, \Delta \mathrm{S}=20 \mathrm{cal} \mathrm{K}^{-1}$ at 300 K . Hence $...

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The mass density of a planet of radius $R$ varies with the distance $r$ from its centre as $\rho(r)=\rho_0\left(1-\frac{r^2}{R^2}\right)$. Then...

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An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R (R is...

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An electron gun is placed inside a long solenoid of radius R on its axis. The solenoid has n turns/length...

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The number of chiral carbons in chloramphenicol is ___________.

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Three containers $C_1, C_2$ and $C_3$ have water at different temperatures. The table below shows the final temperature $T$ when...

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During the nuclear explosion, one of the products is ${ }^{90} \mathrm{Sr}$ with half life of 6.93 years. If $...

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A metallic sphere cools from 50°C to 40°C in 300 s. If atmospheric temperature around is 20°C, then the sphere’s...

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Two solutions, $A$ and $B$, each of $100 L$ was made by dissolving 4 g of NaOH and 9.8 g...

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Concentric metallic hollow spheres of radii R and 4R hold charges $Q_1$ and $Q_2$ respectively. Given that surface charge densities...

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An electron (mass $m$ ) with initial velocity $\vec{v}=v_0 \hat{i}+v_0 \hat{j} \vec{E}=-E_0 \hat{k}$. If $\lambda_0$ is initial de-Broglie wavelength of...

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Which of the following will NOT be observed when a multimeter (operating in resistance measuring mode) probes connected across a...

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A particle moves such that its position vector $\vec{r}(t)=\cos \omega t \hat{i}+\sin \omega t \hat{j}$ where $\omega$ is a constant...

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The current i in the network is

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A perfectly diamagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The...

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As shown in fig. when a spherical cavity (centred at O) of radius 1 is cut out of a uniform...

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The electric field of a plane electromagnetic wave propagating along the x direction in vacuum is $...

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The dipole moments of $\mathrm{CCl}_4, \mathrm{CHCl}_3$ and $\mathrm{CH}_4$ are in the order :

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A very long wire ABDMNDC is shown in figure carrying current I. AB and BC parts are straight, long and...

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A plane electromagnetic wave is propagating along the direction $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$, with its polarization along the direction $\hat{k}$. The correct form...

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Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final...

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A block of mass m attached to a massless spring is performing oscillatory motion of amplitude ‘A’ on a frictionless...

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In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is...

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1-methylethylene oxide when treated with an excess of HBr produces:

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A plane electromagnetic wave of frequency 25 GHz is propagating in vacuum along the z-direction. At a particular point in...

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Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respectively. Both the...

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A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform...

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The number of orbitals associated with quantum numbers $\mathrm{n}=5, \mathrm{~m}_{\mathrm{s}}=+\frac{1}{2}$ is:

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Consider two charged metallic spheres $S_1$ and $S_2$ of radii $R_1$ and $R_2$, respectively. The electric fields $E_1$ (on $S_1$...

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To raise the temperature of a certain mass of gas by 50°C at a constant pressure, 160 calories of heat...

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The theory that can completely/properly explain the nature of bonding in $\left[\mathrm{Ni}(\mathrm{CO})_4\right]$ is :

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A capacitor is made of two square plates each of side 'a' making a very small angle $\alpha$ between them,...

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A wire of length L and mass per unit length $6.0 \times 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$ is put under tension of...

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The IUPAC name of the complex $\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_2\right. \left.\mathrm{Cl}\left(\mathrm{NH}_2 \mathrm{CH}_3\right)\right] \mathrm{Cl}$ is :

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The electron gain enthalpy (in kJ/mol) of fluorine, chlorine, bromine and iodine, respectively, are :

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A particle of mass m and charge q is released from rest in a uniform electric field. If there is...

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Consider the following reactions : Which of these reaction(s) will not produce Saytzeff product ?

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A simple pendulum is being used to determine the value of gravitational acceleration g at a certain place. The length...

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The purest form of commercial iron is

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A particle of mass m is dropped from a height $h$ above the ground. At the same time another particle...

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Amongst the following statements, that which was not proposed by Dalton was :

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Two liquids of densities $\rho_1$ and $\rho_2\left(\rho_2=2 \rho_1\right)$ are filled up behind a square wall of side 10 m as...

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A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was extracted initially with a saturated solution of $\mathrm{NaHCO}_3$...

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As shown in the figure, a battery of emf $E$ is connected to an inductor $L$ and resistance $R$ in...

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What is the product of following reaction?

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A Carnot engine having an efficiency of $\frac{1}{10}$ is being used as a refrigerator. If the work done on the...

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The relative strength of interionic/ intermolecular forces in decreasing order is :

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A galvanometer having a coil resistance $100 \Omega$ gives a full scale deflection when a current of 1 mA is...

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Consider the following reaction: The product ‘X’ is used

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A transverse wave travels on a taut steel wire with a velocity of v when tension in it is $...

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Oxidation number of potassium in $\mathrm{K}_2 \mathrm{O}, \mathrm{K}_2 \mathrm{O}_2$ and $\mathrm{KO}_2$, respectively, is

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An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror....

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The increasing order of $\mathrm{pK}_{\mathrm{b}}$ for the following compounds will be

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Consider a mixture of n moles of helium gas and $2 n$ moles of oxygen gas (molecules taken to be...

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Match the following

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In the given circuit, value of Y is (MFST-6)

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At $35^{\circ} \mathrm{C}$, the vapour pressure of $\mathrm{CS}_2$ is 512 mm Hg and that of acetone is 344 mm Hg...

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A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at...

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Given that the standard potentials $\left(\mathrm{E}^{\circ}\right)$ of $\mathrm{Cu}^{2+} / \mathrm{Cu}$ and $\mathrm{Cu}^{+} / \mathrm{Cu}$ are 0.34 V and 0.522 V...

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The atomic radius of Ag is closest to

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In comparison to the zeolite process for the removal of permanent hardness, the synthetic resins method is

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A beam of electromagnetic radiation of intensity $6.4 \times 10^{-5} \mathrm{~W} / \mathrm{cm}^2$ is comprised of wavelength, $\lambda=$ 310 nm...

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A non-isotropic solid metal cube has coefficients of linear expansion as: $5 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ along the x-axis...

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A loop ABCDEFA of straight edges has six corner points $A(0,0,0), B(5,0,0), C(5,5,0), D(0,5,0)$, $E(0,5,5)$ and $F(0,0,5)$. The magnetic field...

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A Carnot engine operates between two reservoirs of temperatures 900 K and 300 K. The engine performs 1200 J of...

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A particle ( $m=1 \mathrm{~kg}$ ) slides down a frictionless track (AOC) starting from rest at a point A (height...

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Two infinite planes each with uniform surface charge density $+\sigma$ are kept in such a way that the angle between...

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A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical springmass damped oscillator having damping constant...

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Which of the following gives a reversible operation?

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A polarizer-analyser set is adjusted such that the intensity of light coming out of the analyser is just $10 \%$...

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Consider a circular coil of wire carrying constant current I, forming a magnetic dipole. The magnetic flux through an infinite...

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If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of...

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Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right...

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Visible light of wavelength $6000 \times 10^{-8} \mathrm{~cm}$ falls normally on a single slit and produces a diffraction pattern. It...

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As shown in the figure, a bob of mass m is tied by a massless string whose other end portion...

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The current $I 1$ (in A) flowing through $1 \Omega$ resistor in the following circuit is :

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Two moles of an ideal gas with $\frac{C_P}{C_V}=\frac{5}{3}$ are mixed with 3 moles of another ideal gas with $\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{4}{3}$. The...

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The time period of revolution of electron in its ground state orbit in a hydrogen atom is $1.6 \times 10^{-16}$...

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A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg . If the...

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Speed of transverse wave on a straight wire (mass 6.0 g , length 60 cm and area of crosssection 1.0...

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A long solenoid of radius $R$ carries a time $(t)$ dependent current $\mathrm{I}(\mathrm{t})=\operatorname{lot}(1-\mathrm{t})$. A ring of radius $2 R$ is...

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A stellite of mass $m$ is launched vertically upwards with an initial speed $u$ from the surface of the earth....

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The radius of gyration of a uniform rod of length I, about an axis passing through a point $\frac{1}{4}$ away...

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A litre of dry air at STP expands adiabatically to a volume of 3 litres. If $\gamma=1.40$, the work done...

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If the magnetic field in a plane electromagnetic wave is given by $...

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A parallel plate capacitor has plates of area $A$ separated by distance 'd' between them. It is filled with a...

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