Q JEE Main 2026

The number of elements in the set $\left\{x \in\left[0,180^{\circ}\right]: \tan \left(x+100^{\circ}\right)=\tan \left(x+50^{\circ}\right) \tan x \tan \left(x-50^{\circ}\right)\right\}$ is $\_\_\_\_$ .

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Let S be a set of 5 elements and $\mathrm{P}(\mathrm{S})$ denote the power set of S . Let E be...

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Let z=(1+i)(1+2i)(1+3i)...(1+n i), where $i=\sqrt{-1}$. If $|z|^2=44200$, then $n$ is equal to

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Let $(h, k)$ lie on the circle $\mathrm{C}: x^2+y^2=4$ and the point $(2 h+1,3 k+2)$ lie on an ellipse with...

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Let [t] denote the greatest integer less than or equal to t. If the function $...

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

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The smallest positive integral value of $a$, for which all the roots of $x^4-a x^2+9=0$ are real and distinct, is...

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Let $f$ be a function such that $3 f(x)+2 f\left(\frac{m}{19 x}\right)=5 x, x \neq 0$, where $m=\sum_{i=1}^9(i)^2$. Then $f(5)-f(2)$ is...

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Q JEE Main 2026

Let $y=y(x)$ be a differentiable function in the interval $(0, \infty)$ such that $y(1)=2$, and $...

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Consider the following three statements for the function $f:(0, \infty) \rightarrow \mathbb{R}$ defined by $f(x)=\left|\log _e x\right|-|x-1|$ : (I) $f$...

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A volume of $x \mathrm{~mL}$ of $5 \mathrm{M} \mathrm{NaHCO}_3$ solution was mixed with 10 mL of $2 \mathrm{MH}_2 \mathrm{CO}_3$ solution...

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Q JEE MAIN 2026

Using a variable frequency acavoltage source the maximum current measured in the given LCR circuit is 50 mA for $...

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The following diagram shows a Zener diode as a voltage regulator. The Zener diode is rated at $V_{\mathrm{z}}=5 \mathrm{~V}$ and...

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200 cc of $x \times 10^{-3} \mathrm{M}$ potassium dichromate is required to oxidise 750 cc of 0.6 M Mohr's salt...

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The space between the plates of a parallel plate capacitor of capacitance $C$ (without any dielectric) is now filled with...

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In two separate Young's double-slit experimental set-ups and two monochromatic light sources of different wavelengths are used to get fringes...

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The equation of the electric field of an electromagnetic wave propagating through free space is given by: $...

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A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in...

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

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Consider the dissociation equilibrium of the following weak acid $\mathrm{HA} \boxtimes \mathrm{H}^{+}(\mathrm{aq})+\mathrm{A}^{-}(\mathrm{aq})$ If the pKa of the acid is 4...

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Q JEE MAIN 2026

0.53 g of an organic compound $(\mathrm{x})$ when heated with excess of nitric acid (concentrated) and then with silver nitrate...

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In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their...

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X is the number of geometrical isomers exhibited by $\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)\left(\mathrm{H}_2 \mathrm{O}\right) \mathrm{BrCl}\right]$. Y is the number of optically inactive isomer(s)...

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Q JEE MAIN 2026

In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg ,...

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Consider the following redox reaction taking place in acidic medium $$ \mathrm{BH}_4^{-}(a q)+\mathrm{ClO}_3^{-}(a q) \longrightarrow \mathrm{H}_2 \mathrm{BO}_3^{-}(a q)+\mathrm{Cl}^{-}(a q) $$...

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Two small balls with masses m and 2 m are attached to both ends of a rigid rod of length...

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A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity ( $...

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500 mL of 1.2 M KI solution is mixed with 500 mL of $0.2 \mathrm{MKMnO}_4$ solution in basic medium. The...

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Q JEE MAIN 2026

The correct statement among the following is:

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In period 4 of the periodic table, the elements with highest and lowest atomic radii are respectively.

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Given below are two statements: Statement 1: The number of pairs, from the following, in which both the ions are...

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Which of the following point in Figure 2 most accurately represents the nodal surface as shown in Figure 1

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The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to...

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$$ \mathrm{Ph}-\mathrm{CH}=\mathrm{CH}_2 \xrightarrow[\mathrm{HBr}]{(\mathrm{PhCOO})_2} \text { Product } $$ Consider the above reaction A. The reaction proceeds through a more stable...

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In the given pentapeptide, find out an essential amino acid $(\mathrm{Y})$ and the sequence present in the pentapeptide:

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Consider the following reactions giving major product. Identify the correct reaction.

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Given below are two statements: Statement I: Griss-llosvay test is used for the detection of nitrite ion, which involves the...

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Regarding the hydrides of group 15 elements $\mathrm{EH}_3(\mathrm{E}=\mathrm{N}, \mathrm{P}, \mathrm{As}, \mathrm{Sb})$, select the correct statement from the following: A. The...

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Which one of the following is not a measurable quantity?

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Given below are two statements: Statement I: The number of species among $\mathrm{BF}_4^{-}, \mathrm{SiF}_4, \mathrm{XeF}_4$ and $\mathrm{SF}_4$, that have unequal...

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The speed of a longitudinal wave in a metallic bar is $400 \mathrm{~m} / \mathrm{s}$. If the density and Young's...

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Given below are the four isomeric compounds (P,Q, S)

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A particle starts moving from time $t=0$ and its coordinate is given as $x(t)=4 t^3-3 t$ A. The particle returns...

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Given below are two statements for the following reaction sequence.

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An organic compound undergoes first order decomposition. The time taken for decomposition to $\left(\frac{1}{8}\right)^{\text {th }}$ and $\left(\frac{1}{10}\right)^{\text {th }}$...

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Identify the correct statements : A. Electrostatic field lines form closed loops . B. The electric field lines point radially...

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The time period of a simple harmonic oscillator is $T=2 \pi \sqrt{\frac{k}{m}}$. Measured value of mass $(m)$ of the object...

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Consider a weak base ' B ' of $\mathrm{pK}_{\mathrm{b}}=5.699$ ' $x$ ' mL of 0.02 M HCl and ' y...

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Method used for separation of mixture of products ( B and C ) obtained in the following reaction is

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Consider the following reaction sequence

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At $T(K), 2$ moles of liquid $A$ and 3 moles of liquid $B$ are mixed. The vapour pressure of ideal...

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CORRECT order of stability for the following is $\mathrm{CH}_2=\mathrm{CH}^{-}, \mathrm{CH}_3-\mathrm{CH}_2^{-}, \mathrm{CH} \equiv \mathrm{C}^{-}$

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Q JEE MAIN 2026

$20.0 \mathrm{dm}^3$ of an ideal gas ' X ' at 600 K and 0.5 MPa undergoes isothermal reversible expansion until...

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The equivalent resistance between the points $A$ and $B$ in the following circuit is $\frac{x}{5} \Omega$. The value of $x$...

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A convex lens of refractive index 1.5 and focal length $f=18 \mathrm{~cm}$ is immersed in water. The difference in focal...

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A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from...

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The ratio of de Broglie wavelength of a deutron with kinetic energy $E$ to that of an alpha particle with...

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If $\sum_{r=1}^{2 s}\left(\frac{r}{r^4+r^2+1}\right)=\frac{p}{q}$, where $p$ and $q$ are positive integers such that $\operatorname{gcd}(p, q)=1$, then $p+q$ is equal to $\_\_\_\_$。

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The displacement of a particle, executing simple harmonic motion with time period $T$, is expressed as $x(t)=A \sin \omega t$,...

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If the distance of the point $\mathrm{P}(43, \alpha, \beta), \beta

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A particle of mass $m$ falls from rest through a resistive medium having resistive force, $F=-k v$, where $v$ is...

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Let $A=\left[\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right]$ and $B$ be two matrices such that $A^{100}=100 B+I$. Then the sum...

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Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side...

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Let $f$ be a differentiable function satisfying $f(x)=1-2 x+\int_0^x \mathrm{e}^{(x-t)} f(t) \mathrm{dt}, x \in \mathbf{R}$ and let $...

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Grignard reagent $\mathrm{RMgBr}(\mathrm{P})$ reacts with water and forms a gas $(\mathrm{Q})$. One gram of Q occupies $1.4 \mathrm{dm}^3$ at STP....

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The magnetic field at the centre of a current carrying circular loop of radius $R$ is $16 \mu \mathrm{~T}$. The...

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Three persons enter in a lift at the ground floor. The lift will go upto $...

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When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark...

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Molar conductivity of a weak acid HQ of concentration 0.18 M was found to be $1 / 30$ of the...

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Given below are two statements: Statement I : A plane wave after passing through prism remains as plane wave but...

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Given below are two statements : Statement I: $25^{13}+20^{13}+8^{13}+3^{13}$ is divisible by 7 . Statement II: The integral part of...

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A block of mass 5 kg is moving on an inclined plane which makes an angle of $30^{\circ}$ with the...

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Let $Q(a, b, c)$ be the image of the point $P(3,2,1)$ in the line $\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}$. Then the distance of $Q$...

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Let $P Q R$ be a triangle such that $\overrightarrow{P Q}=-2 \hat{i}-\hat{j}+2 \hat{k}$ and $...

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Two wires $A$ and $B$ made of different materials of lengths 6.0 cm and 5.4 cm , respectively and area...

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A chromium complex with a formula $\mathrm{CrCl}_3 \cdot 6 \mathrm{H}_2 \mathrm{O}$ has a spin only magnetic moment value of 3.87...

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The value of $\sum_{\mathrm{r}=1}^{20}\left(\left|\sqrt{\pi\left(\int_0^{\mathrm{r}} \mathrm{x}|\sin \pi \mathrm{x}| \mathrm{dx}\right)}\right|\right)$ is $\_\_\_\_$ .

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The half-life of ${ }^{65} \mathrm{Zn}$ is 245 days. After $x$ days, $75 \%$ of original activity remained. The value...

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Let $$ \begin{aligned} & A=\{z \in \mathbb{C}:|z-2| \leqslant 4\} \text { and } \\ & B=\{z \in \mathbb{C}:|z-2|+|z+2|=5\} \end{aligned} $$...

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If $k=\tan \left(\frac{\pi}{4}+\frac{1}{2} \cos ^{-1}\left(\frac{2}{3}\right)\right)+\tan \left(\frac{1}{2} \sin ^{-1}\left(\frac{2}{3}\right)\right)$, then the number of solutions of the equation $...

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For the two cells having same EMF $E$ and internal resistance $r$, the current passing through the external resistor $...

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For some $\theta \in\left(0, \frac{\pi}{2}\right)$, let the eccentricity and the length of the latus rectum of the hyperbola $...

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In a G.P., if the product of the first three terms is 27 and the set of all possible values...

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In the following $p-V$ diagram the equation of state along the curved path is given by $(V-2)^2=4 a p$ where...

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0.25 g of an organic compound " A " containing carbon, hydrogen and oxygen was analysed using the combustion method....

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Let $y=y(x)$ be the solution of the differential equation $$ x \frac{d y}{d x}-\sin 2 y=x^3\left(2-x^3\right) \cos ^2 y, x...

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The magnitudes of power of a biconvex lens (refractive index 1.5) and that of a plano-concave lens (refractive index $=1.7$...

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Given below are two statements:

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Assuming in forward bias condition there is a voltage drop of 0.7 V across a silicon diode, the current through...

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For three unit vectors $\vec{a}, \vec{b}, \vec{c}$ satisfying $|\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}|^2+|\overrightarrow{\mathrm{b}}-\overrightarrow{\mathrm{c}}|^2+|\overrightarrow{\mathrm{c}}-\overrightarrow{\mathrm{a}}|^2=9$ and $|2 \overrightarrow{\mathrm{a}}+\mathrm{k} \overrightarrow{\mathrm{b}}+\mathrm{k} \overrightarrow{\mathrm{c}}|=3$, the positive value of k is...

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$A \longrightarrow B$ (first reaction) $\mathrm{C} \longrightarrow \mathrm{D}$ (second reaction) Consider the above two first-order reactions. The rate constant for...

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If the distances of the point $(1,2, a)$ from the line $\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}$ along the lines $\mathrm{L}_1: \frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b}$ and $\mathrm{L}_2: \frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c}$...

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For strong electrolyte $\Lambda_m$ increases slowly with dilution and can be represented by the equation $$ \Lambda_{\mathrm{m}}=\Lambda_{\mathrm{m}}^{\cdot}-A c^{1 / 2}...

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"X" is an oxoanion of the lightest element of group 7 (in the periodic table). The metal is in +6...

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Two positively charged particles and have been accelerated across the same potential difference of 200 keV as shown below.

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At 298 K , the mole percentage of $\mathrm{N}_2(\mathrm{~g})$ in air is $80 \%$. Water is in equilibrium with air...

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Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15...

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The common difference of the A.P: $a_1, a_2, \ldots, a_{\mathrm{m}}$ is 13 more than the common difference of the A.P....

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The heat of atomisation of methane and ethane are ' $\mathrm{x}{ }^{\prime} \mathrm{kJmol}^{-1}$ and ' $\mathrm{y}{ }^{\prime} \mathrm{kJmol}^{-1}$ respectively. The...

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Let $\mathrm{A}_2 \mathrm{~B}$ and $C$ be three $2 \times 2$ matrices with real entries such that $B=(I+A)^{-1}$ and $\mathrm{A}+\mathrm{C}=\mathrm{I}$. If...

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Which of the following best represents the temperature versus heat supplied graph for water, in the range of $-20^{\circ} \mathrm{C}$...

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From the following, how many compounds contain at least one secondary alcohol?

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The electric field of an electromagnetic wave travelling through a medium is given by $...

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The mean and variance of 10 observations are 9 and 34.2 , respectively. If 8 of these observations are 2,3,5,10,11,13,15,21,...

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The value of $...

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The number of isoelectronic species among $\mathrm{Sc}^{3+}, \mathrm{Cr}^{2+}, \mathrm{Mn}^{3+}, \mathrm{Co}^{3+}$ and $\mathrm{Fe}^{3+}$ is ' $n^{\prime}$. If ' $n$ ' moles...

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Given below are two statements:

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The correct order of acidic strength of the major products formed in the given reactions, is : A. $...

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Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop...

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The area of the region $\mathrm{R}=\left\{(x, y): x y \leq 8,1 \leq y \leq x^2, x \geq 0\right\}$ is

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A student performed analysis of aliphatic organic compound ' $X$ ' which on analysis gave $\mathrm{C}=61.01 \%$, $...

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Given below are two statements: Statement I: Cross aldol condensation between two different aldehydes will always produce four different products....

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Let $f$ be a polynomial function such that $f\left(\mathrm{x}^2+1\right)=\mathrm{x}^4+5 \mathrm{x}^2+2$, for all $\mathrm{x} \in \mathbb{R}$. Then $\int_0^3 f(\mathrm{x}) \mathrm{dx}$ is...

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Structures of four disaccharides are given below. Among the given disaccharides, the non-reducing sugar is :

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Given below are two statementsi Statement I: The function $f: \mathbf{R} \rightarrow \mathbf{R}$ defined by $f(x)=\frac{x}{1+|x|}$ is one-one. Statement II:...

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Two circular dises of radius each 10 cm are joined at their centres by a rod of length 30 cm...

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If $\int\left(\frac{1-5 \cos ^2 x}{\sin ^5 x \cos ^2 x}\right) d x=f(x)+\mathrm{C}$, where C is the constant of integration, then...

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The wavelength of spectral line obtained in the spectrum of $\mathrm{Li}^{2+}$ ion, when the transition takes place between two levels...

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Consider the following reactions $$ \begin{aligned} & \mathrm{Na}_2 \mathrm{~B}_4 \mathrm{O}_7 \xrightarrow{\Delta} 2 \mathrm{X}+\mathrm{Y} \\ & \mathrm{CuSO}_4+\mathrm{Y} \xrightarrow{\text { Non-Luminous flame...

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In the potentiometer, when the cell in the secondary circuit is shunted with $4 \Omega$ resistance, the balance is obtained...

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The sum of the coefficients of $x^{499}$ and $x^{500}$ in $(1+x)^{1000}+x(1+x)^{999}+x^2(1+x)^{998}+\ldots+x^{1000}$ is :

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If $\alpha, \beta$, where $\alpha

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Match List - I with List - II according to shape. Choose the correct answer from the options given below...

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The electric current in the circuit is given as $i=i_0(t / T)$. The r.m.s current for the period $t=0$ to...

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In the Group analysis of cations, $\mathrm{Ba}^{2+} \& \mathrm{Ca}^{2+}$ are precipitated respectively as

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A bag contains 10 balls out of which $k$ are red and $(10-k)$ are black, where $...

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Let $f(x)=\int \frac{\mathrm{d} x}{x^{\left(\frac{2}{3}\right)}+2 x^{\left(\frac{1}{2}\right)}}$ be such that $f(0)=-26+24 \log _{\mathrm{e}}(2)$. If $f(1)=\mathrm{a}+\mathrm{b} \log _{\mathrm{e}}(3)$, where $\mathrm{a}, \mathrm{b} \in \mathbf{Z}$,...

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10 kg of ice at $-10^{\circ} \mathrm{C}$ is added to 100 kg of water to lower its temperature from $...

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Let $\mathrm{S}=\left\{x^3+a x^2+b x+c: a, b, c \in \mathrm{~N}\right.$ and $\left.a, b, c \leq 20\right\}$ be a set of polynomials....

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The correct order of $\mathrm{C}, \mathrm{N}, \mathrm{O}$ and F in terms of second ionisation potential is

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Let $y=y(x)$ be the solution of the differential equation $x \frac{\mathrm{~d} y}{\mathrm{~d} x}-y=x^2 \cot x, x \in(0, \pi)$. If $y\left(\frac{\pi}{2}\right)=\frac{\pi}{2}$,...

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Let . Let be the number of 9 -digit numbers formed using the digits of the set S such that...

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Consider the following aqueous solutions. I. 2.2 g Glucose in 125 mL of solution. II. 1.9 g Calcium chloride in...

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Let $\mathrm{P}_1: y=4 x^2$ and $\mathrm{P}_2: y=x^2+27$ be two parabolas. If the area of the bounded region enclosed between $P_1$...

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Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line $...

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Let $z$ be a complex number such that $|z-6|=5$ and $|z+2-6 i|=5$. Then the value of $z^3+3 z^2-15 z+141$ is...

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$X$ and $Y$ are the number of electrons involved, respectively during the oxidation of $I^{-}$to $I_2$ and $S^{2-}$ to $S$...

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Let $f(x)=\lim _{\boldsymbol{\theta} \rightarrow 0}\left(\frac{\cos \pi x-x^{\left(\frac{2}{\boldsymbol{\theta}}\right)} \sin (x-1)}{1+x^{\left(\frac{2}{\boldsymbol{\theta}}\right)}(x-1)}\right), x \in \mathbf{R}$. Consider the following two statements : (I) $f(x)$...

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The wavelength of photon ' $A$ ' is 400 nm . The frequency of photon ' $B$ ' is $...

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In Dumas method for estimation of nitrogen, 0.50 g of an organic compound gave 70 mL of nitrogen collected at...

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If $\frac{\tan (\mathrm{A}-\mathrm{B})}{\tan \mathrm{A}}+\frac{\sin ^2 \mathrm{C}}{\sin ^2 \mathrm{~A}}=1, \mathrm{~A}, \mathrm{~B}, \mathrm{C} \in\left(0, \frac{\pi}{2}\right)$, then

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Let $P$ be a point in the plane of the vectors $\overrightarrow{A B}=3 \hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{A C}=\hat{i}-\hat{j}+3 \hat{k}$ such that...

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The hydrogen spectrum consists of several spectral lines in Lyman series $\left(\mathrm{L}_1, \mathrm{~L}_2, \mathrm{~L}_3 \ldots ; \mathrm{L}_1\right.$ has lowest energy...

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Consider the following statements about manganate and permanganate ions. Identify the correct statements. A. The geometry of both manganate and...

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The plot of $\log _{10} \mathrm{~K} v s \frac{1}{\mathrm{~T}}$ gives a straight line. The intercept and slope respectively are (where...

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Q JEE MAIN 2026

$\frac{6}{3^{26}}+\frac{10 \cdot 1}{3^{25}}+\frac{10 \cdot 2}{3^{24}}+\frac{10 \cdot 2^2}{3^{23}}+\ldots+\frac{10 \cdot 2^{24}}{3}$ is equal to :

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Consider two Group IV metal ions $\mathrm{X}^{2+}$ and $\mathrm{Y}^{2+}$. A solution containing $0.01 \mathrm{MX}^{2+}$ and $0.01 \mathrm{MY}^{2+}$ is saturated with...

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The sum of all the elements in the range of $$ \begin{aligned} & f(x)=\operatorname{Sgn}(\sin x)+\operatorname{Sgn}(\cos x)+\operatorname{Sgn}(\tan x)+\operatorname{Sgn}(\cot x), x \neq...

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The reactions which produce alcohol as the product are: A. $\mathrm{CH}_4+\mathrm{O}_2 \xrightarrow[\Delta]{\mathrm{Mo}_2 \mathrm{O}_3}$ B. $...

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Electricity is passed through an acidic solution of $\mathrm{Cu}^{2+}$ till all the $\mathrm{Cu}^{2+}$ was exhausted, leading to the deposition of...

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Identify the correct statements: The presence of $-\mathrm{NO}_2$ group in benzene ring A. activates the ring towards electrophilic substitutions. B....

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Given below are two statements: Statement I: $\mathrm{K}>\mathrm{Mg}>\mathrm{Al}>\mathrm{B}$ is the correct order in terms of metallic character. Statement II: Atomic...

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Q JEE MAIN_2026

The cyclic cations having the same number of hyperconjugation are Choose the correct answer from the options given below :

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Let $y=x$ be the equation of a chord of the circle $\mathrm{C}_1$ (in the closed half-plane $x \geq 0$ )...

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The value of $\sum_{k=1}^{\infty}(-1)^{k+1}\left(\frac{k(k+1)}{k!}\right)$ is

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Consider the elements $\mathrm{N}, \mathrm{P}, \mathrm{O}, \mathrm{S}, \mathrm{Cl}$ and F . The number of valence electrons present in the elements...

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Q JEE MAIN 2026

If $g(x)=3 x^2+2 x-3, f(0)=-3$ and $4 g(f(x))=3 x^2-32 x+72$, then $f(g(2))$ is equal to:

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Let the circle $x^2+y^2=4$ intersect $x$-axis at the points $\mathrm{A}(\mathrm{a}, 0), \mathrm{a}>0$ and $\mathrm{B}(\mathrm{b}, 0)$. Let $...

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Find out the statements which are not true. A. Resonating structures with more number of covalent bonds and lesser charge...

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Q JEE MAIN_2026_

Observe the following equilibrium in a 1 L flask. $$ A(g) \rightleftharpoons B(g) $$ At $\mathrm{T}(\mathrm{K})$, the equilibrium concentrations of...

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Q JEE MAIN_2026

Given below are two statements : Statement I : The increasing order of boiling point of hydrogen halides is $\mathrm{HCl}

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Arrange the following carbanions in the decreasing order of stability. Choose the correct answer from the options given below:

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For the given reaction; $$ \mathrm{CaCO}_3+2 \mathrm{HCl} \longrightarrow \mathrm{CaCl}_2+\mathrm{H}_2 \mathrm{O}+\mathrm{CO}_2 $$ If $90 \mathrm{gCaCO}_3$ is added to 300 mL of...

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Q JEE MAIN 2026

The probability distribution of a random variable X is given below : If $E(X)=\frac{263}{15}$, then $P(X

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A soap bubble of surface tension $0.04 \mathrm{~N} / \mathrm{m}$ is blown to a diameter of 7 cm . If...

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A student has planned to prepare acetanilide from aniline using acetic anhydride. The student has started from 9.3 g of...

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Q JEE MAIN_2026_

Which of the following reaction is NOT correctly represented ?

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Let the ellipse $\mathrm{E}: \frac{x^2}{144}+\frac{y^2}{169}=1$ and the hyperbola $\mathrm{H}: \frac{x^2}{16}-\frac{y^2}{\lambda^2}=-1$ have the same foci. If e and L respectively denote...

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An ellipse has its center at $(1,-2)$, one focus at $(3,-2)$ and one vertex at $(5,-2)$. Then the length of...

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One mole of $\mathrm{Cl}_2(\mathrm{~g})$ was passed into 2 L of cold 2 M KOH solution. After the reaction, the concentrations...

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A point charge $q=1 \mu \mathrm{C}$ is located at a distance 2 cm from one end of a thin insulating...

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Total number of alkali insoluble solid sulphonamides obtained by reaction of given amines with Hinsberg's reagent is________. Aniline, N-Methylaniline, Methanamine,...

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If the solution curve $y=f(x)$ of the differential equation $$ \left(x^2-4\right) y^{\prime}-2 x y+2 x\left(4-x^2\right)^2=0, x>2, $$ passes through the...

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Considering the principal values of inverse trigonometric functions, the value of the expression $\tan \left(2 \sin ^{-1}\left(\frac{2}{\sqrt{13}}\right)-2 \cos ^{-1}\left(\frac{3}{\sqrt{10}}\right)\right)$ is...

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Q JEE MAIN 2026

The wavelength of light absorbed for the following complexes are in the order

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A student has been given 0.314 g of an organic compound and asked to estimate Sulphur. During the experiment, the...

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The correct increasing order of spin-only magnetic moment values of the complex ions $\left[\mathrm{MnBr}_4\right]^{2-}(\mathrm{A}),\left[\mathrm{Cu}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}(\mathrm{B}),\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}(\mathrm{C})$ and $\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}(\mathrm{D})$ is :

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Pair of species among the following having same bond order as well as paramagnetic character will be-

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Let the arithmetic mean of $\frac{1}{a}$ and $\frac{1}{b}$ be $\frac{5}{16}, a>2$. If $\alpha$ is such that $a, 4, \alpha, b$...

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Consider the following gaseous equilibrium in a closed container of volume ' $V$ ' at $T(K)$. $$ \mathrm{P}_2(\mathrm{~g})+\mathrm{Q}_2(\mathrm{~g}) \boxtimes \quad...

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Q JEE MAIN 2026

Let [.] denote the greatest integer function. Then $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{12(3+[x])}{3+[\sin x]+[\cos x]}\right) \mathrm{d} x$ is equal to :

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Consider the following two reactions A and B. Numerical value of [molar mass of $x+$ molar mass of $y$ ]...

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Two liquids $A$ and $B$ form an ideal solution at temperature $T K$. At $T K$, the vapour pressures of...

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Let S denote the set of 4-digit numbers abcd such that $a>b>c>d$ and P denote the set of 5-digit numbers...

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Given below are two statements: Statement I: ' $\mathrm{C}-\mathrm{Cl}^{\prime}$ bond is stronger in $\mathrm{CH}_2=\mathrm{CH}-\mathrm{Cl}$ than $\mathrm{CH}_3-\mathrm{CH}_2-\mathrm{Cl}$ Statement II: The given...

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Let $A=\left[\begin{array}{ccc}0 & 2 & -3 \\ -2 & 0 & 1 \\ 3 & -1 & 0\end{array}\right]$ and $B$...

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The number of possible tripeptides formed involving alanine (ala), glycine (gly) and valine (val), where no amino acid has been...

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At $27^{\circ} \mathrm{C}$ in presence of a catalyst, activation energy of a reaction is lowered by $10 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The...

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The unsaturated ether on acidic hydrolysis produces carbonyl compounds as shown below:- $$ \begin{aligned} \mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}- & \mathrm{O}-\mathrm{CH}=\mathrm{CH}_2 \\ & \downarrow...

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A hydroxy compound $(\mathrm{X})$ with molar mass $122 \mathrm{~g} \mathrm{~mol}^{-1}$ is acetylated with acetic anhydride, using a large excess of...

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The number of elements in the set $\mathrm{S}=\left\{x: x \in[0,100]\right.$ and $\left.\int_0^x t^2 \sin (x-t) d t=x^2\right\}$ is $\_\_\_\_$ .

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A student is given one compound among the following compounds that gives positive test with Tollen's reagent. The compound is...

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If the image of the point $\mathrm{P}(a, 2, a)$ in the line $\frac{x}{2}=\frac{y+a}{1}=\frac{z}{1}$ is Q and the image of Q...

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Q JEE MAIN 2026

Distance between an object and three times magnified real image is 40 cm. The focal length of the mirror used...

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

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The velocity (v) - Distance (x) graph is shown in figure. Which graph represents acceleration(a) versus distance $(x)$ variation of...

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'W' g of a non-volatile electrolyte solid solute of molar mass ${ }^{\prime} \mathrm{M}^{\prime} \mathrm{gmol}^{-1}$ when dissolved in 100 mL...

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Choose the INCORRECT statement

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In the Young's double slit experiment the intensity produced by each one of the individual slits is $I_{\mathrm{o}}$. The distance...

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Q JEE MAIN 2026

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

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Let $\sum_{k=1}^n a_k=\alpha n^2+\beta n$. If $a_{10}=59$ and $a_6=7 a_1$, then $\alpha+\beta$ is equal to

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Consider three metal chlorides $\mathrm{x}, \mathrm{y}$ and z , where x is water soluble at room temperature, $y$ is sparingly...

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A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased...

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An equilateral triangle OAB is inscribed in the parabola $y^2=4 x$ with the vertex O at the vertex of the...

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Given below are two statements: Statement I: The number of paramagnetic species among $\left[\mathrm{CoF}_6\right]^{3-},\left[\mathrm{TiF}_6\right]^{3-}, \mathrm{V}_2 \mathrm{O}_5$ and $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$ is 3...

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A flexible chain of mass m hangs between two fixed points at the same level. The inclination of the chain...

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Consider a mixture ' X ' which is made by dissolving 0.4 mol of $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{SO}_4\right] \mathrm{Br}$ and 0.4 mol...

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Q JEE MAIN 2026

Identify the correct truth table of the given logic circuit.

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The correct stability order of the following diazonium salts is

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Total number of unpaired electrons present in the central metal atoms/ions of $\left[\mathrm{Ni}(\mathrm{CO})_4\right],\left[\mathrm{NiCl}_4\right]^{2-},\left[\mathrm{PtCl}_2\left(\mathrm{NH}_3\right)_2\right],\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$ and $\left[\mathrm{Pt}(\mathrm{CN})_4\right]^{2-}$ is $\_\_\_\_$ .

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If the mean and the variance of the data are $\mu$ and 19 respectively, then the value of $\lambda+\mu$ is

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Among the following, the CORRECT combinations are A. $\mathrm{IF}_3 \rightarrow \mathrm{~T}$-shaped $\left(\mathrm{sp}^3 \mathrm{~d}\right)$ B. $\mathrm{IF}_5 \rightarrow$ Square pyramidal $\left(\mathrm{sp}^3 \mathrm{~d}^2\right)$...

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A moving coil galvanometer of resistance $100 \Omega$ shows a full scale deflection for a current of 1 mA ....

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If $z=\frac{\sqrt{3}}{2}+\frac{i}{2}, i=\sqrt{-1}$, then $\left(z^{201}-i\right)^8$ is equal to

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A cubical block of density $\rho_b=600 \mathrm{~kg} / \mathrm{m}^3$ floats in a liquid of density $\rho_{\mathrm{e}}=900 \mathrm{~kg} / \mathrm{m}^3$. If...

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Let $\mathrm{A}=\{0,1,2, \ldots, 9\}$. Let R be a relation on A defined by $(x, y) \in \mathrm{R}$ if and only...

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Two liquids A and B form an ideal solution. At 320 K, the vapour pressure of the solution, containing 3...

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The number of ways, in which 16 oranges can be distributed to four children such that each child gets at...

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$$ X_2(g)+Y_2(g) \boxtimes \quad 2 Z(g) $$ $\mathrm{X}_2(\mathrm{~g})$ and $\mathrm{Y}_2(\mathrm{~g})$ are added to a 1 L flask and it is...

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Let $\mathrm{I}(x)=\int \frac{3 d x}{(4 x+6)\left(\sqrt{4 x^2+8 x+3}\right)}$ and $\mathrm{I}(0)=\frac{\sqrt{3}}{4}+20$. If $\mathrm{I}\left(\frac{1}{2}\right)=\frac{a \sqrt{2}}{b}+\mathrm{c}$, where $...

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Three parallel plate capacitors each with area $A$ and separation $d$ are filled with two dielectric ( $k_1$ and $\mathrm{k}_2$...

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A student has been given a compound " $x$ " of molecular formula- $\mathrm{C}_6 \mathrm{H}_7 \mathrm{~N} \cdot x$ ' is...

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The least value of $\left(\cos ^2 \theta-6 \sin \theta \cos \theta+3 \sin ^2 \theta+2\right)$ is

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The area of the region enclosed between the circles $x^2+y^2=4$ and $x^2+(y-2)^2=4$ is:

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Given below are two statements:

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The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an...

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Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One...

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A solution is prepared by dissolving 0.3 g of a non-volatile non-electrolyte solute ' A ' of molar mass $...

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When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V...

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Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors such that $\vec{a} \times \vec{b}=2(\vec{a} \times \vec{c})$. If $|\vec{a}|=1,|\vec{b}|=4,|\vec{c}|=2$, and the angle between...

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Given below are statements about some molecules/ions. Identify the CORRECT statements. A. The dipole moment value of $\mathrm{NF}_3$ is higher...

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The work functions of two metals $\left(M_A\right.$ and $\left.M_B\right)$ are in the $1: 2$ ratio. When these metals are exposed...

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Let PQ be a chord of the hyperbola $\frac{x^2}{4}-\frac{y^2}{b^2}=1$, perpendicular to the $x$-axis such that OPQ is an equilateral triangle,...

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Two identical circular loops P and Q each of radius r are lying in parallel planes such that they have...

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Arrange the following alkenes in decreasing order of stability. Choose the correct answer from the options given below:

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If the points of intersection of the ellipses $x^2+2 y^2-6 x-12 y+23=0$ and $4 x^2+2 y^2-20 x-12 y+35=0$ lie on...

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$\mathrm{A} \rightarrow \mathrm{D}$ is an endothermic reaction occurring in three steps (elementary). (i) $\mathrm{A} \rightarrow \mathrm{B} \Delta \mathrm{H}_i=+\mathrm{ve}$ (ii) $...

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A thin uniform rod $(\mathrm{X})$ of mass M and length L is pivoted at a height $\left(\frac{L}{3}\right)$ as shown in...

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The oxidation state of chromium in the final product formed in the reaction between KI and acidified $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$...

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The sum of all the real solutions of the equation $\log _{(x+3)}\left(6 x^2+28 x+30\right)=5-2 \log _{(6 x+10)}\left(x^2+6 x+9\right)$ is equal...

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Given below are two statements: Statement I: Hybridisation, shape and spin only magnetic moment of $\mathrm{K}_3\left[\mathrm{Co}\left(\mathrm{CO}_3\right)_3\right]$ is $\mathrm{sp}^3 \mathrm{~d}^2$, octahedral...

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A mixed ether ${ }^{(P)}$, when heated with excess of hot concentrated hydrogen iodide produces two different alkyl iodides which...

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The system of linear equations $$ \begin{aligned} & x+y+z=6 \\ & 2 x+5 y+a z=36 \\ & x+2 y+3 z=b...

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Consider two sets $\mathrm{A}=\{x \in \mathbb{Z}:(|x-3|-3) \mid \leq 1\}$ and $\mathrm{B}=\left\{x \in \mathbb{R}-\{1,2\}: \frac{(x-2)(x-4)}{x-1} \log _e(|x-2|)=0\right\}$. Then the number of...

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Let $A(1,2)$ and $C(-3,-6)$ be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to...

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In case of vertical circular motion of a particle by a thread of length $r$ if the tension in the...

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Let $\vec{a}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}, \vec{b}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}, \vec{c}=\lambda \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\vec{v}=\vec{a} \times \vec{b}$. If $\vec{v} \cdot \vec{c}=11$ and the length of...

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A regular hexagon is formed by six wires each of resistance $r \Omega$ and the corners are joined to the...

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Let $\frac{\pi}{2}

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Five persons $P_1, P_2, P_3, P_4$ and $P_5$ recorded object distance $(u)$ and image distance $(v)$ using same convex lens...

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If $f(x)=\left\{\begin{array}{cc}\frac{a|x|+x^2-2(\sin |x|)(\cos |x|)}{x} & , x \neq 0 \\ b & , x=0\end{array}\right.$ is continuous at $x=0$, then $a+b$...

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In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division...

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The reading of the ammeter (A) in steady state in the following circuit (assuming negligible internal resistance of the ammeter)...

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Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of $10 \mathrm{~cm} / \mathrm{s}$...

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In the given figure the blocks $\mathrm{A}, \mathrm{B}$ and $C$ weigh $4 \mathrm{~kg}, 6 \mathrm{~kg}$ and 8 kg respectively. The...

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The number of $3 \times 2$ matrices A , which can be formed using the elements of the set $\{-2,-1,0,1,2\}$...

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Let ( $2 \alpha, \alpha$ ) be the largest interval in which the function $f(t)=\frac{|t+1|}{t^2}, t2$, is $\_\_\_\_$

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A voltage regulating circuit consisting of Zener diode, having break-down voltage of 10 V and maximum power dissipation of 0.4...

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A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature $50^{\circ} \mathrm{C}$....

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A short bar magnet placed with its axis at $30^{\circ}$ with an external field of 800 Gauss, experiences a torque...

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Three masses and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are...

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The number of numbers greater than 5000 , less than 9000 and divisible by 3, that can be formed using...

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Let a line L passing through the point $\mathrm{P}(1,1,1)$ be perpendicular to the lines $\frac{x-4}{4}=\frac{y-1}{1}=\frac{z-1}{1}$ and $\frac{x-17}{1}=\frac{y-71}{1}=\frac{z}{0}$. Let the line...

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There are three co-centric conducting spherical shells $\mathrm{A}, \mathrm{B}$ and $C$ of radii $\mathrm{a}, \mathrm{b}$ and $c$ respectively $(c>b>a)$ and...

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A boy throws a ball into air at $45^{\circ}$ from the horizontal to land it on a roof of a...

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An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and...

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Let a differentiable function f satisfy the equation $\int_0^{36} f\left(\frac{t x}{36}\right) d t=4 \alpha f(x)$. If $y=f(x)$ is a standard...

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The number of the real solutions of the equation: $x|x+3|+|x-1|-2=0$ is

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Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy...

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Let $\mathrm{A}_1$ be the bounded area enclosed by the curves $y=x^2+2, x+y=8$ and $y$-axis that lies in the first quadrant....

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The mean and variance of a data of 10 observations are 10 and 2 , respectively. If an observations $\alpha$...

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The electrostatic potential in a charged spherical region of radius $r$ varies as $V=a r^3+b$, where $a$ and $b$ are...

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In Carius method 0.2425 g of an organic compound gave 0.5253 g silver chloride. The percentage of chlorine in the...

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From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then...

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A brass wire of length 2 m and radius 1 mm at $27^{\circ} \mathrm{C}$ is held taut between two rigid...

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Let $\alpha, \beta \in \mathbb{R}$ be such that the function $f(x)=\left\{\begin{array}{ll}2 \alpha\left(x^2-2\right)+2 \beta x & , x

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Identify the INCORRECT statements from the following: A. Notation ${ }_{12}^{24} \mathrm{Mg}$ represents 24 protons and 12 neutrons. B. Wavelength...

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Given below are two statements: Statement I: For all elements, greater the mass of the nucleus, greater is the binding...

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Consider an A.P.: $a_1, a_2, \ldots, a_{\mathrm{n}} ; a_1>0$. If $a_2-a_1=\frac{-3}{4}, a_{\mathrm{n}}=\frac{1}{4} a_1$, and $\sum_{\mathrm{i}=1}^{\mathrm{n}} a_{\mathrm{i}}=\frac{525}{2}$, then $\sum_{\mathrm{i}=1}^{17} a_1$ is...

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Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as...

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Two resistors $2 \Omega$ and $3 \Omega$ are connected in the gaps of bridge as shown in figure. The null...

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Which statements are NOT TRUE about $\mathrm{XeO}_2 \mathrm{~F}_2$ ? A. It has a see-saw shape. B. Xe has 5 electron...

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Let $\mathrm{S}=\frac{1}{25!}+\frac{1}{3!23!}+\frac{1}{5!21!}+\ldots$ up to 13 terms. If $13 \mathrm{~S}=\frac{2^k}{n!}, k \in \mathrm{~N}$, then $n+k$ is equal to

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An object is projected with kinetic energy K from a point A at an angle 60° with the horizontal. The...

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Let $A(1,0), B(2,-1)$ and $C\left(\frac{7}{3}, \frac{4}{3}\right)$ be three points. If the equation of the bisector of the angle A B...

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Which of the following statements are TRUE about Haloform reaction?:

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A spring of force constant $15 \mathrm{~N} / \mathrm{m}$ is cut into two pieces. If the ratio of their length...

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Let $R$ be a relation defined on the set $\{1,2,3,4\} \times\{1,2,3,4\}$ by $\mathrm{R}=\{((a, b),(c, d)): 2 a+3 b=3 c+4 d\}$....

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In hydrogen atom spectrum, (R → Rydberg's constant) A. the maximum wavelength of the radiation of Lyman series is $...

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Q JEE MAIN 2026

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

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Let $f(t)=\int\left(\frac{1-\sin \left(\log _e t\right)}{1-\cos \left(\log _e t\right)}\right) d t, t>1$. If $f\left(e^{\pi / 2}\right)=-e^{\pi / 2}$ and $...

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Observe the following reactions at $\mathrm{T}(\mathrm{K})$. I. A → products. II. $5 \mathrm{Br}^{-}(\mathrm{aq})+\mathrm{BrO}_3^{-}(\mathrm{aq})+6 \mathrm{H}^{+}(\mathrm{aq}) \rightarrow 3 \mathrm{Br}_2(\mathrm{aq})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{l})$ Both...

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If $\cot x=\frac{5}{12}$ for some $x \in\left(\pi, \frac{3 \pi}{2}\right)$, then $...

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For the series LCR circuit connected with $220 \mathrm{~V}, 50 \mathrm{~Hz}$ a.c source as shown in the figure, the power...

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Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total...

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In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and...

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Let $\mathrm{S}=\left\{z \in \mathbb{C}:\left|\frac{z-6 i}{z-2 i}\right|=1\right.$ and $\left.\left|\frac{z-8+2 i}{z+2 i}\right|=\frac{3}{5}\right\}$. Then $\sum_{z \in \mathrm{~S}}|z|^2$ is equal to

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The number of 4 -letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is ______.

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The value of $\frac{\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}}{\cos 20^{\circ} \cos 40^{\circ} \cos 60^{\circ} \cos 80^{\circ}}$ is equal to

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Two electrons are moving in orbits of two hydrogen like atoms with speeds $3 \times 10^5 \mathrm{~m} / \mathrm{s}$ and...

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JEE Main Chemistry Medium

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From the first 100 natural numbers, two numbers first $a$ and then $b$ are selected randomly without replacement. If the...

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The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest...

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Let $f$ be a twice differentiable non-negative function such that $(f(x))^2=25+\int_0^x\left((f(\mathrm{t}))^2+\left(f^{\prime}(\mathrm{t})\right)^2\right) d t$. Then the mean of $...

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The exit surface of a prism with refractive index $n$ is coated with a material having refractive index $\frac{n}{2}$. When...

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Let the area of the region bounded by the curve $y=\max \{\sin x, \cos x\}$, lines $x=0, x=\frac{3 \pi}{2}$, and...

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Given below are two statements: Statement I: The second ionisation enthalpy of Na is larger than the corresponding ionisation enthalpy...

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The crystal field splitting energy of $\left[\mathrm{Co}(\text { oxalate })_3\right]^{3-}$ complex is ' $n$ ' times that of the $...

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Two resistors of $100 \Omega$ each are connected in series with a 9 V battery. A voltmeter of $400 \Omega$...

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Let $|\mathrm{A}|=6$, where A is a $3 \times 3$ matrix. If $...

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Let each of the two ellipses $\mathrm{E}_1: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1,(a>b)$ and $\mathrm{E}_2: \frac{x^2}{\mathrm{~A}^2}+\frac{y^2}{\mathrm{~B}^2}=1,(\mathrm{~A}

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Consider all the structural isomers with molecular formula $\mathrm{C}_5 \mathrm{H}_{11} \mathrm{Br}$ are separately treated with $\mathrm{KOH}(\mathrm{aq})$ to give respective substitution...

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Let the direction cosines of two lines satisfy the equations: $4 l+m-n=0$ and $2 m n+10 n l+3 l m=0$....

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Density of water at $4^{\circ} \mathrm{C}$ and $20^{\circ} \mathrm{C}$ are $1000 \mathrm{~kg} / \mathrm{m}^3$ and $998 \mathrm{~kg} / \mathrm{m}^3$ respectively....

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If the domain of the function $$ f(x)=\log _{\left(10 x^2-17 x+7\right)}\left(18 x^2-11 x+1\right) $$ is $...

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lodoform test can differentiate between A. Methanol and Ethanol B. $\mathrm{CH}_3 \mathrm{COOH}$ and $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{COOH}$ C. Cyclohexene and cyclohexanone...

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x mg of pure HCl was used to make an aqueous solution. 25.0 mL of $0.1 \mathrm{MBa}(\mathrm{OH})_2$ solution is used...

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A building construction work can be completed by two masons A and B together in 22.5 days. Mason A alone...

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Let $\vec{a}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}, \vec{b}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$ and $\vec{c}=\vec{a} \times \vec{b}$. Let $\vec{d}$ be a vector such that $|\vec{d}-\vec{a}|=\sqrt{11},|\vec{c} \times \vec{d}|=3$ and...

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A cylindrical block of mass $M$ and area of cross section $A$ is floating in a liquid of density $\rho$...

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For the following gas phase equilibrium reaction at constant temperature, $$ \mathrm{NH}_3(\mathrm{~g}) \rightleftharpoons 1 / 2 \mathrm{~N}_2(\mathrm{~g})+3 / 2 \mathrm{H}_2(\mathrm{~g})...

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Let $729,81,9,1, \ldots$. be a sequence and $\mathrm{P}_n$ denote the product of the first $n$ terms of this sequence. If...

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Given below are two statements: Statement I: $\left(\mathrm{CH}_3\right)_3 \stackrel{\oplus}{\mathrm{C}}$ is more stable than $\stackrel{\oplus}{\mathrm{C}} \mathrm{H}_3$ as nine hyperconjugation interactions are...

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Let $\alpha$ and $\beta$ respectively be the maximum and the minimum values of the function $$ f(\theta)=4\left(\sin ^4\left(\frac{7 \pi}{2}-\theta\right)+\sin ^4(11...

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Three charges $+2 q,+3 q$ and $-4 q$ are situated at $(0,-3 a),(2 a, 0)$ and $(-2 a, 0)$ respectively...

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For the thermal decomposition of reaction AB(g), the following is constructed. The half life of the reaction is ' $x$...

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Let the lines $\mathrm{L}_1: \vec{r}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}+\lambda(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}), \lambda \in \mathbb{R} \quad$ and $...

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Let $\mathrm{S}=\{z: 3 \leq 2 z-3(1+\mathrm{i}) \mid \leq 7\}$ be a set of complex numbers. Then $...

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Match the LIST-I with LIST-II Choose the correct answer from

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A wire of uniform resistance $\lambda \Omega / \mathrm{m}$ is bent into a circle of radius $r$ and another piece...

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Let a circle of radius 4 pass through the origin O , the points $\mathrm{A}(-\sqrt{3} a, 0)$ and $\mathrm{B}(0,-\sqrt{2} b)$,...

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Consider the general reaction given below at 400 K $$ x \mathrm{~A}(\mathrm{~g}) \rightleftharpoons y \mathrm{~B}(\mathrm{~g}) . $$ The values of...

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The velocity of sound in air is doubled when the temperature is raised from $0^{\circ} \mathrm{C}$ to $\alpha^{\circ} \mathrm{C}$. The...

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Number of solutions of $\sqrt{3} \cos 2 \theta+8 \cos \theta+3 \sqrt{3}=0, \theta \in[-3 \pi, 2 \pi]$ is :

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Suppose there is a uniform circular disc of mass Mkg and radius rm shown in figure. The shaded regions are...

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Elements X and Y belong to Group 15. The difference between the electronegativity values of ' X ' and phosphorus...

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The vertices $B$ and $C$ of a triangle $A B C$ lie on the line $\frac{x}{1}=\frac{1-y}{-2}=\frac{z-2}{3}$. The coordinates of $A$...

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The correct statements from the following are : A. Ionic radii of trivalent cations of group 13 elements decreases down...

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A ball of radius $r$ and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains...

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The moment of inertia of a square loop made of four uniform solid cylinders, each having radius $R$ and length...

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The size of the images of an object, formed by a thin lens are equal when the object is placed...

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Identify the CORRECT set of details from the following : A. $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$ : Inner orbital complex ; d $...

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Compound ‘P’ undergoes the following sequence of reactions : ‘P’ is :

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The average energy released per fission for the nucleus of ${ }_{92}^{235} \mathrm{U}$ is 190 MeV . When all the...

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Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as...

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Given below are two statements : Statement I: Sublimation is used for the separation and purification of compounds with low...

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A small metallic sphere of diameter 2 mm and density $10.5 \mathrm{~g} / \mathrm{cm}^3$ is dropped in glycerine having viscosity...

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Both human DNA and RNA are chiral molecules. The chirality in DNA and RNA arises due to the presence of

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When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that...

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A simple pendulum of string length 30 cm performs 20 oscillations in 10 s . The length of the string...

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

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The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k=3$ and permeability of $...

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Consider the above electrochemical cell where a metal electrode ( $M$ ) is undergoing redox reaction by forming $...

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The sum of all possible values of $\mathrm{n} \in \mathbf{N}$, so that the coefficients of $x_2 x^2$ and $x^3$ in...

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Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current...

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Identify the molecule $(\mathrm{X})$ with maximum number of lone pairs of electrons (obtained using Lewis dot structure) among $...

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If the function $f(x)=\frac{e^x\left(e^{\tan x-x}-1\right)+\log _e(\sec x+\tan x)-x}{\tan x-x}$ is continuous at $x=0$, then the value of $f(0)$ is equal...

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Let the mean and variance of 8 numbers $-10,-7,-1, x, y, 9,2,16$ be $\frac{7}{2}$ and $\frac{293}{4}$, respectively. Then the mean...

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A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane...

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From the given following (A to D) cyclic structures, those which will not react with Tollen's reagent are :

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A prism of angle $75^{\circ}$ and refractive index $\sqrt{3}$ is coated with thin film of refractive index 1.5 only at...

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The value of $\frac{{ }^{100} C_{50}}{51}+\frac{{ }^{100} C_{51}}{52}+\ldots .+\frac{{ }^{100} C_{100}}{101}$ is:

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It is noticed that $\mathrm{Pb}^{2+}$ is more stable than $\mathrm{Pb}^{4+}$ but $\mathrm{Sn}^{2+}$ is less stable than $\mathrm{Sn}^{4+}$. Observe the following...

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One mole of an ideal diatomic gas expands from volume V to 2 V isothermally at a temperature $27^{\circ} \mathrm{C}$...

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The statements that are incorrect about the nickel(II) complex of dimethylglyoxime are : A. It is red in colour. B....

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Among the statements :

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The de Broglie wavelength of an oxygen molecule at $27^{\circ} \mathrm{C}$ is $x \times 10^{-12} \mathrm{~m}$. The value of $x$...

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For the given logic gate circuit, which of the following is the correct truth table?

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Four persons measure the length of a rod as $20.00 \mathrm{~cm}, 19.75 \mathrm{~cm}, 17.01 \mathrm{~cm}$ and 18.25 cm . The...

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Which of the following pair of nuclei are isobars of the element?

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Given above is the concentration vs time plot for a dissociation reaction : $\mathrm{A} \rightarrow \mathrm{nB}$ Based on the data...

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Consider the following compounds Arrange these compounds in the increasing order of reactivity with nitrating mixture.

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

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An air bubble of volume $2.9 \mathrm{~cm}^3$ rises from the bottom of a swimming pool of 5 m deep. At...

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Given, (A) $\mathrm{n}=5, \mathrm{~m}_{\ell}=-1$ (B) $\mathrm{n}=3,1=2, \mathrm{~m}_{\ell}=-1, \mathrm{~m}_{\mathrm{s}}=+\frac{1}{2}$ The maximum number of electron(s) in an atom that can have the...

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Let $\cos (\alpha+\beta)=-\frac{1}{10}$ and $\sin (\alpha-\beta)=\frac{3}{8}$, where $0

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But-2-yne and hydrogen (one mole each) are separately treated with (i) $\mathrm{Pd} / \mathrm{C}$ and (ii) $\mathrm{Na} /$ liq. $\mathrm{NH}_3$...

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MX is a sparingly soluble salt that follows the given solubility equilibrium at 298 K . $...

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Identify the metal ions among $\mathrm{Co}^{2+}, \mathrm{Ni}^{2+}, \mathrm{Fe}^{2+}, \mathrm{V}^{3+}$ and $\mathrm{Ti}^{2+}$ having a spin-only magnetic moment value more than 3.0...

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Let $S$ be the set of the first 11 natural numbers. Then the number of elements in $...

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Given below are two statements : Statement I: $\left[\mathrm{CoBr}_4\right]^{2-}$ ion will absorb light of lower energy than $\left[\mathrm{CoCl}_4\right]^{2-}$ ion. Statement...

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Let $[\cdot]$ be the greatest integer function. If $\alpha=\int_0^{64}\left(x^{1 / 3}-\left[x^{1 / 3}\right]\right) \mathrm{d} x$, then $...

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Let a vector $\overrightarrow{\mathrm{a}}=\sqrt{2} \hat{i}-\hat{j}+\lambda \hat{k}, \lambda>0$, make an obtuse angle with the vector $\overrightarrow{\mathrm{b}}=-\lambda^2 \hat{i}+4 \sqrt{2} \hat{j}+4 \sqrt{2} \hat{k}$...

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Suppose $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P. and $a^2, 2 b^2, c^2$ are in G.P. If $a

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A cup of water at $5^{\circ} \mathrm{C}$ (system) is placed in a microwave oven and the oven is turned on...

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A substance ${ }^{\prime} \mathrm{X}$ ' ( 1.5 g ) dissolved in 150 g of a solvent ${ }^{\prime} \mathrm{Y}$...

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A thin convex lens of focal length 5 cm and a thin concave lens of focal length 4 cm are...

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Let $n$ be the number obtained on rolling a fair die. If the probability that the system $$ \begin{aligned} &...

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The osmotic pressure of a living cell is 12 atm at 300 K . The strength of sodium chloride solution...

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Consider the following sequence of reactions. Assuming that the reaction proceeds to completion, then 137 mg of 4 -nitrotoluene will...

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Let $[\bullet]$ denote the greatest integer function, and let $f(x)=\min \left\{\sqrt{2} x, x^2\right\}$. Let $\mathrm{S}=\left\{x \in(-2,2)\right.$ : the function $\mathrm{g}(x)=|x|\left[x^2\right]$...

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A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of...

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Let L be the line $\frac{x+1}{2}=\frac{y+1}{3}=\frac{z+3}{6}$ and let S be the set of all points $(\mathrm{a}, \mathrm{b}, \mathrm{c})$ on L...

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Inductance of a coil with $10^4$ turns is 10 mH and it is connected to a dc source of 10...

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' $x$ ' is the product which is obtained from propanenitrile and stannous chloride in the presence of hydrochloric acid...

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The first and second ionization constants of $\mathrm{H}_2 \mathrm{X}$ are $2.5 \times 10^{-8}$ and $1.0 \times 10^{-13}$ respectively. The concentration...

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The value of the integral $\int_{\frac{\pi}{24}}^{\frac{5 \pi}{24}} \frac{\mathrm{~d} x}{1+\sqrt[3]{\tan 2 x}}$ is :

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In the given electrochemical cell, $\mathrm{Ag}(\mathrm{s})|\mathrm{AgCl}(\mathrm{s})| \mathrm{FeCl}_2(\mathrm{aq}), \mathrm{FeCl}_3(\mathrm{aq}) \mid \mathrm{Pt}(\mathrm{s})$ at 298 K , the cell potential $\left(\mathrm{E}_{\text {cell }}\right)$...

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A circular disc has radius $R_1$ and thickness $T_1$. Another circular disc made of the same material has radius $R_2$...

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Let $f(x)=\left\{\begin{array}{ll}\frac{\mathrm{a} x^2+2 \mathrm{ax}+3}{4 x^2+4 x-3} & , x \neq-\frac{3}{2}, \frac{1}{2} \\ \mathrm{~b} & , x=-\frac{3}{2}, \frac{1}{2}\end{array}\right.$ be continuous at...

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A small bob $A$ of mass $m$ is attached to a massless rigid rod of length 1 m pivoted at...

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The correct sequence of reagents for the above conversion of X to Y is :

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A thin prism with angle 5° of refractive index 1.72 is combined with another prism of refractive index 1.9 to...

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On heating a mixture of common salt and $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ in equal amount along with concentrated $\mathrm{H}_2 \mathrm{SO}_4$ in...

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The correct trend in the first ionization enthalpies of the elements in the $3^{\text {rd }}$ period of periodic table...

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If $\alpha$ and $\beta(\alpha

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Two charges $7 \mu \mathrm{C}$ and $-2 \mu \mathrm{C}$ are placed at $(-9,0,0) \mathrm{cm}$ and $(9,0,0) \mathrm{cm}$ respectively in an...

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Given below are two statements: Statement I: The correct order in terms of bond dissociation enthalpy is $\mathrm{Cl}_2>\mathrm{Br}_2>\mathrm{F}_2>\mathrm{I}_2$. Statement II:...

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Which one of the following graphs accurately represents the plot of partial pressure of $\mathrm{CS}_2$ vs its mole fraction in...

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Let $y=y(x)$ be the solution of the differential equation $x^4 \mathrm{~d} y+\left(4 x^3 y+2 \sin x\right) \mathrm{d} x=0$, $x>0, y\left(\frac{\pi}{2}\right)=0$....

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Two shorts dipoles ( $\mathrm{A}, \mathrm{B}$ ), A having charges $\pm 2 \mu \mathrm{C}$ and length 1 cm and B...

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Let $\mathrm{A}=\{-2,-1,0,1,2,3,4\}$. Let R be a relation on A defined by $x \mathrm{Ry}$ if and only if $...

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A paratrooper jumps from an aeroplane and opens a parachute after $2 s$ of free fall and starts deaccelerating with...

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Let the line $y-x=1$ intersect the ellipse $\frac{x^2}{2}+\frac{y^2}{1}=1$ at the points A and B . Then the angle made by...

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Which of the following statements regarding the energy of the stationary state is true in the following one - electron...

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The current passing through a conducting loop in the form of equilateral triangle of side $4 \sqrt{3} \mathrm{~cm}$ is 2...

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parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius...

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A block is sliding down on an inclined plane of slope $\theta$ and at an instant $t=0$ this block is...

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For a closed circuit Daniell cell, which of the following plots is the accurate one at a given temperature?

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Let the domain of the function $f(x)=\log _3 \log _5\left(7-\log _2\left(x^2-10 x+85\right)\right)+\sin ^{-1}\left(\left|\frac{3 x-7}{17-x}\right|\right)$ be ( $\alpha, \beta$ ]. Then...

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The electric field of a plane electromagnetic wave, travelling in an unknown nonmagnetic medium is given by, $$ E_y=20 \sin...

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Let $\vec{a}=2 \hat{i}-\hat{j}+\hat{k}$ and $\vec{b}=\lambda \hat{j}+2 \hat{k}, \lambda \in Z$ be two vectors. Let $\vec{c}=\vec{a} \times \vec{b}$ and $\vec{d}$ be...

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Given below are some of the statements about Mn and $\mathrm{Mn}_2 \mathrm{O}_7$. Identify the correct statements. A. Mn forms the...

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A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio...

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Let $f(x)=[x]^2-[x+3]-3, x \in \mathbf{R}$, where $[\cdot]$ is the greatest integer function. Then Options

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Two loudspeakers ( $L_1$ and $L_2$ ) are placed with a separation of 10 m , as shown in figure....

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A rectangle is formed by the lines $x=0, y=0, x=3$ and $y=4$. Let the line L be perpendicular to $...

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Given below are four compounds: (a) n-propyl choride (b) iso-propyl chloride (c) sec-butyl chloride (d) neo-pentyl chloride Percentage of carbon...

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The internal energy of a monoatomic gas is 3 nRT . One mole of helium is kept in a cylinder...

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Let the locus of the mid-point of the chord through the origin O of the parabola $y^2=4 x$ be the...

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Three identical coils $C_1, C_2$ and $C_3$ are closely placed such that they share a common axis. $C_2$ is exactly...

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The mass of benzanilide obtained from the benzoylation reaction of 5.8 g of aniline, if yield of product is $...

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If the enthalpy of sublimation of Li is $155 \mathrm{~kJ} \mathrm{~mol}^{-1}$, enthalpy of dissociation of $\mathrm{F}_2$ is $150 \mathrm{~kJ} \mathrm{~mol}^{-1}$,...

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Among the statements (S1) : If $\mathrm{A}(5,-1)$ and $\mathrm{B}(-2,3)$ are two vertices of a triangle, whose orthocentre is $(0,0)$, then...

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The correct increasing order of $\mathrm{C}-\mathrm{H}(\mathrm{A}), \mathrm{C}-\mathrm{O}(\mathrm{B}), \mathrm{C}=\mathrm{O}(\mathrm{C})$ and $C \equiv N(D)$ bonds in terms of covalent bond length is:

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Among the following oxides of 3 d elements, the number of mixed oxides are $\_\_\_\_$ $...

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The area of the region $\mathrm{A}=\left\{(x, y): 4 x^2+y^2 \leq 8\right.$ and $\left.y^2 \leq 4 x\right\}$ is:

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Let $\overrightarrow{\mathrm{a}}=-\hat{i}+\hat{j}+2 \hat{k}, \overrightarrow{\mathrm{~b}}=\hat{i}-\hat{j}-3 \hat{k}, \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{d}}=\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{a}}$. Then $(\vec{a}-\vec{b}) \cdot \vec{d}$ is equal to:

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Given below are two statements: Statement I: Crystal Field Stabilization Energy $(\mathrm{CFSE})$ of $\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$ is greater than that of...

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Consider $A \xrightarrow{k_1} B$ and $C \xrightarrow{k_2} D$ are two reactions. If the rate constant $\left(k_1\right)$ of the $...

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If $\lim _{x \rightarrow 0} \frac{\mathrm{e}^{(\mathrm{a}-1) x}+2 \cos \mathrm{~b} x+(\mathrm{c}-2) \mathrm{e}^{-x}}{x \cos x-\log _{\mathrm{e}}(1+x)}=2$, then $\mathrm{a}^2+\mathrm{b}^2+\mathrm{c}^2$ is equal to:

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Match the LIST-I with LIST-II

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An insulated cylinder of volume $60 \mathrm{~cm}^3$ is filled with a gas at $27^{\circ} \mathrm{C}$ and 2 atmospheric pressure, Then...

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Consider the following electrochemical cellin $$ \mathrm{Pt}\left|\mathrm{O}_2(\mathrm{~g})(\mathrm{lbar})\right| \mathrm{HCl}(\mathrm{aq}) \| \mathrm{M}^{2+}(\mathrm{aq}, 1.0 \mathrm{M}) \mid \mathrm{M}(\mathrm{~s}) $$ The pH above which, oxygen...

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If the mean deviation about the median of the numbers $\mathrm{k}, 2 \mathrm{k}, 3 \mathrm{k}, \ldots \ldots, 1000 \mathrm{k}$ is...

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Let $f(x)=\int \frac{\left(2-x^2\right) \cdot \mathrm{e}^x}{(\sqrt{1+x})(1-x)^{3 / 2}} \mathrm{~d} x$. If $f(0)=0$, then $f\left(\frac{1}{2}\right)$ is equal to :

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A conducting circular loop is rotated about its diameter at a constant angular speed of 100rad / s in a...

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The correct order of the rate of the reaction for the following reaction with respect to nucleophiles is :$...

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Let $S$ and $S^{\prime}$ be the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ and $P(\alpha, \beta)$ be a point on the ellipse...

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The energy of first (lowest) Balmer line of H atom is $x \mathrm{~J}$. The energy (in J ) of second...

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A simple pendulum has a bob with mass $m$ and charge q . The pendulum string has negligible mass. When...

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Let the domain of the function $f(x)=\log _3 \log _5 \log _7\left(9 x-x^2-13\right)$ be the interval $(\mathrm{m}, \mathrm{n})$. Let the...

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A cylindrical conductor of length 2 m and area of cross-section $0.2 \mathrm{~mm}^2$ carries an electric current of 1.6 A...

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Let $f$ and $g$ be functions satisfying $f(x+y)=f(x) f(y), f(1)=7$ and $g(x+y)=g(x y), g(1)=1$, for all $x, y \in \mathbf{N}$....

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The correct statements are: A. Activation energy for enzyme catalysed hydrolysis of sucrose is lower than that of acid catalysed...

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If $X=\left[\begin{array}{c}x \\ y \\ z\end{array}\right]$ is a solution of the system of equations $A X=B$, where $...

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Electric field in a region is given by $\vec{E}=A x \hat{i}+B y \hat{j}$, where $A=10 \mathrm{~V} / \mathrm{m}^2$ and $...

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Two masses $m$ and 2 m are connected by a light string going over a pulley (disc) of mass 30...

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If $y=y(x)$ satisfies the differential equation $16(\sqrt{x+9 \sqrt{x}})(4+\sqrt{9+\sqrt{x}}) \cos y \mathrm{~d} y=(1+2 \sin y) \mathrm{d} x, x>0$ and $y(256)=\frac{\pi}{2}, y(49)=\alpha$,...

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Given below are two statements: Statement I: The correct order in terms of atomic/ionic radii is $\mathrm{Al}>\mathrm{Mg}>\mathrm{Mg}^{2+}>\mathrm{Al}^{3+}$. Statement II: The...

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Consider the following reaction : The product Y formed is :

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Dissociation of a gas $\mathrm{A}_2$ takes place according to the following chemical reaction. At equilibrium, the total pressure is 1...

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The volume of an ideal gas increases 8 times and temperature becomes $(1 / 4)^{\text {th }}$ of initial temperature...

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A capacitor $P$ with capacitance $10 \times 10^{-6} \mathrm{~F}$ is fully charged with a potential difference of 6.0 V and...

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The correct order of reactivity of the following benzyl halides towards reaction with KCN is :

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Sodium fusion extract of an organic compound $(\mathrm{Y})$ with $\mathrm{CHCl}_3$ and chlorine water gives violet color to the $\mathrm{CHCl}_3$ layer....

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An electric power line having total resistance of $2 \Omega$, delivers 1 kW of power at 250 ym the percentage...

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Consider an equilateral prism (refractive index $\sqrt{2}$ ). A ray of light is incident on its one surface at a...

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Decomposition of A is a first order reaction at $\mathrm{T}(\mathrm{K})$ and is given by $\mathrm{A}(\mathrm{g}) \longrightarrow \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$. In a closed...

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Which of the following are true for a single slit diffraction ? A. Width of central maxima increases with increase...

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The temperature at which the rate constants of the given below two gaseous reactions become equal is _____K. (Nearest integer)...

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Let ABC be a triangle. Consider four points $\mathrm{p}_1, \mathrm{p}_2, \mathrm{p}_3, \mathrm{p}_4$ on the side AB , five points $...

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$$ \mathrm{A}+2 \mathrm{~B} \longrightarrow \mathrm{AB}_2 $$ 36.0 g of 'A' (Molar mass: $60 \mathrm{~g} \mathrm{~mol}^{-1}$ ) and 56.0 g of...

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If $\frac{\cos ^2 48^{\circ}-\sin ^2 12^{\circ}}{\sin ^2 24^{\circ}-\sin ^2 6^{\circ}}=\frac{\alpha+\beta \sqrt{5}}{2}$, where $\alpha, \beta \in \mathbb{N}$, then $\alpha+\beta$ is equal...

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Consider the following electrochemical cell at 298 K $\mathrm{Pt}\left|\mathrm{HSnO}_2^{-}(\mathrm{aq})\right| \mathrm{Sn}(\mathrm{OH})_6{ }^{2-}(\mathrm{aq})\left|\mathrm{OH}^{-}(\mathrm{aq})\right| \mathrm{Bi}_2 \mathrm{O}_3(\mathrm{~s}) \mid \mathrm{Bi}(\mathrm{s})$. If the reaction quotient at...

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If $\int(\sin x)^{\frac{-11}{2}}(\cos x)^{\frac{-5}{2}} d x=-\frac{p_1}{q_1}(\cot x)^{\frac{9}{2}}-\frac{p_2}{q_2}(\cot x)^{\frac{5}{2}}-\frac{p_3}{q_3}(\cot x)^{\frac{1}{2}}+\frac{p_4}{q_4}(\cot x)^{\frac{-3}{2}}+\mathrm{C}$, where $p_i$ and $q_i$ are positive integers with $\operatorname{gcd}\left(p_i, q_i\right)=1$...

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

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The IUPAC name of the following compound is :

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The correct truth table for the given input data of the following logic gate is : Inputs

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Let $A$ be a $3 \times 3$ matrix such that $A+A^T=O$. If $...

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The cycloalkene ( $X$ ) on bromination consumes one mole of bromine per mole of ( $X$ ) and gives...

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When 1 g of compound $(\mathrm{X})$ is subjected to Kjeldahl's method for estimation of nitrogen, $...

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Let $\alpha=\frac{-1+i \sqrt{3}}{2}$ and $\beta=\frac{-1-i \sqrt{3}}{2}, i=\sqrt{-1}$. If$(7-7 \alpha+9 \beta)^{20}+(9+7 \alpha-7 \beta)^{20}+(-7+9 \alpha+7 \beta)^{20}+(14+7 \alpha+7 \beta)^{20}=m^{10}$

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Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end...

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Given below are two statements: Statement I: The Henry's law constant $\mathrm{K}_{\mathrm{H}}$ is constant with respect to variations in solution's...

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Identify the correct statements : A. Hydrated salts can be used as primary standard. B. Primary standard should not undergo...

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Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio...

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As compared with chlorocyclohexane, which of the following statements correctly apply to chlorobenzene? A. The magnitude of negative charge is...

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If the sum of the first four terms of an A.P. is 6 and the sum of its first six...

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Among $\mathrm{H}_2 \mathrm{~S}, \mathrm{H}_2 \mathrm{O}, \mathrm{NF}_3, \mathrm{NH}_3$ and $\mathrm{CHCl}_3$, identify the molecule $(\mathrm{X})$ with lowest dipole moment value. The number...

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Given below are two statements : Statement I : For a mechanical system of many particles total kinetic energy is...

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Let the solution curve of the differential equation $x d y-y d x=\sqrt{x^2+y^2} d x, x>0, y(1)=0$, be $y=y(x)$. Then...

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Two p -block elements X and Y form fluorides of the type $\mathrm{EF}_3$. The fluoride compound $\mathrm{XF}_3$ is a Lewis...

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Which of the following mixture gives a buffer solution with $\mathrm{pH}=9.25$ ? Given: $\mathrm{pK}_{\mathrm{b}}\left(\mathrm{NH}_4 \mathrm{OH}\right)=4.75$

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In parallax method for the determination of focal length of a concave mirror, the object should always be placed :

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The number of solutions of $\tan ^{-1} 4 x+\tan ^{-1} 6 x=\frac{\pi}{6}$, where $-\frac{1}{2 \sqrt{6}}

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A cylindrical tube $A B$ of length $l$, closed at both ends contains an ideal gas of 1 mol having...

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The correct order of the rate of reaction of the following reactants with nucleophile by $\mathrm{S}_{\mathrm{N}} 1$ mechanism is :...

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' A ' is a neutral organic compound $\left(\mathrm{M} . \mathrm{F}: \mathrm{C}_8 \mathrm{H}_9 \mathrm{ON}\right)$. On treatment with aqueous $...

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Correct statements regarding Arrhenius equation among the following are. A. Factor $e^{-E a / R T}$ corresponds to fraction of...

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A uniform bar of length 12 cm and mass 20 m lies on a smooth horizontal table. Two point masses...

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If the chord joining the points $\mathrm{P}_1\left(x_1, y_1\right)$ and $\mathrm{P}_2\left(x_2, y_2\right)$ on the parabola $y^2=12 x$ subtends a right angle...

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Given below are two statements: Statement I: Sucrose is dextrorotatory. However, sucrose upon hydrolysis gives a solution having mixture of...

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The minimum frequency of photon required to break a particle of mass 15.348 amu into $4 \alpha$ particles is $\_\_\_\_$...

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Given below are two statements : Statement I: Elements ' $X$ ' and ' $Y$ ' are the most and...

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In an open organ pipe $v_3$ and $v_6$ are $3^{\text {rd }}$ and $6^{\text {th }}$ harmonic frequencies, respectively. If...

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The coefficient of $x^{48}$ in $(1+x)+2(1+x)^2+3(1+x)^3+\ldots+100(1+x)^{100}$ is equal to

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Given below are two statements: Statement I: The halogen that makes longest bond with hydrogen in HX, has the smallest...

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$\left[\mathrm{Ni}\left(\mathrm{PPh}_3\right)_2 \mathrm{Cl}_2\right]$ is a paramagnetic complex. Identify the INCORRECT statements about this complex. A. The complex exhibits geometrical isomerism. B....

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Given below are two statements : Statement I: A satellite is moving around earth in the orbit very close to...

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

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The value of $\int_{\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{1}{[x]+4}\right) d x$, where $[\cdot]$ denotes the greatest integer function, is

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Net gravitational force at the center of a square is found to be $F_1$ when four particles having mass M...

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$\mathrm{A} \rightarrow$ product (First order reaction). Three sets of experiment were performed for a reaction under similar experimental conditions: Run...

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The compound $\mathrm{A}, \mathrm{C}_8 \mathrm{H}_8 \mathrm{O}_2$ reacts with acetophenone to form a single product via cross-Aldol condensation. The compound A...

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If $\epsilon, E$ and $t$ represent the free space permittivity, electric field and time respectively, then the unit of $...

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If the domain of the function $f(x)=\sin ^{-1}\left(\frac{5-x}{3+2 x}\right)+\frac{1}{\log _{\varepsilon}(10-x)}$ is $(-\infty, \alpha] \cup[\beta, \gamma)-\{\delta\}$, then $6(\alpha+\beta+\gamma+\delta)$ is equal to

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Given below are two statements: Statement I: Benzene is nitrated to give nitrobenzene, which on further treatment with $...

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At $\mathrm{T}(\mathrm{K}), 100 \mathrm{~g}$ of $98 \% \mathrm{H}_2 \mathrm{SO}_4(\mathrm{w} / \mathrm{w})$ aqueous solution is mixed with 100 g of $...

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If $\mathrm{A}=\left[\begin{array}{ll}2 & 3 \\ 3 & 5\end{array}\right]$, then the determinant of the matrix $\left(\mathrm{A}^{2025}-3 \mathrm{~A}^{2024}+\mathrm{A}^{2023}\right)$ is

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Consider the following reduction processes : $$ \begin{aligned} & \mathrm{Al}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Al}(\mathrm{~s}), \mathrm{E}^0=-1.66 \mathrm{~V} \\ & \mathrm{Fe}^{3+}+\mathrm{e}^{-} \longrightarrow \mathrm{Fe}^{2+},...

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Let the set of all values of $r$, for which the circles $(x+1)^2+(y+4)^2=r^2$ and $x^2+y^2-4 x-2 y-4=0$ intersect at two...

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Given below are two statements : Statement I: An object moves from position $r_1$ to position $r_2$ under a conservative...

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Given below are two statements Statement I: $\mathrm{C}\mathrm{Po}>\mathrm{O}$ is the correct order in terms of the magnitude of electron gain...

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Choose the correct answer from the options given below:

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The dibromo compound $[P]$ (molecular formula: $\mathrm{C}_9 \mathrm{H}_{10} \mathrm{Br}_2$ ) when heated with excess sodamide followed by treatment with dilute...

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The correct order of reactivity of $\mathrm{CH}_3 \mathrm{Br}$ in methanol with the following nucleophiles is $\mathrm{F}^{-}, \mathrm{I}^{-}, \mathrm{C}_2 \mathrm{H}_5 \mathrm{O}^{-}$and...

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If the image of the point $\mathrm{P}(1,2, a)$ in the line $\frac{x-6}{3}=\frac{y-7}{2}=\frac{7-\mathrm{z}}{2}$ is $\mathrm{Q}(5, b, \mathrm{c})$, then $a^2+b^2+c^2$ is equal...

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If the line $\alpha x+2 y=1$, where $\alpha \in \mathbb{R}$, does not meet the hyperbola $x^2-9 y^2=9$, then a possible...

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Using a simple pendulum experiment $g$ is determined by measuring its time period $T$. Which of the following plots represent...

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The number of elements in the relation $\mathrm{R}=\left\{(x, y): 4 x^2+y^2

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Let $f:[1, \infty) \rightarrow \mathbb{R}$ be a differentiable function. If $6 \int_1^x f(t) d t=3 x f(x)+x^3-4$ for all $...

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Consider the following data: $\Delta_f \mathrm{H}^{!} \quad($ Methane, g$)=-\mathrm{XkJ} \mathrm{mol}^{-1}$ Enthalpy of sublimation of graphite $=\mathrm{Y} \mathrm{kJ} \mathrm{mol}^{-1}$ Dissociation enthalpy...

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Let $\mathrm{P}(10,2 \sqrt{15})$ be a point on the hyperbola $\frac{x^2}{\mathrm{a}^2}-\frac{y^2}{\mathrm{~b}^2}=1$, whose foci are S and $\mathrm{S}^{\prime}$. If the length of...

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The number of distinct real solutions of the equation $x|x+4|+3|x+2|+10=0$ is

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Figure shows the circuit that contains three resistances ( $9 \Omega$ each) and two inductors ( 4 mH each). The...

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Let $\mathrm{C}_{\mathrm{r}}$ denote the coefficient of $x^{\mathrm{r}}$ in the binomial expansion of $...

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By usual analysis, 1.00 g of compound $(\mathrm{X})$ gave 1.79 g of magnesium pyrophosphate. The percentage of phosphorus in compound...

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Let $\mathrm{S}=\left\{z \in \mathbb{C}: 4 z^2+\bar{z}=0\right\}$. Then $\sum_{z \in \mathrm{~S}}|z|^2$ is equal to:

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The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series...

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Aqueous HCl reacts with $\mathrm{MnO}_2(\mathrm{~s})$ to form $\mathrm{MnCl}_2(\mathrm{aq}), \mathrm{Cl}_2(\mathrm{~g})$ and $\mathrm{H}_2 \mathrm{O}(l)$. What is the weight (in g ) of...

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If a random variable X has the probability distribution then $\mathrm{P}(3

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Five positive charges each having charge $q$ are placed at the vertices of a pentagon as shown in the figure....

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Let $\alpha, \beta$ be the roots of the quadratic equation $12 x^2-20 x+3 \lambda=0, \lambda \in Z$. If $...

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Let $\mathrm{P}(\alpha, \beta, \gamma)$ be the point on the line $\frac{x-1}{2}=\frac{y+1}{-3}=z$ at a distance $4 \sqrt{14}$ from the point $(1,-1,0)$...

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Consider two boxes containing ideal gases $A$ and $B$ such that their temperatures, pressures and number densities are same. The...

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Let $f(x)=x^{2025}-x^{2000}, x \in[0,1]$ and the minimum value of the function $f(x)$ in the interval $[0,1]$ be $(80)^{80}(n)^{-81}$. Then $n$...

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Consider the above sequence of reactions. The number of bromine atom(s) in the final product (P) will be:

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

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A first row transition metal ( $M$ ) does not liberate $H_2$ gas from dilute HCl .1 mol of aqueous...

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Q JEE MAIN 2026

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

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Q JEE MAIN 2026

Find the correct combination of and D inputs which can cause the LED to glow.

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Consider a solution of $\mathrm{CO}_2(\mathrm{~g})$ dissolved in water in a closed container. Which one of the following plots correctly represents...

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Let the line $x=-1$ divide the area of the region $\left\{(x, y): 1+x^2 \leq y \leq 3-x\right\}$ in the ratio...

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Q JEE MAIN 2026

consider the following spectral lines for atomic hydrogen : A. First line of Paschen series B. Second line of Balmer...

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When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height...

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Two distinct numbers $a$ and $b$ are selected at random from $1,2,3, \ldots, 50$. The probability, that their product ab...

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Given below are two statements : Statement I: The first ionization enthalpy of Cr is lower than that of Mn...

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Given below are two statements: Statement I: Pressure of a fluid is exerted only on a solid surface in contact...

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In the reaction, $2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \rightarrow 2 \mathrm{Al}^{3+}(\mathrm{aq})+6 \mathrm{Cl}^{-}(\mathrm{aq})+3 \mathrm{H}_2(\mathrm{~g})$

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A 'p'-block element $(\mathrm{E})$ and hydrogen form a binary cation $\left(\mathrm{EH}_{\mathrm{x}}\right)^{+}$, while $\mathrm{EH}_3$ on treatment with $\mathrm{K}_2 \mathrm{HgI}_4$ in alkaline...

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3, 3-Dimethyl-2-butanol cannot be prepared by : Choose the correct answer from the options given below :

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Let the relation $R$ on the set $M=\{1,2,3, \ldots, 16\}$ be given by $$ \mathrm{R}=\{(x, y): 4 y=5 x-3, x,...

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The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr...

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A projectile is thrown upward at an angle $60^{\circ}$ with the horizontal. The speed of the projectile is $...

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Given below are two statements: Statement I: Phenol on treatment with $\mathrm{CHCl}_3$ / aq. KOH under refluxing condition, followed by...

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The wavelength of light, while it is passing through water is 540 nm . The refractive index of water is...

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Let $\overrightarrow{\mathrm{AB}}=2 \hat{i}+4 \hat{j}-5 \hat{k}$ and $\overrightarrow{\mathrm{AD}}=\hat{i}+2 \hat{j}+\lambda \hat{k}, \lambda \in \mathbb{R}$. Let the projection of the vector $\vec{v}=\hat{i}+\hat{j}+\hat{k}$ on...

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A meter bridge with two resistances $\mathrm{R}_1$ and $\mathrm{R}_2$ as shown in figure was balanced (null point) at 40 cm...

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The formal changes on the atoms marked as (1) to (4) in the Lewis representation of $\mathrm{HnO}_3$ molecule respectively are

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A laser beam has intensity of $4.0 \times 10^{14} \mathrm{~W} / \mathrm{m}^2$. The amplitude of magnetic field associated with beam...

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Light is incident on a metallic plate having work function $110 \times 10^{-20} \mathrm{~J}$. If the produced photoelectrons have zero...

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In a microscope the objective is having focal length $f_0=2 \mathrm{~cm}$ and eye-piece is having focal length $f_e=4 \mathrm{~cm}$. The...

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The escape velocity from a spherical planet $A$ is $10 \mathrm{~km} / \mathrm{s}$. The escape velocity from another planet $B$...

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10 mole of oxygen is heated at constant volume from $30^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$. The change in the internal...

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Consider the transition metal ions $\mathrm{Mn}^{3+}, \mathrm{Cr}^{3+}, \mathrm{Fe}^{3+}$ and $\mathrm{Co}^{3+}$ and all form low spin octahedral complexes. The correct decreasing...

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The heat generated in 1 minute between points $A$ and $B$ in the given circuit, when a battery of $...

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Two identical thin rods of mass $M \mathrm{~kg}$ and length $L \mathrm{~m}$ are connected as shown in figure. Moment of...

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XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and separation...

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A collimated beam of light of diameter 2 mm is propagating along $x$-axis. The beam is required to be expanded...

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An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at...

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Six point charges are kept $60^{\circ}$ apart from each other on the circumference of a circle of radius $R$ as...

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A point charge of $10^{-8} \mathrm{C}$ is placed at origin. The work done in moving a point charge $...

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$7.9 \mathrm{MeV} \alpha$-particle scatters from a target material of atomic number 79 . From the given data the estimated diameter...

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Initially a satellite of 100 kg is in a circular orbit of radius $1.5 \mathrm{R}_{\mathrm{E}}$. This satellite can be moved...

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Two strings $(A, B)$ having linear densities $\mu_A=2 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ and, $\mu_B=4 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$...

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The given circuit works as :

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A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of...

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An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at...

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A diatomic gas $(\gamma=1.4)$ does 100 J of work when it is expanded isobarically. Then the heat given to the...

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In a Young's double slit experiment set up, the two slits are kept 0.4 mm apart and screen is placed...

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A particle having electric charge $3 \times 10^{-19} \mathrm{C}$ and mass $6 \times 10^{-27} \mathrm{~kg}$ is accelerated by applying an...

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The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal...

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A uniform rod of mass $m$ and length $l$ suspended by means of two identical inextensible light strings as shown...

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An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $\sigma=10 \mathrm{mho} / \mathrm{m}$. The ratio of...

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If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus...

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As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes...

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A body of mass 2 kg is moving along $x$-direction such that its displacement as function of time is given...

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A light wave described by $E=60\left[\sin \left(3 \times 10^{15}\right) t+\sin \left(12 \times 10^{15}\right) t\right]$ (in SI units) falls on a...

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A large drum having radius $R$ is spinning around its axis with angular velocity $\omega$, as shown in figure. The...

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An infinitely long straight wire carrying current $I$ is bent in a planer shape as shown in the diagram. The...

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If P is a point on the circle $x^2+y^2=4, \mathrm{Q}$ is a point on the straight line $5 x+y+2=0$ and...

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The energy of an electron in an orbit of the Bohr's atom is $-0.04 E_0 \mathrm{eV}$ where $\mathrm{E}_0$ is the...

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If $...

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Let the maximum value of $\left(\sin ^{-1} x\right)^2+\left(\cos ^{-1} x\right)^2$ for $x \in\left[-\frac{\sqrt{3}}{2}, \frac{1}{\sqrt{2}}\right]$ be $\frac{m}{n} \pi^2$, where $\operatorname{gcd}(m, n)=1$....

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If $\int_0^1 4 \cot ^{-1}\left(1-2 x+4 x^2\right) \mathrm{d} x=\operatorname{atan}^{-1}(2)-\operatorname{blog}_{\mathrm{e}}(5)$, where $\mathrm{a}, \mathrm{b} \in \mathbf{N}$, then $(2 \mathrm{a}+\mathrm{b})$ is equal to

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Two known resistances of $R \Omega$ and $2 R \Omega$ and one unknown resistance $X \Omega$ are connected in a...

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Let $[\cdot]$ denote the greatest integer function and $f(x)=\lim _{\mathrm{n} \rightarrow \infty} \frac{1}{\mathrm{n}^3} \sum_{\mathrm{k}=1}^{\mathrm{n}}\left[\frac{\mathrm{k}^2}{3^x}\right]$. Then $12 \sum_{\mathrm{j}=1}^{\infty} f(\mathrm{j})$ is equal...

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A river of width 200 m is flowing from west to east with a speed of . A boat, moving...

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The largest $\mathrm{n} \in \mathbf{N}$, for which $7^{\mathrm{n}}$ divides $101!$, is :

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Let z be the complex number satisfying $|z-5| \leq 3$ and having maximum positive principal argument. Then $...

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Surface tension of two liquids (having same densities), $T_1$ and $T_2$, are measured using capillary rise method utilizing two tubes...

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If the system of equations $$ \begin{aligned} & 3 x+y+4 z=3 \\ & 2 x+\alpha y-z=-3 \\ & x+2 y+z=4...

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Let $\mathrm{A}=\{2,3,5,7,9\}$. Let R be the relation on A defined by $x \mathrm{R} y$ if and only if $...

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

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A spherical body of radius $r$ and density $\sigma$ falls freely through a viscous liquid having density $\rho$ and viscosity...

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For a triangle A B C, let $\vec{p}=\overrightarrow{B C}, \vec{q}=\overrightarrow{C A}$ and $\vec{r}=\overrightarrow{B A}$. If $|\vec{p}|=2 \sqrt{3},|\vec{q}|=2$ and $\cos \theta=\frac{1}{\sqrt{3}}$,...

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For the matrices $\mathrm{A}=\left[\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{ll}-29 & 49 \\ -13 & 18\end{array}\right]$, if $...

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Keeping the significant figures in view, the sum of the physical quantities 52.01 m, 153.2 m and 0.123 m is...

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Let $\mathrm{A}=\left\{x:\left|x^2-10\right| \leq 6\right\}$ and $\mathrm{B}=\{x:|x-2|>1\}$. Then

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Let $a_1, \frac{a_2}{2}, \frac{a_3}{2^2}, \ldots, \frac{a_{10}}{2^9}$ be a G.P. of common ratio $\frac{1}{\sqrt{2}}$. If $a_1+a_2+\ldots+a_{10}=62$, then $a_1$ is equal to:

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If the area of the region $\left\{(x, y): 1-2 x \leq y \leq 4-x^2, x \geq 0, y \geq 0\right\}$...

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A random variable X takes values $0,1,2,3$ with probabilities $\frac{2 a+1}{30}, \frac{8 a-1}{30}, \frac{4 a+1}{30}, b$ respectively, where $...

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A battery with EMF $E$ and internal resistance $r$ is connected across a resistance $R$ The power consumption in $R$...

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Given below are two statements : Statement I: In a Young's double slit experiment, the angular separation of fringes will...

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Let $\alpha$ and $\beta$ be the roots of the equation $x^2+2 a x+(3 a+10)=0$ such that $\alpha

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The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of . The frequency of this simple...

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Let the line $\mathrm{L}_1$ be parallel to the vector $-3 \hat{i}+2 \hat{j}+4 \hat{k}$ and pass through the point $(2,6,7)$, and...

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Let the line L pass through the point $(-3,5,2)$ and make equal angles with the positive coordinate axes. If the...

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Consider the following reactions : $$ \begin{aligned} & \mathrm{NaCl}+\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7+\mathrm{H}_2 \mathrm{SO}_4 \rightarrow \mathrm{~A}+\mathrm{KHSO}_4+\mathrm{NaHSO}_4+\mathrm{H}_2 \mathrm{O} \\ & \mathrm{~A}+\mathrm{NaOH} \rightarrow \mathrm{~B}+\mathrm{NaCl}+\mathrm{H}_2...

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The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of...

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Consider the following equation:

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Let one end of a focal chord of the parabola $y^2=16 x$ be $(16,16)$. If $\mathrm{P}(\alpha, \beta)$ divides this focal...

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Use the following data : One mole each of $\mathrm{A}_2(\mathrm{~g})$ and $\mathrm{B}_2(\mathrm{~g})$ are taken in a 1 L closed flask...

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Let $y^2=12 x$ be the parabola with its vertex at O . Let P be a point on the parabola...

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The pH and conductance of a weak acid $(\mathrm{HX})$ was found to be 5 and $4 \times 10^{-5} \mathrm{~S}$, respectively....

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If the line $\alpha x+4 y=\sqrt{7}$, where $\alpha \in \mathbf{R}$, touches the ellipse $3 x^2+4 y^2=1$ at the point P...

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Pre-exponential factors of two different reactions of same order are identical. Let activation energy of first reaction exceeds the activation...

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Two cars A and B each of mass $10^3$kg are moving on parallel tracks separated by a distance of 10...

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Given below are two statements : Statement I: When an electric discharge is passed through gaseous hydrogen, the hydrogen molecules...

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Let $f(x)=x^3+x^2 f^{\prime}(1)+2 x f^{\prime \prime}(2)+f^{\prime \prime \prime}(3), x \in \mathbf{R}$. Then the value of $f^{\prime}(5)$ is:

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For the reaction, $\mathrm{N}_2 \mathrm{O}_4 \rightleftharpoons 2 \mathrm{NO}_2$, graph is plotted as shown below. Identify correct statements. A. Standard free...

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The r.m.s. speed of oxygen molecules at 47ºC is equal to that of the hydrogen molecules kept at ….. ºC....

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Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a twice differentiable function such that $f^{\prime \prime}(x)>0$ for all $x \in \mathbf{R}$ and...

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Which of the following graphs between pressure 'p' versus volume 'V' represents the maximum work done?

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The electric field in a plane electromagnetic wave is given by : $$ E_y=69 \sin \left[0.6 \times 10^3 x-1.8 \times...

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The positive integer $n$, for which the solutions of the equation $x(x+2)+(x+2)(x+4)+\cdots+(x+2 n-2)(x+2 n)=\frac{8 n}{3}$ are two consecutive even integers,...

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Identify the correct statements. A. Arginine and Tryptophan are essential amino acids. B. Histidine does not contain heterocyclic ring in...

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A parallel plate capacitor has capacitance $C$, when there is vacuum within the parallel plates. A sheet having thickness $...

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Identify correct statements from the following : A. Propanal and propanone are functional isomers. B. Ethoxyethane and methoxypropane are metamers....

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$6 \int_0^\pi|(\sin 3 x+\sin 2 x+\sin x)| d x$ is equal to $\_\_\_\_$ .

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Given below are two statements: Statement I: Among $\left.\left[\mathrm{Cu}\left(\mathrm{NH}_3\right)_4\right]^{2+},\left[\mathrm{Ni}(\mathrm{en})_3\right)\right]^{2+},\left[\mathrm{Ni}\left(\mathrm{NH}_3\right)_6\right]^{2+}$ and $\left[\mathrm{Mn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$, $\left[\mathrm{Mn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$ has the maximum number of unpaired...

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A capacitor C is first charged fully with potential difference of V0 and disconnected from the battery. The charged capacitor...

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A current carrying solenoid is placed vertically and a particle of mass $m$ with charge $Q$ is released from rest....

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Given below are two statements : Statement I : The number of species among $\mathrm{SF}_4, \mathrm{NH}_4^{+},\left[\mathrm{NiCl}_4\right]^{2-}, \mathrm{XeF}_4,\left[\mathrm{PiCl}_4\right]^{2-}, \mathrm{SeF}_4$ and $\left.[\mathrm{NiCN})_4\right]^{2-}$,...

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Consider a modified Bernoulli equation. $$ \left(P+\frac{A}{B t^2}\right)+\rho g(h+B t)+\frac{1}{2} \rho V^2=\text { constant } $$ If $t$ has the...

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$\mathrm{MnO}_4{ }^{2-}$, in acidic medium, disproportionates to :

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From the following, the least stable structure is :

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A 4 kg mass moves under the influence of a force $\vec{F}=\left(4 t^3 \hat{i}-3 t \hat{j}\right) \mathrm{N}$ where $t$ is...

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For some $\quad \alpha, \beta \in \mathbf{R}, \quad$ let $\quad A=\left[\begin{array}{ll}\alpha & 2 \\ 1 & 2\end{array}\right] \quad$ and $...

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The total length of potentiometer wire AB is 50 cm in the arrangement as shown in figure. If P is...

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An organic compound " P " of molecular formula $\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_3$ gives positive lodoform test but negative Tollen's test....

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Q JEE MAIN 2026

In an experiment the values of two spring constants were measured as $k_1=(10 \pm 0.2) \mathrm{N} / \mathrm{m}$ and $...

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An organic compound $(\mathrm{P})$ on treatment with aqueous ammonia under hot condition forms compound $(\mathrm{Q})$ which on heating with $\mathrm{Br}_2$...

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Let $S=\{(m, n): m, n \in\{1,2,3, \ldots, 50\}\}$. If the number of elements ( $\mathrm{m}, \mathrm{n}$ ) in S such...

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Let $a_1=1$ and for $n \geq 1, a_{n+1}=\frac{1}{2} a_n+\frac{n^2-2 n-1}{n^2(n+1)^2}$. Then $\left|\sum_{n=1}^{\infty}\left(a_n-\frac{2}{n^2}\right)\right|$ is equal to

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Elements $P$ and $Q$ form two types of non-volatile, non-ionizable compounds $P Q$ and $P Q_2$. When 1 g of...

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Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in...

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The charge stored by the capacitor C in the given circuit in the steady state is ….$\mu \mathrm{C}$.

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Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a twice differentiable function such that the quadratic equation $f(x) \mathrm{m}^2-2 f^{\prime}(x) \mathrm{m}+f^{\prime \prime}(x)=0$...

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In Carius method, 0.75 g of an organic compound gave 1.2 g of barium sulphate, find percentage of sulphur (molar...

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Consider two identical metallic spheres of radius R each having charge Q and mass m. Their centers have an initial...

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14.0 g of calcium metal is allowed to react with excess HCl at 1.0 atm pressure and 273 K ....

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Let O be the vertex of the parabola $x^2=4 y$ and Q be any point on it. Let the locus...

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A conducting circular loop of area $1.0 \mathrm{~m}^2$ mmmmm is placed perpendicular to a magnetic field which varies as $...

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The sum of all the roots of the equation $(x-1)^2-5|x-1|+6=0$, is :

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80 mL of a hydrocarbon on mixing with 264 mL of oxygen in a closed U-tube undergoes complete combustion. The...

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A gas based geyser heats water flowing at the rate of 5.0 litres per minute from 27ºC to 87ºC. The...

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The value of $\operatorname{cosec} 10^{\circ}-\sqrt{3} \sec 10^{\circ}$ is equal to :

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Given below are two statements : Statement I: The number of pairs among $\left[\mathrm{SiO}_2, \mathrm{CO}_2\right],\left[\mathrm{SnO}, \mathrm{SnO} \mathrm{O}_2\right],\left[\mathrm{PbO}, \mathrm{PbO}_2\right]$ and $...

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If $x^2+x+1=0$, then the value of $\left(x+\frac{1}{x}\right)^4+\left(x^2+\frac{1}{x^2}\right)^4+\left(x^3+\frac{1}{x^3}\right)^4+\ldots .+\left(x^{25}+\frac{1}{x^{25}}\right)^4$ is:

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Potential energy (V) versus distance (x) is given by the graph. Rank various regions as per the magnitudes of the...

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If the coefficient of x in the expansion of $\left(a x^2+b x+c\right)(1-2 x)^{26}$ is -56 and the coefficients of $x^2$...

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A hydrocarbon ' P ' $\left(\mathrm{C}_4 \mathrm{H}_8\right)$ on reaction with HCl gives an optically active compound ' Q ' $...

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Let PQ and MN be two straight lines touching the circle $x^2+y^2-4 x-6 y-3=0$ at the points A and B...

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Identify A in the following reaction.

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Let $(\alpha, \beta, \gamma)$ be the co-ordinates of the foot of the perpendicular drawn from the point $(5,4,2)$ on the...

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Which of the following represents the correct trend for the mentioned property? A. $\mathrm{F}>\mathrm{P}>\mathrm{S}>\mathrm{B}$ - First lonization Energy B. $\mathrm{Cl}>\mathrm{F}>\mathrm{S}>\mathrm{P}$...

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Consider the following reactions. $\mathrm{PbCl}_2+\mathrm{K}_2 \mathrm{CrO}_4 \rightarrow \mathrm{~A}+2 \mathrm{KCl}$ (Hot solution) $$ \begin{aligned} & \mathrm{A}+\mathrm{NaOH} \rightleftharpoons \mathrm{~B}+\mathrm{Na}_2 \mathrm{CrO}_4 \\ &...

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Let the mean and variance of 7 observations $2,4,10, x, 12,14, y, x>y$, be 8 and 16 respectively. Two numbers...

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The value of $\int_{-\pi / 6}^{\pi / 6}\left(\frac{\pi+4 x^{11}}{1-\sin (|x|+\pi / 6)}\right) d x$ is equal to:

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Let the foci of a hyperbola coincide with the foci of the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$. If the eccentricity of the hyperbola...

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Let $f: \mathbf{R} \rightarrow(0, \infty)$ be a twice differentiable function such that $f(3)=18, f^{\prime}(3)=0$ and $f^{\prime \prime}(3)=4$. Then $...

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The number of strictly increasing functions $f$ from the set $\{1,2,3,4,5,6\}$ to the set $\{1,2,3, \ldots, 9\}$ such that $...

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Let $y=y(x)$ be the solution curve of the differential equation $\left(1+x^2\right) d y+\left(y-\tan ^{-1} x\right) d x=0, y(0)=1$. Then the...

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Let $\vec{c}$ and $\vec{d}$ be vectors such that $|\vec{c}+\vec{d}|=\sqrt{29}$ and $\vec{c} \times(2 \hat{i}+3 \hat{j}+4 \hat{k})=(2 \hat{i}+3 \hat{j}+4 \hat{k}) \times \vec{d}$....

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Let $a_1, a_2, a_3, \ldots$ be a G.P. of increasing positive terms such that $a_2 \cdot a_3 \cdot a_4=64$ and...

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Let $\overrightarrow{\mathrm{a}}=-\hat{i}+2 \hat{j}+2 \hat{k}, \overrightarrow{\mathrm{~b}}=8 \hat{i}+7 \hat{j}-3 \hat{k}$ and $\overrightarrow{\mathrm{c}}$ be a vector such that $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}}$. If $...

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Let a point A lie between the parallel lines $L_1$ and $L_2$ such that its distances from $L_1$ and $L_2$...

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The number of relations, defined on the set $\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}\}$, which are both reflexive and symmetric, is equal...

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Q JEE MAIN 2026

The area of the region, inside the ellipse $x^2+4 y^2=4$ and outside the region bounded by the curves $y=|x|-1$ and...

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If the domain of the function $f(x)=\cos ^{-1}\left(\frac{2 x-5}{11-3 x}\right)+\sin ^{-1}\left(2 x^2-3 x+1\right)$ is the interval $[\alpha, \beta]$, then $...

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