Q JEE Advance 2013

Consider the lines $L_1: \frac{x-1}{2}=\frac{y}{-1}=\frac{z+3}{1}, L_2: \frac{x-4}{1}=\frac{y+3}{1}=\frac{z+3}{2}$ and the planes $P_1: 7 x+y+2 z=3$, $P_2: 3 x+5 y-6 z=4$. Let...

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Q JEE Advance 2013

Match List I with List II and select the correct answer using the code given below the lists :

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A line $L: y=m x+3$ meets $y$ - axis at $E(0,3)$ and the arc of the parabola $...

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Of the three independent events $\mathrm{E}_1, \mathrm{E}_2$ and $\mathrm{E}_3$, the probability that only $\mathrm{E}_1$ occurs is $\alpha$, only $\mathrm{E}_2$ occurs...

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A box $B_1$ contains 1 white ball, 3 red balls and 2 black balls. Another box $B_2$ contains 2 white...

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Consider the set of eight vectors $V=\{a \hat{i}+b \hat{j}+c \hat{k}: a, b, c \in\{-1,1\}\}$. Three non-coplanar vectors can be chosen...

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Q JEE Advance 2013

A box $B_1$ contains 1 white ball, 3 red balls and 2 black balls. Another box $B_2$ contains 2 white...

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The coefficients of three consecutive terms of $(1+x)^{n+5}$ are in the ratio $5: 10: 14$. Then $n=$

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A vertical line passing through the point $(h, 0)$ intersects the ellipse $\frac{x^2}{4}+\frac{y^2}{3}=1$ at the points $P$ and $Q$. Let...

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Let $S=S_1 \cap S_2 \cap S_3$, where $$ \begin{aligned} & S_1=\{z \in C:|z|0\right\} \text { and } \\ & S_3:\{z...

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Q JEE Advance 2013

For 3×3 matrices M and N, which of the following statement(s) is (are) NOT correct?

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Q JEE Advance 2013

Let $S=S_1 \cap S_2 \cap S_3$, where $$ \begin{aligned} & S_1=\{z \in C:|z|0\right\} \text { and } \\ & S_3:\{z...

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Q JEE Advance 2013

Let $f(x)=x \sin \pi x, x>0$. Then for all natural numbers $n, f^{\prime}(x)$ vanishes at

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A line $l$ passing through the origin is perpendicular to the lines $$ \begin{aligned} & l_1:(3+\mathrm{t}) \hat{\mathrm{i}}+(-1+2 \mathrm{t}) \hat{\mathrm{j}}+(4+2 \mathrm{t})...

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Q JEE Advance 2013

Let $P Q$ be a focal chord of the parabola $y^2=4 a x$. The tangents to the parabola at $P$...

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Let $S_n=\sum_{k=1}^{4 n}(-1)^{\frac{k(k+1)}{2}} k^2$. Then $S_n$ can take value(s)

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Let $P Q$ be a focal chord of the parabola $y^2=4 a x$. The tangents to the parabola at $P$...

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A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $8: 15$ is converted into an...

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The number of points in $(-\infty, \infty)$, for which $x^2-x \sin x-\cos x=0$, is

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Let $f:\left[\frac{1}{2}, 1\right] \rightarrow R$ (the set of all real numbers) be a positive, non-constant and differentiable function such that...

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A curve passes through the point $\left(1, \frac{\pi}{6}\right)$. Let the slope of the curve at each point $(x, y)$ be...

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The function $f(x)=2|x|+|x+2|-||x+2|-2| x| |$ has a local minimum or a local maximum at $x=$

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The area enclosed by the curves $y=\sin x+\cos x$ and $y=|\cos x-\sin x|$ over the interval $\left[0, \frac{\pi}{2}\right]$ is

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Let $\omega$ be a complex cube root of unity with $\omega \neq 1$ and $\mathrm{P}=\left[\mathrm{p}_{\mathrm{ij}}\right]$ be a $\mathrm{n} \times \mathrm{n}$...

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Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}$. Then the probability that the problem...

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Q JEE Advance 2013

If $3^x=4^{x-1}$, then $x=$

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Let $w=\frac{\sqrt{3}+i}{2}$ and $P=\left\{w^n: n=1,2,3, \ldots.\right\}$. Further $H_1=\left\{z \in C: \operatorname{Re} z>\frac{1}{2}\right\}$ and $H_2=\left\{z \in C: \operatorname{Re} z

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In a triangle $P Q R, P$ is the largest angle and $\cos P=\frac{1}{3}$. Further the incircle of the triangle...

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Two lines $\mathrm{L}_1: \mathrm{x}=5, \frac{\mathrm{y}}{3-\alpha}=\frac{\mathrm{z}}{-2}$ and $\mathrm{L}_2: \mathrm{x}=\alpha, \frac{\mathrm{y}}{-1}=\frac{\mathrm{z}}{2-\alpha}$ are coplanar. Then $\alpha$ can take value(s)

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Circle(s) touching $x$-axis at a distance 3 from the origin and having an intercept of length $2 \sqrt{7}$ on $y$-axis...

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Perpendicular are drawn from points on the line $\frac{x+2}{2}=\frac{y+1}{-1}=\frac{z}{3}$ to the plane $x+y+z=3$. The feet of perpendiculars lie on the...

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For $a \in R$ (the set of all real numbers), $a \neq-1, \lim _{n \rightarrow \infty} \frac{\left(1^a+2^a+\ldots+n^a\right)}{(n+1)^{a-1}[(n a+1)+(n a+2)+\ldots+(n a+n)]}=\frac{1}{60}$....

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For $a>b>c>0$, the distance between $(1,1)$ and the point of intersection of the lines $a x+b y+c=0$ and $...

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Let complex numbers $\alpha$ and $\frac{1}{\bar{\alpha}}$ lies on circles $\left(x-x_0\right)^2+\left(y-y_0\right)^2=r^2$ and $\left(x-x_0\right)^2+\left(y-y_0\right)^2=4 r^2$, respectively. If $\mathrm{z}_0=\mathrm{x}_0+\mathrm{iy}$ satisfies the equation $2\left|\mathrm{z}_0\right|^2=\mathrm{r}^2+2$,...

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Let $\overrightarrow{P R}=3 \hat{i}+\hat{j}-2 \hat{k}$ and $\overrightarrow{S Q}=\hat{i}-3 \hat{j}-4 \hat{k}$ determine diagonals of a parallelogram $P Q R S$ and...

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A tetrapeptide has -COOH group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine (Phe) and alanine (Ala), on...

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The value of $\cot \left(\sum_{n=1}^{23} \cot ^{-1}\left(1+\sum_{k=1}^n 2 k\right)\right)$ is

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EDTA ${ }^4$ is ethylenediaminetetraacetate ion. The total number of $\mathrm{N}-\mathrm{CO}-\mathrm{O}$ bond angles in $[\mathrm{CO}(\text { EDTA })]^{1-}$ complex ion...

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The atomic masses of He and Ne are 4 and 20 a.m.u., respectively. The value of the de Broglie wavelength...

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An aqueous solution ox $\mathbf{X}$ is added slowly to an aqueous solution of $\mathbf{Y}$ as shown in list I ....

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Match the chemical conversions in List I with the appropriate reagents in List II and select the correct answer using...

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The total number of carboxylic acid groups in the product P is

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The total number of lone-pairs of electrons in melamine is

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Among P, Q, R and S, the aromatic compound(s) is/are

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The hyperconjugative stabilities of tert-butyl cation and 2-butene, respectively, are due to

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The reactions of $\mathrm{Cl}_2$ gas with cold-dilute and hot-concentrated NaOH in water give sodium salts to two (different) oxoacids of...

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The reactions of $\mathrm{Cl}_2$ gas with cold-dilute and hot-concentrated NaOH in water give sodium salts to two (different) oxoacids of...

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The initial rate of hydrolysis of methyl acetate $(1 \mathrm{M})$ by a weak acid $(\mathrm{HA}, 1 \mathrm{M})$ is $...

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The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is(are)

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Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s) is (are)

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A fixed mass ' $m$ ' of a gas is subjected to transormation of states from $K$ to $L$ to...

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Sulfide ores are common for the metals

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A fixed mass ' $m$ ' of a gas is subjected to transormation of states from $K$ to $L$ to...

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Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at $25^{\circ} \mathrm{C}$. For this process, the correct statement...

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Upon treatment with ammoniacal $\mathrm{H}_2 \mathrm{~S}$, the metal ion that precipitates as a sulfide is

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$\mathbf{P}$ and $\mathbf{Q}$ are isomers of dicarboxylic acid $\mathrm{C}_4 \mathrm{H}_4 \mathrm{O}_4$. Both decolorize $\mathrm{Br}_2 / \mathrm{H}_2 \mathrm{O}$. On heating, $\mathbf{P}$...

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The arrangement of $\mathrm{X}^{-}$ions around $\mathrm{A}^{+}$ion in solid AX is given in the figure (not drawn to scale). If the...

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Concentrated nitric acid, upon long standing, turns yellow-brown due to the formation of

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$\mathbf{P}$ and $\mathbf{Q}$ are isomers of dicarboxylic acid $\mathrm{C}_4 \mathrm{H}_4 \mathrm{O}_4$. Both decolorize $\mathrm{Br}_2 / \mathrm{H}_2 \mathrm{O}$. On heating, $\mathbf{P}$...

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In the reaction, $$ P+Q \longrightarrow R+S $$ the time taken for $75 \%$ reaction of $P$ is twice the...

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An aqueous solution of a mixture of two inorganic salts, when treated with dilute HCl , gave a precipitate (P)...

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An aqueous solution of a mixture of two inorganic salts, when treated with dilute HCl , gave a precipitate (P)...

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The compound that does NOT liberate $\mathrm{CO}_2$, on treatment with aqueous sodium bicarbonate solution, is

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The thermal dissociation equilibrium of $\mathrm{CaCO}_3(s)$ is studied under different conditions. $$ \mathrm{CaCO}_3(\mathrm{~s}) \rightleftharpoons \mathrm{CaO}(\mathrm{~s})+\mathrm{CO}_2(\mathrm{~g}) $$ For this equilibrium, the...

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KI in acetone, undergoes $S_N 2$ reaction with each $P, Q, R$ and $S$. The rates of the reaction vary...

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The standard enthalpies of formation of $\mathrm{CO}_2(\mathrm{~g}), \mathrm{H}_2 \mathrm{O}(\mathrm{l})$ and glucose $(\mathrm{s})$ at $25^{\circ} \mathrm{C}$ are $...

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The carbon-based reduction method is NOT used for the extraction of

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In the nuclear transmutation $$ { }_4^9 \mathrm{Be}+\mathrm{X} \longrightarrow{ }_4^8 \mathrm{Be}+\mathrm{Y} $$ $(\mathbf{X}, \mathbf{Y})$ is (are)

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A freshly prepared sample of a radioisotope of half-life 1386 s has activity $10^3$ disintegrations per second. Given that $...

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The correct statement(s) about $\mathrm{O}_3$ is (are)

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A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5...

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A bob of mass m , suspended by a string of length $I_1$, is given a minimum velocity required to...

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The work functions of Silver and Sodium are 4.6 and 2.3 eV , respectively. The ratio of the slope of...

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After completion of the reactions (I and II), the organic compound(s) in the reaction mixtures is (are)

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A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of $...

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The major product(s) of the following reaction is (are)

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In the following reaction, the product(s) formed is(are)

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The $\mathrm{K}_{\mathrm{sp}}$ of $\mathrm{Ag}_2 \mathrm{CrO}_4$ is $1.1 \times 10^{-12}$ at 298 K . The solubility (in $\mathrm{mol} / \mathrm{L}$ )...

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Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of...

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One mole of a monatomic ideal gas is taken along two cyclic processes $E \rightarrow F \rightarrow G \rightarrow E$...

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A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of $...

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Match List I with List II and select the correct answer using the codes given below the lists:

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The mass of a nucleus ${ }_Z^A X$ is less that the sum of the masses of $(A-Z)$ number of...

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The mass of a nucleus ${ }_Z^A X$ is less that the sum of the masses of $(A-Z)$ number of...

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A point charge $Q$ is moving in a circular orbit of radius $R$ in the $x-y$ plane with an angular...

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A point charge $Q$ is moving in a circular orbit of radius $R$ in the $x-y$ plane with an angular...

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A thermal power plant produces electric power of 600 kW at 4000 V , which is to be transported to...

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A thermal power plant produces electric power of 600 kW at 4000 V , which is to be transported to...

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A small block of mass 1 kg is released from rest at the top of a rough track. The track...

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A small block of mass 1 kg is released from rest at the top of a rough track. The track...

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A solid sphere of radius $R$ and density $\rho$ is attached to one end of a mass-less spring of force...

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A particle of mass $M$ and positive charge $Q$, moving with a constant velocity $\vec{u}_1=4 \hat{i} \mathrm{~ms}^{-1}$, enters a region...

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The figure below shows the variation of specific heat capacity (C) of a solid as a function of temperature (T)....

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In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C . The switch...

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A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, $y(x$, $...

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Two non-conducting spheres of radii $R_1$ and $R_2$ and carrying uniform volume charge densities $+\rho$ and $-\rho$, respectively, are placed...

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Two non-conducting solid spheres of radii R and $2 R$, having uniform volume charge densities $\rho_1$ and $\rho_2$ respectively, touch...

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Two non-reactive monoatomic ideal gases have their atomic masses in the ratio $2: 3$. The ratio of their partial pressures,...

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In the Young's double slit experiment using a monochromatic light of wavelength $\lambda$, the path difference (in terms of an...

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A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of...

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Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along...

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Two rectangular blocks, having indentical dimensions, can be arranged either in configuration I or in configuration II as shown in...

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A ray of light travelling in the direction $\frac{1}{2}(\hat{i}+\sqrt{3} \hat{j})$ is incident on a plane mirror. After reflection, it travels...

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One end of a horizontal thick copper wire of length $2 L$ and radius $2 R$ is welded to an...

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The work done on a particle of mass $m$ by a force, $K\left[\frac{x}{\left(x^2+y^2\right)^{3 / 2}} \hat{i}+\frac{y}{\left(x^2+y^2\right)^{3 / 2}} \hat{j}\right]$ (...

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The diameter of a cylinder is measured using a vernier callipers with no zero error. It is found that the...

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The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is...

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A particle of mass $m$ is projected from the ground with an initial speed $u_0$ at an angle $\alpha$ with...

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