Q JEE Advanced 2014

Let $z_k=\cos \left(\frac{2 k \pi}{10}\right)+i \sin \left(\frac{2 k \pi}{10}\right) ; k=1,2, \ldots 9$.

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Q JEE Advanced 2014

Let $f_1: R \rightarrow R, f_2:[0, \infty) \rightarrow R, f_3: R \rightarrow R$ and $f_4: R \rightarrow[0, \infty)$ be defined...

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Q JEE Advanced 2014

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Q JEE Advanced 2014

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Q JEE Advanced 2014

Given that for each $\mathbf{a} \in(0,1)$ $ \lim _{h \rightarrow 0^{+}} \int_h^{1-h} t^{-a}(1-t)^{a-1} d t $ exists. Let this limit...

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Q JEE Advanced 2014

Given that for each $\mathrm{a} \in(0,1)$ $ \lim _{h \rightarrow 0^{+}} \int_h^{1-h} t^{-a}(1-t)^{a-1} d t $ exists. Let this limit...

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Q JEE Advanced 2014

Let $\mathrm{a}, \mathrm{r}, \mathrm{s}, \mathrm{t}$ be nonzero real numbers. Let $\mathrm{P}\left(\mathrm{at}^2, 2 \mathrm{at}\right), \mathrm{Q}, \mathrm{R}\left(\mathrm{ar}^2, 2 \mathrm{ar}\right)$ and (as $...

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Q JEE Advanced 2014

Let $a, r, s, t$ be nonzero real numbers. Let $...

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Q JEE Advanced 2014

Box 1 contains three cards bearing numbers $1,2,3$; box 2 contains five cards bearing numbers $1,2,3$, 4,5 ; and box...

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Q JEE Advanced 2014

Box 1 contains three cards bearing numbers $1,2,3$; box 2 contains five cards bearing numbers $1,2,3$, 4,5 ; and box...

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Q JEE Advanced 2014

The following integral $\int_{\frac{\pi}{4}}^{\frac{\pi}{2}}(2 \operatorname{cosec} x)^{17} d x$ is equal to

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Q JEE Advanced 2014

For $x \in(0, \pi)$, the equation $\sin x+2 \sin 2 x-\sin 3 x=3$ has

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Q JEE Advanced 2014

Coefficient of $x^{11}$ in the expansion of $\left(1+x^2\right)^4\left(1+x^3\right)^7\left(1+x^4\right)^{12}$ is

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Q JEE Advanced 2014

Let $f:[0,2] \rightarrow R$ be a function which is continuous on $[0,2]$ and is differentiable on $(0,2)$ with $f(0)=1$. Let...

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Q JEE Advanced 2014

The function $y=f(x)$ is the solution of the differential equation $\frac{d y}{d x}+\frac{x y}{x^2-1}=\frac{x^4+2 x}{\sqrt{1-x^2}}$ in ( $-1,1$ ) satisfying...

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Q JEE Advanced 2014

The common tangents to the circle $x^2+y^2=2$ and the parabola $y^2=8 x$ touch the circle at the points $P$, $Q$...

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Q JEE Advanced 2014

In a triangle the sum of two sides is $x$ and the product of the same two sides is $y$....

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Q JEE Advanced 2014

Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in...

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Q JEE Advanced 2014

Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl...

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Q JEE Advanced 2014

The quadratic equation p(x) = 0 with real coefficients has purely imaginary roots. Then the equation p(p(x)) = 0 has

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Q JEE Advanced 2014

Match the four starting materials (P, Q, R, S) given in List I with the corresponding reaction schemes (I, II,...

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Q JEE Advanced 2014

Different possible thermal decomposition pathways for peroxyesters are shwon below. Match each pathway from List I with an appropriate structure...

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Q JEE Advanced 2014

Match the orbital overlap figures shown in List-I with the description given in List-II and select the correct answer using...

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Q JEE Advanced 2014

Match each coordination compound in List-I with an appropriate pair of characteristics from List-II and select the correct answer using...

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Q JEE Advanced 2014

An aqueous solution of metal ion M1 reacts separately with reagents Q and R in excess to give tetrahedral and...

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Q JEE Advanced 2014

An aqueous solution of metal ion M1 reacts separately with reagents Q and R in excess to give tetrahedral and...

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Q JEE Advanced 2014

Schemes 1 and 2 describe sequential transformation of alkynes M and N. Consider only the major products formed in each...

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Q JEE Advanced 2014

Schemes 1 and 2 describe sequential transformation of alkynes M and N. Consider only the major products formed in each...

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Q JEE Advanced 2014

$\mathbf{X}$ and $\mathbf{Y}$ are two volatile liquids with molar weights of $10 \mathrm{~g} \mathrm{~mol}^{-1}$ and $40 \mathrm{~g} \mathrm{~mol}^{-1}$ respectively. Two...

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Q JEE Advanced 2014

$\mathbf{X}$ and $\mathbf{Y}$ are two volatile liquids with molar weights of $10 \mathrm{~g} \mathrm{~mol}^{-1}$ and $40 \mathrm{~g} \mathrm{~mol}^{-1}$ respectively. Two...

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Q JEE Advanced 2014

The product formed in the reaction of $\mathrm{SOCl}_2$ with white phosphorous is :

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Q JEE Advanced 2014

Under ambient conditions, the total number of gases released as products in the final step of the reaction scheme shown...

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Q JEE Advanced 2014

The major product in the following reaction is :

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Q JEE Advanced 2014

Hydrogen peroxide in its reaction with $\mathrm{KIO}_4$ and $\mathrm{NH}_2 \mathrm{OH}$ respectively, is acting as a

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Q JEE Advanced 2014

The acidic hydrolysis of ether (X) shown below is fastest when :

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Q JEE Advanced 2014

Isomers of hexane, based on their branching, can be divided into three distinct classes as shown in the figure The...

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Q JEE-ADVANCED-2014

Let $n \geq 2$ be an integer. Take $n$ distinct points on a circle and join each pair of points...

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Q JEE-ADVANCED-2014

Let $a, b, c$ be positive integers such that $\frac{b}{a}$ is an integer. If $a, b, c$ are in geometric...

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Q JEE Advanced 2014

For the identification of -naphthol using dye test, it is necesary to use :

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Q JEE Advanced 2014

For the elementary reaction M → N, the rate of disappearance of M increases by a factor of 8 upon...

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Q JEE-ADVANCED-2014

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non-coplanar unit vectors such that the angle between every pair of them is...

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Q JEE Advanced 2014

For the process $ \mathrm{H}_2 \mathrm{O}(\ell) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{~g}) $ at $\mathrm{T}=100^{\circ} \mathrm{C}$ and 1 atmosphere pressure, the correct choice...

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Q JEE-ADVANCED-2014

The value of $\int_0^1 4 x^3\left\{\frac{d^2}{d x^2}\left(1-x^2\right)^5\right\} d x$ is

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Q JEE Advanced 2014

Assuming 2s-2p mixing is NOT operative, the paramagnetic species among the following is :

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Q JEE-ADVANCED-2014

Let $\mathrm{n}_1

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Q JEE-ADVANCED-2014

For a point $P$ in the plane, let $d_1(P)$ and $d_2(P)$ be the distance of the point $P$ from the...

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Q JEE-ADVANCED-2014

Let $f: R \rightarrow R$ and $g: R \rightarrow R$ be respectively given by $f(x)=|x|+1$ and $g(x)=x^2+1$. Define $...

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Q JEE-ADVANCED-2014

The largest value of the non-negative integer a for which $\lim _{x \rightarrow 1}\left\{\frac{-a x+\sin (x-1)+a}{x+\sin (x-1)-1}\right\}^{\frac{1-x}{1-\sqrt{x}}}=\frac{1}{4}$ is

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Q JEE Advanced 2014

A block of mass $m_1=1 \mathrm{~kg}$ another mass $m_2=2 \mathrm{~kg}$, are placed together (see figure) on an inclined plane with...

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Q JEE-ADVANCED-2014

Let $f:[0,4 \pi] \rightarrow[0, \pi]$ be defined by $f(x)=\cos ^{-1}(\cos x)$. The number of points $x \in[0,4 \pi]$ satisfying the...

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Q JEE Advanced 2014

Four combinations of two thin lenses are given in List-I. The radius of curvature of all curved surface is r...

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Q JEE-ADVANCED-2014

The slope of the tangent to the curve $\left(y-x^5\right)^2=x\left(1+x^2\right)^2$ at the point $(1,3)$ is

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Q JEE Advanced 2014

Four charge $Q_1, Q_2, Q_3$, and $Q_4$, of same magnitude are fixed along the $x$ axis at $x=-2 a-a,+a$ and...

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Q JEE Advanced 2014

A person in a lift is holding a water jar, which has a small hole at the lower end of...

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Q JEE Advanced 2014

A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube...

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Q JEE Advanced 2014

A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube...

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Q JEE Advanced 2014

In the figure a container is shown to have a movable (without friction) piston on top. The container and the...

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Q JEE Advanced 2014

In the figure a container is shown to have a movable (without friction) piston on top. The container and the...

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Q JEE Advanced 2014

The figure shows a circular loop of radius a with two long parallel wires (numbered 1 and 2) all in...

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Q JEE Advanced 2014

The figure shows a circular loop of radius a with two long parallel wires (numbered 1 and 2) all in...

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Q JEE Advanced 2014

A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index...

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Q JEE-ADVANCED-2014

Let $a \in R$ and let $f: R \rightarrow R$ be given by $f(x)=x^5-5 x+a$. Then

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Q JEE-ADVANCED-2014

A circle $S$ passes through the point $(0,1)$ and is orthogonal to the circles $(x-1)^2+y^2=16$ and $x^2+y^2=1$. Then

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Q _JEE-ADVANCED-2014

Let $f:\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \rightarrow R$ be given by $f(x)=(\log (\sec x+\tan x))^3$. Then

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Q JEE Advanced 2014

Parallel rays of light of intensity $\mathrm{I}=912 \mathrm{Wm}^{-2}$ are incident on a spherical balck body kept in surroundings of temperature...

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Q JEE-ADVANCED-2014

Let $f:(0, \infty) \rightarrow R$ be given by $f(x)=\int_{\frac{1}{x}}^x e^{-\left(t+\frac{1}{t}\right)} \frac{d t}{t}$. Then

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Q JEE Advanced 2014

During an experiment with a metre bridge, the galvanometer shows a null point when the joceky is pressed at 40.0...

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Q JEE-ADVANCED-2014

Let $M$ and $N$ be two $3 \times 3$ matrices such that $M N=N M$. Further, if $M \neq N^2$...

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Q JEE Advanced 2014

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the...

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Q JEE Advanced 2014

A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm . The maximum speeds...

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Q JEE Advanced 2014

A wire, which passes through the hole is a small bead, is bent in the form of quarter of a...

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Q JEE Advanced 2014

If $\lambda_{\mathrm{Cu}}$ is the wavelength of $\mathrm{K}_\alpha \mathrm{X}$-ray line of copper (atomic number 29) and $\lambda_{\text {Mo }}$ is the...

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Q JEE-ADVANCED-2014

From a point $P(\lambda, \lambda, \lambda)$, perpendiculars $P Q$ and $P R$ are drawn respectively on the lines $y=x, z=1$...

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Q JEE Advanced 2014

Charges $Q, 2 Q$ and $4 Q$ are uniformly distributed in three dielectric solid spheres 1,2 and 3 of radii...

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Q JEE-ADVANCED-2014_P1

Let $\vec{x}, \vec{y}$ and $\vec{z}$ be three vectors each of magnitude $\sqrt{2}$ and the angle between each pair of them...

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Q JEE Advanced 2014

A planet of radius $\mathrm{R}=\frac{1}{10} \times$ (radius of Earth) has the same mass density as Earth. Scientists dig a well...

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Q JEE Advanced 2014

A glass capillary tube is of the shape of a truncated cone with an apex angle $\alpha$ so that its...

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Q JEE-ADVANCED-2014

Let M be a 2 × 2 symmetric matrix with integer entries. Then M is invertible if

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Q JEE-ADVANCED-2014

For every pair of continuous functions $\mathrm{f}, \mathrm{g}:[0,1] \rightarrow \mathrm{R}$ such that $\max \{f(x): x \in[0,1]\}=\max \{g(x): x \in[0,1]\}$, the...

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Q JEE-ADVANCED-2014

Let $f:[a, b] \rightarrow[1, \infty)$ be a continuous function and let $g: R \rightarrow R$ be defined as

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Q JEE-ADVANCED-2014

A list of species having the formula $X Z_4$ is given below. $\mathrm{XeF}_4, \mathrm{SF}_4, \mathrm{SiF}_4 . \mathrm{BF}_4{ }^{-}, \mathrm{BrF}_4{ }^{-},\left[\mathrm{Cu}\left(\mathrm{NH}_3\right)_4\right]^{2+},\left[\mathrm{FeCl}_4\right]^{2-},\left[\mathrm{CoCl}_4\right]^{2-}$...

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Q JEE-ADVANCED-2014

Consider all possible isomeric ketones, including stereoisomers of MW $=100$. All these isomers are idependently reacted with $\mathrm{NaBH}_4$ (NOTE :...

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Q JEE-ADVANCED-2014

Among $\mathrm{PbS}, \mathrm{CuS}, \mathrm{HgS}, \mathrm{MnS}, \mathrm{Ag}_2 \mathrm{~S}, \mathrm{NiS}, \mathrm{CoS}, \mathrm{Bi}_2 \mathrm{~S}_3$ and $\mathrm{SnS}_2$, the total number of BLACK coloured sulphides...

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Q JEE-ADVANCED-2014

The total number(s) of stable conformers with non-zero dipole moment for the following compound is (are)

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Q JEE-ADVANCED-2014

Consider the following list of reagents : Acidified $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$, alkaline $\mathrm{KMnO}_4, \mathrm{CuSO}_4, \mathrm{H}_2 \mathrm{O}_2, \mathrm{Cl}_2, \mathrm{O}_3, \mathrm{FeCl}_3, \mathrm{HNO}_3$...

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Q JEE-ADVANCED-2014

$\mathbf{M X}_{\mathbf{2}}$ dissociates into $\mathbf{M}^{\mathbf{2 +}}$ and $\mathbf{X}$ - ions in an aqueous solution, with a degree of dissociation (...

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Q JEE-ADVANCED-2014

A compound $\mathbf{H}_{\mathbf{2}} \mathbf{X}$ with molar weight of 80 g is dissolved in a solvent having density of $...

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Q JEE-ADVANCED-2014

If the value of Avogadro number is $6.023 \times 10^{23} \mathrm{~mol}^{-1}$ and the value of Boltzmann constant is $...

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Q JEE-ADVANCED-2014

The total number of distinct naturally occurring amino acids obtained by complete acidic hydrolysis of the peptide shown below is

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Q JEE-ADVANCED-2014

In an atom, the total number of electrons having quantum numbers $n=4,\left|m_{\ell}\right|=1$ and $\mathrm{m}_{\mathrm{s}}=-1 / 2$ is

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Q JEE-ADVANCED-2014

The correct statement(s) for orthoboric acid is/are

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Q JEE-ADVANCED-2014

An ideal gas in a thermally insulated vessel at internal pressure $=P_1$, volume $=V_1$ and absolute temperature $=T_1$ expands irreversibly...

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Q JEE-ADVANCED-2014

The correct combination of names for isomeric alcohols with molecular formula $\mathrm{C}_4 \mathrm{H}_{10} \mathrm{O}$ is/are

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Q JEE-ADVANCED-2014

The reactivity of compound Z with different halogens under appropriate conditions is given below :

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Q JEE-ADVANCED-2014

Hydrogen bonding plays a central role in the following phenomena :

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Q CHEMISTRY_JEE-ADVANCED-2014_P1

Upon heating with $\mathrm{Cu}_2 \mathrm{~S}$, the reagent(s) that give copper metal is/are

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Q JEE-ADVANCED-2014

In a galvanic cell, the salt bridge

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Q JEE-ADVANCED-2014

In the reaction shown below, the major product(s) formed is/are

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Q JEE-ADVANCED-2014

For the reaction : $$ \mathrm{I}^{-}+\mathrm{ClO}_3^{-}+\mathrm{H}_2 \mathrm{SO}_4 \longrightarrow \mathrm{Cl}^{-}+\mathrm{HSO}_4^{-}+\mathrm{I}_2 $$ The correct statement(s) in the balanced equation is/are :

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Q JEE-ADVANCED-2014

Airplanes $A$ and $B$ are flying with constant velocity in the same vertical plane at angles $30^{\circ}$ and $60^{\circ}$ with...

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Q JEE-ADVANCED-2014

Consider an elliptically shaped rail PQ in the vertical plane with $\mathrm{OP}=3 \mathrm{~m}$ and $\mathrm{OQ}=4 \mathrm{~m}$. A block of mass...

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Q JEE-ADVANCED-2014

A uniform circular disc of mass 1.5 kg and radius 0.5 m is initially at rest on a horizontal frictionless...

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Q JEE-ADVANCED-2014

A horizontal circular platform of radius 0.5 m and mass 0.45 kg is free to rotate about its axis. Two...

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Q JEE-ADVANCED-2014

A rocket is moving in a gravity free space with a constant acceleration of $2 \mathrm{~ms}^{-2}$ along $+x$ direction (see...

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Q JEE-ADVANCED-2014

A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a $4990 \Omega$ resistance, it can...

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Q JEE-ADVANCED-2014

A thermodynamic system is taken form an initial state i with internal energy $\mathrm{U}_{\mathrm{i}}=100 \mathrm{~J}$ to the final state f...

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Q JEE-ADVANCED-2014

To find the distance $d$ over which a signal can be seen clearly in foggy conditions, a railways engineer uses...

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Q JEE-ADVANCED-2014

Durring Searle's experiment, zero of the Vernier scale lies between $3.20 \times 10^{-2} \mathrm{~m}$ and $3.25 \times 10^{-2} \mathrm{~m}$ of...

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Q JEE-ADVANCED-2014

Two parallel wires in the plane of the paper are distance $X_0$ apart. A point charge is moving with speed...

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Q JEE-ADVANCED-2014

At time $\mathrm{t}=0$, terminal A in the circuit shown in the figure is connected to B by a key and...

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Q JEE-ADVANCED-2014

A transparent thin film of uniform thickness and refractive index $n_1=1.4$ is coated on the convex spherical surface of radius...

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Q JEE-ADVANCED-2014

A parallel plate capacitor has a dielectric slab of dielectric constant $K$ between its plates that covers $1 / 3$...

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Q JEE-ADVANCED-2014

A student is performing an experiment using a resonance column and a tuning fork of frequency $244 \mathrm{~s}^{-1}$. He is...

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Q JEE-ADVANCED-2014

Let $E_1(r), E_2(r)$ and $E_3(r)$ be the respective electric fields at a distance $r$ from a point charge $Q$, an...

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Q JEE-ADVANCED-2014

Two ideal batteries of emf $\mathrm{V}_1$ and $\mathrm{V}_2$ and three resistances $\mathrm{R}_1, \mathrm{R}_2$ and $\mathrm{R}_3$ are connected as shown in...

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Q JEE-ADVANCED-2014

In the figure, a ladder of mass $m$ is shown leaning against a wall. It is in static equilibrium making...

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Q JEE-ADVANCED-2014

One end of a taut string of length 3m along the x-axis is fixed at x = 0. The speed...

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Q JEE-ADVANCED-2014

Heater of electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to...

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