JEE Advanced 2014 Question Paper with Solutions

A rocket is moving in a gravity free space with a constant acceleration of 2 ms –2 along + x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in + x direction with a speed of 0.3 ms –1 relative to the rocket. At the same time, another ball is thrown in - x direction with a speed of 0.2 ms –1 from its right end relative to the rocket. The time in seconds when the two balls hit each other is

If the piston is pushed at a speed of 5 mm s $-$ 1 , the air comes out of the nozzle with a speed of

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

In an atom, the total number of electrons having quantum numbers n = 4, |m l | = 1 and m s = –1/2 is

The correct combination of names for isomeric alcohols with molecular formula C 4 H 10 O is/are

A list of species having the formula XZ 4 is given below. XeF 4 , SF 4 ,SiF 4 , B F 4 − , B r F 4 − , [Cu(NH 3 ) 4 ] 2+ , [FeCl 4 ] 2- , [CoCl 4 ] 2- and [PtCl 4 ] 2- Defining shape on the basis of the location of X and Z atoms, the total number of species having a square planar shape is

Consider the following list of reagents, acidified K 2 Cr 2 O 7 , alkaline KMnO 4 , CuSO 4 , H 2 O 2 , Cl 2 , O 3 , FeCl 3 , HNO 3 and Na 2 S 2 O 3 . The total number of reagents that can oxidise aqueous iodide to iodine is

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

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

Let $a, r, s, t$ be nonzero real numbers. Let $P\,\,\left( {a{t^2},2at} \right),\,\,Q,\,\,\,R\,\,\left( {a{r^2},2ar} \right)$ and $S\,\,\left( {a{s^2},2as} \right)$ be distinct points on the parabola ${y^2} = 4ax$ . Suppose that $PQ$ is the focal chord and lines $QR$ and $PK$ are parallel, where $K$ is the point $(2a,0)$ The value of $r$ is

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

At time t = 0, terminal A in the circuit shown in the figure is connected to B by a key and an alternating current I(t) = I 0 cos ( $\omega$ t), with I 0 = 1 A and $\omega$ = 500 rad s -1 starts flowing in it with the initial direction shown in the figure. At $t = {{7\pi } \over {6\omega }}$ , the key is switched from B to D. Now onwards only A and D are connected. A total charge Q flows from the battery to charge the capacitor fully. If C = 20 $\mu$ F, R = 10 $\Omega$ and the battery is ideal with emf of 50 V, identify the correct statement(s).

A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990 $\Omega$ resistance, it can be converted into a voltmeter of range 0-30V. If connected to a ${{2n} \over {249}}\Omega$ resistance, it becomes an ammeter of range 0-1.5 A. The value of n is

A light source, width emits two wavelengths $\lambda$ 1 = 400 nm and $\lambda$ 2 = 600 nm, is used in a Young's double-slit experiment. If recorded fringe widths for $\lambda$ 1 and $\lambda$ 2 are $\beta$ 1 and $\beta$ 2 and the number of fringes for them within a distance y on one side of the central maximum are m 1 and m 2 , respectively, then

When d $\approx$ a but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height h above the loop. In that case

Let $f:(a,b) \to [1,\infty )$ be a continuous function and g : R $\to$ R be defined as g ( x ) = { 0 , x < a ∫ a x f ( t ) d t , a ≤ x ≤ b ∫ a b f ( t ) d t , x > b Then,

From a point $P\left( {\lambda ,\lambda ,\lambda } \right),$ perpendicular $PQ$ and $PR$ are drawn respectively on the lines $y=x, z=1$ and $y=-x, z=-1.$ If $P$ is such that $\angle QPR$ is a right angle, then the possible value(s) of $\lambda$ is/(are)

Box $1$ contains three cards bearing numbers $1,2,3;$ box $2$ contains five cards bearing numbers $1,2,3,4,5;$ and box $3$ contains seven cards bearing numbers $1,2,3,4,5,6,7.$ A card is drawn from each of the boxes. Let ${x_i}$ be number on the card drawn from the ${i^{th}}$ box, $i=1,2,3.$ The probability that ${x_1},$ , ${x_2},$ ${x_3}$ are in an arithmetic progression, is

Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is

The function $y=f(x)$ is the solution of the differential equation ${{dy} \over {dx}} + {{xy} \over {{x^2} - 1}} = {{{x^4} + 2x} \over {\sqrt {1 - {x^2}} }}\,$ in $(-1,1)$ satisfying $f(0)=0$ . Then $\int\limits_{ - {{\sqrt 3 } \over 2}}^{{{\sqrt 3 } \over 2}} {f\left( x \right)} \,d\left( x \right)$ is

In a galvanic cell, the salt bridge

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

Consider all possible isomeric ketones including stereoisomers of MW = 100. All these isomers are independently reacted with NaBH 4 (Note : stereoisomers are also reacted separately). The total number of ketones that give a racemic product(s) is/are

The pair(s) of reagents that yield paramagnetic species is/are

Among PbS, CuS, HgS, MnS, Ag 2 S, NiS, CoS, Bi 2 S 3 and SnS 2 the total number of black coloured sulphides is