WB JEE 2019

Paper was held on
Sun, May 26, 2019 11:00 AM

## Chemistry

One of the products of the following reaction is P.Structure of P is

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For the reaction below, the product is Q.The compound Q is

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Cyclopentanol on reaction with NaH followed by CS2 and CH3I produces a/an

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The compound, which evolves carbon dioxide on treatment with aqueous solution of sodium bicarbonate at 25$$^\circ$$C, is

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The indicated atom is not a nucleophilic site in

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The charge carried by 1 millimole of Mn+ ions is 193 coulombs. The value of n is

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Which of the following mixtures will have the lowest pH at 298 K?

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Consider the following two first order reactions occurring at 298 K with same initial concentration of A :(1) A $$\to$$

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For the equilibrium, H2O(l) $$\rightleftharpoons$$ H2O(v), which of the following is correct?

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For a van der Waals' gas, the term $$\left( {{{ab} \over {{V^2}}}} \right)$$ represents some

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In the equilibrium, H2 + I2 $$\rightleftharpoons$$ 2HI, if at a given temperature the concentration of the reactants are

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If electrolysis of aqueous CuSO4 solution is carried out using Cu-electrodes, the reaction taking place at the anode is

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Which one of the following electronic arrangements is absurd?

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The quantity hv/KB corresponds to

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In the crystalline solid MSO4 . nH2O of molar mass 250 g mol$$-$$1, the percentage of anhydrous salt is 64 by weight. Th

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At S.T.P. the volume of 7.5 g of a gas is 5.6 L. The gas is

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The half-life period of $${}_{53}{I^{125}}$$ is 60 days. The radioactivity after 180 days will be

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Consider, the radioactive disintegration $${}_{82}{A^{210}}\buildrel {} \over
\longrightarrow B\buildrel {} \over
\lon

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The second ionization energy of the following elements follows the order

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The melting points of (i) BeCl2 (ii) CaCl2 and (iii) HgCl2 follows the order

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Which of these species will have non-zero magnetic moment?

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The first electron affinity of C, N and O will be of the order

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The H - N - H angle in ammonia is 107.6$$^\circ$$ while the H - P - H angle in phosphine is 93.5$$^\circ$$. Relative to

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The reactive species in chlorine bleach is

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The conductivity measurement of a coordination compound of cobalt (III) shows that it dissociates into 3 ions in solutio

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In the Bayer's process, the leaching of alumina is done by using

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Which atomic species cannot be used as a nuclear fuel?

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The molecule/molecules that has/have delocalised lone pair(s) of electrons is/are

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The conformations of n-butane, commonly known as eclipsed, gauche and anti-conformations can be interconverted by

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The correct order of the addition reaction rates of halogen acids with ethylene is

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The total number of isomeric linear dipeptides which can be synthesised from racemic alanine is

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The kinetic study of a reaction like vA $$\to$$ P at 300 K provides the following curve, where concentration is taken in

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At constant pressure, the heat of formation of a compound is not dependent on temperature, when

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A copper coin was electroplated with Zn and then heated at high temperature until there is a change in colour. What will

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Oxidation of allyl alcohol with a peracid gives a compound of molecular formula C3H6O2, which contains an asymmetric car

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Haloform reaction with I2 and KOH will be respond by

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Identify the correct statement(s) :

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Compounds with spin only magnetic moment equivalent to five unpaired electrons are

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Which of the following chemicals may be used to identify three unlabelled beakers containing conc. NaOH, conc. H2SO4 and

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The compound (s), capable of producing achiral compound on heating at 100$$^\circ$$ is/are

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## Mathematics

$$\mathop {\lim }\limits_{x \to {0^ + }} ({x^n}\ln x),\,n > 0$$

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If $$\int {\cos x\log \left( {\tan {x \over 2}} \right)} dx$$ = $$\sin x\log \left( {\tan {x \over 2}} \right)$$ + f(x),

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y = $$\int {\cos \left\{ {2{{\tan }^{ - 1}}\sqrt {{{1 - x} \over {1 + x}}} } \right\}} dx$$ is an equation of a family o

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The value of the integration $$\int\limits_{ - {\pi \over 4}}^{\pi /4} {\left( {\lambda |\sin x| + {{\mu \sin x} \over

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The value of $$\mathop {\lim }\limits_{x \to 0} {1 \over x}\left[ {\int\limits_y^a {{e^{{{\sin }^2}t}}dt - } \int\limits

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If $$\int {{2^{{2^x}}}.\,{2^x}dx} = A\,.\,{2^{{2^x}}} + C$$, then A is equal to

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The value of the integral $$\int\limits_{ - 1}^1 {\left\{ {{{{x^{2015}}} \over {{e^{|x|}}({x^2} + \cos x)}} + {1 \over {

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$$\mathop {\lim }\limits_{n \to \infty } {3 \over n}\left[ {1 + \sqrt {{n \over {n + 3}}} + \sqrt {{n \over {n + 6}}}

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The general solution of the differential equation $$\left( {1 + {e^{{x \over y}}}} \right)dx + \left( {1 - {x \over y}}

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General solution of $${(x + y)^2}{{dy} \over {dx}} = {a^2},a \ne 0$$ is (C is an arbitrary constant)

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Let P(4, 3) be a point on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. If the normal at P in

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If the radius of a spherical balloon increases by 0.1%, then its volume increases approximately by

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The three sides of a right angled triangle are in GP (geometric progression). If the two acute angles be $$\alpha$$ and

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If $$\log _2^6 + {1 \over {2x}} = {\log _2}\left( {{2^{{1 \over x}}} + 8} \right)$$, then the value of x are

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Let z be a complex number such that the principal value of argument, arg z > 0. Then, arg z $$-$$ arg($$-$$ z) is

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The general value of the real angle $$\theta$$, which satisfies the equation, $$(\cos \theta + i\sin \theta )(\cos 2\th

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Let a, b, c be real numbers such that a + b + c < 0 and the quadratic equation ax2 + bx + c = 0 has imaginary roots.

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A candidate is required to answer 6 out of 12 questions which are divided into two parts A and B, each containing 6 ques

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There are 7 greeting cards, each of a different colour and 7 envelopes of same 7 colours as that of the cards. The numbe

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72n + 16n $$-$$1 (n$$ \in $$ N) is divisible by

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The number of irrational terms in the expansion of $${\left( {{3^{{1 \over 8}}} + {5^{{1 \over 4}}}} \right)^{84}}$$ is

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Let A be a square matrix of order 3 whose all entries are 1 and let I3 be the identity matrix of order 3. Then, the matr

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If M is any square matrix of order 3 over R and if M' be the transpose of M, then adj(M') $$-$$ (adj M)' is equal to

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If $$A = \left( {\matrix{
5 & {5x} & x \cr
0 & x & {5x} \cr
0 & 0 & 5 \cr
} } \

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Let A and B be two square matrices of order 3 and AB = O3, where O3 denotes the null matrix of order 3. Then,

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Let P and T be the subsets of k, y-plane defined byP = {(x, y) : x > 0, y > 0 and x2 + y2 = 1}T = {(x, y) : x >

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Let $$f:R \to R$$ be defined by $$f(x) = {x^2} - {{{x^2}} \over {1 + {x^2}}}$$ for all $$x \in R$$. Then,

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Let the relation $$\rho $$ be defined on R as a$$\rho $$b if 1 + ab > 0. Then,

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A problem in mathematics is given to 4 students whose chances of solving individually are $${{1 \over 2}}$$, $${{1 \over

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If X is a random variable such that $$\sigma$$(X) = 2.6, then $$\sigma$$(1 $$-$$ 4X) is equal to

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If $${e^{\sin x}} - {e^{-\sin x}} - 4 = 0$$, then the number of real values of x is

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The angles of a triangle are in the ratio 2 : 3 : 7 and the radius of the circumscribed circle is 10 cm. The length of t

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A variable line passes through a fixed point $$({x_1},{y_1})$$ and meets the axes at A and B. If the rectangle OAPB be c

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A straight line through the point (3, $$-$$2) is inclined at an angle 60$$^\circ$$ to the line $$\sqrt 3 x + y = 1$$. If

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A variable line passes through the fixed point $$(\alpha ,\beta )$$. The locus of the foot of the perpendicular from the

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If the point of intersection of the lines 2ax + 4ay + c = 0 and 7bx + 3by $$-$$ d = 0 lies in the 4th quadrant and is eq

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A variable circle passes through the fixed point A(p, q) and touches X-axis. The locus of the other end of the diameter

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If P(0, 0), Q(1, 0) and R$$\left( {{1 \over 2},{{\sqrt 3 } \over 2}} \right)$$ are three given points, then the centre o

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For the hyperbola $${{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1$$, which of the foll

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S and T are the foci of an ellipse and B is the end point of the minor axis. If STB is equilateral triangle, the eccentr

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The equation of the directrices of the hyperbola $$3{x^2} - 3{y^2} - 18x + 12y + 2 = 0$$ is

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P is the extremity of the latusrectum of ellipse $$3{x^2} + 4{y^2} = 48$$ in the first quadrant. The eccentric angle of

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The direction ratios of the normal to the plane passing through the points (1, 2, $$-$$3), ($$-$$1, $$-$$2, 1) and paral

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The equation of the plane, which bisects the line joining the points (1, 2, 3) and (3, 4, 5) at right angles is

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The limit of the interior angle of a regular polygon of n sides as n $$ \to $$ $$\infty $$ is

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Let f(x) > 0 for all x and f'(x) exists for all x. If f is the inverse function of h and $${h'(x) = {1 \over {1 + \lo

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Consider the function f(x) = cos x2. Then,

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$$\mathop {\lim }\limits_{x \to {0^ + }} {({e^x} + x)^{1/x}}$$

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Let f(x) be a derivable function, f'(x) > f(x) and f(0) = 0. Then,

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Let $$f:[1,3] \to R$$ be a continuous function that is differentiable in (1, 3) an f'(x) = | f(x) |2 + 4 for all x$$ \in

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Let $$a = \min \{ {x^2} + 2x + 3:x \in R\} $$ and $$b = \mathop {\lim }\limits_{\theta \to 0} {{1 - \cos \theta } \over

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Let a > b > 0 and I(n) = a1/n $$-$$ b1/n, J(n) = (a $$-$$ b)1/n for all n $$ \ge $$ 2, then

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Let $$\widehat \alpha $$, $$\widehat \beta $$, $$\widehat \gamma $$ be three unit vectors such that $$\widehat \alpha \,

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The position vectors of the points A, B, C and D are $$3\widehat i - 2\widehat j - \widehat k$$, $$2\widehat i - 3\wideh

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A particle starts at the origin and moves 1 unit horizontally to the right and reaches P1, then it moves $${1 \over 2}$$

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For any non-zero complex number z, the minimum value of | z | + | z $$-$$ 1 | is

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The system of equations$$\eqalign{
& \lambda x + y + 3z = 0 \cr
& 2x + \mu y - z = 0 \cr
& 5x + 7y

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Let f : X $$ \to $$ Y and A, B are non-void subsets of Y, then (where the symbols have their usual interpretation)

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Let S, T, U be three non-void sets and f : S $$ \to $$ T, g : T $$ \to $$ U be so that gof : s $$ \to $$ U is surjective

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The polar coordinate of a point P is $$\left( {2, - {\pi \over 4}} \right)$$. The polar coordinate of the point Q which

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The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then, the eccentricity e is

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The value of $$\mathop {\lim }\limits_{x \to {0^ + }} {x \over p}\left[ {{q \over x}} \right]$$ is

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Let $$f(x) = {x^4} - 4{x^3} + 4{x^2} + c,\,c \in R$$. Then

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The graphs of the polynomial x2 $$-$$ 1 and cos x intersect

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A point is in motion along a hyperbola $$y = {{10} \over x}$$ so that its abscissa x increases uniformly at a rate of 1

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Let $${I_n} = \int\limits_0^1 {{x^n}} {\tan ^{ - 1}}xdx$$. If $${a_n}{I_{n + 2}} + {b_n}{I_n} = {c_n}$$ for all n $$ \ge

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Two particles A and B move from rest along a straight line with constant accelerations f and h, respectively. If A takes

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The area bounded by y = x + 1 and y = cos x and the X-axis, is

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Let x1, x2 be the roots of $${x^2} - 3x + a = 0$$ and x3, x4 be the roots of $${x^2} - 12x + b = 0$$. If $${x_1} < {x

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If $$\theta \in R$$ and $${{1 - i\cos \theta } \over {1 + 2i\cos \theta }}$$ is real number, then $$\theta $$ will be (

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Let $$A = \left[ {\matrix{
3 & 0 & 3 \cr
0 & 3 & 0 \cr
3 & 0 & 3 \cr
} } \right

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Straight lines x $$-$$ y = 7 and x + 4y = 2 intersect at B. Points A and C are so chosen on these two lines such that AB

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Equation of a tangent to the hyperbola 5x2 $$-$$ y2 = 5 and which passes through an external point (2, 8) is

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Let f and g be differentiable on the interval I and let a, b $$ \in $$ I, a < b. Then,

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Consider the function $$f(x) = {{{x^3}} \over 4} - \sin \pi x + 3$$

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## Physics

A ray of light is reflected by a plane mirror. $${\widehat e_0}$$, $$\widehat e$$ and $$\widehat n$$ be the unit vectors

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A parent nucleus X undergoes $$\alpha$$-decay with a half-life of 75000 yrs. The daughter nucleus Y undergoes $$\beta$$-

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A proton and an electron initially at rest are accelerated by the same potential difference. Assuming that a proton is 2

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To which of the following the angular velocity of the electron in the n-th Bohr orbit is proportional?

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In the circuit shown, what will be the current through the 6V zener?

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Each of the two inputs A and B can assume values either 0 or 1. Then which of the following will be equal to $$\overline

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The correct dimensional formula for impulse is given by

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The density of the material of a cube can be estimated by measuring its mass and the length of one of its sides. If the

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Two weights of the mass m1 and m2 (> m1) are joined by an inextensible string of negligible mass passing over a fixed

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A body starts from rest, under the action of an engine working at a constant power and moves along a straight line. The

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Two particles are simultaneously projected in the horizontal direction from a point P at a certain height. The initial v

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Assume that the earth moves around the sun in a circular orbit of radius R and there exists a planet which also move aro

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A compressive force is applied to a uniform rod of rectangular cross-section so that its length decreases by 1%. If the

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A small spherical body of radius r and density $$\rho $$ moves with the terminal velocity v in a fluid of coefficient of

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Two black bodies A and B have equal surface areas are maintained at temperatures 27$$^\circ$$C and 177$$^\circ$$C respec

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What will be the molar specific heat at constant volume of an ideal gas consisting of rigid diatomic molecules?

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Consider the given diagram. An ideal gas is contained in a chamber (left) of volume V and is at an absolute temperature

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Five identical capacitors, of capacitance 20$$\mu$$F each, are connected to a battery of 150V, in a combination as shown

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Eleven equal point charges, all of them having a charge +Q, are placed at all the hour positions of a circular clock of

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A negative charge is placed at the midpoint between two fixed equal positive charges, separated by a distance 2d. If the

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To which of the following quantities, the radius of the circular path of a charged particle moving at right angles to a

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An electric current 'I' enters and leaves a uniform circular wire of radius r through diametrically opposite points. A p

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A current 'I' is flowing along an infinite, straight wire, in the positive Z-direction and the same current is flowing a

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A square conducting loop is placed near an infinitely long current carrying wire with one edge parallel to the wire as s

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What is the current I shown in the given circuit?

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When the value of R in the balanced Wheatstone bridge, shown in the figure, is increased from 5$$\Omega $$ to 7$$\Omega

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When a 60 mH inductor and a resistor are connected in series with an AC voltage source, the voltage leads the current by

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A point object is placed on the axis of a thin convex lens of focal length 0.05 m at a distance of 0.2 m from the lens a

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In Young's experiment for the interference of light, the separation between the slits is d and the distance of the scree

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When the frequency of the light used is changed from $$4 \times {10^{14}}{s^{ - 1}}$$ to $$5 \times {10^{14}}{s^{ - 1}}$

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A capacitor of capacitance C is connected in series with a resistance R and DC source of emf E through a key. The capaci

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A horizontal fire hose with a nozzle of cross-sectional area $${5 \over {\sqrt {21} }} \times {10^{ - 3}}{m^2}$$ deliver

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Two identical blocks of ice move in opposite directions with equal speed and collide with each other. What will be the m

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A particle with charge q moves with a velocity v in a direction perpendicular to the directions of uniform electric and

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A parallel plate capacitor in series with a resistance of 100$$\Omega $$, an inductor of 20 mH and an AC voltage source

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Electrons are emitted with kinetic energy T from a metal plate by an irradiation of light of intensity J and frequency v

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The initial pressure and volume of a given mass of an ideal gas with $$\left( {{{{C_p}} \over {{C_V}}} = \gamma } \right

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A projectile thrown with an initial velocity of 10 ms$$-$$1 at an angle $$\alpha$$ with the horizontal, has a range of 5

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In the circuit shown in the figure all the resistance are identical and each has the value r$$\Omega $$. The equivalent

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A metallic loop is placed in a uniform magnetic field B with the plane of the loop perpendicular to B. Under which condi

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