WB JEE 2020

Paper was held on
Sun, Feb 2, 2020 4:30 AM

## Chemistry

For the above three esters, the order of rates of alkaline hydrolysis is

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Ph$$ - $$
CDO$$\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_{Warm}^{50\% aq.NaOH}} $$
Ph$$ - $$
COO$$\mathop H\limi

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The correct order of acidity for the following compounds is :

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The reduction product of ethyl 3-oxobutanoate by NaBH4 in methanol is

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What is the major product of the following reaction?

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The maximum number of electrons in an atom in which the last electron filled has the quantum numbers n = 3, l = 2 and m

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In the face centered cubic lattice structure of gold the closest distance between gold atoms is ('a' being the edge leng

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The equilibrium constant for the following reactions are given at 25$$^\circ $$C$$2A$$ $$\rightleftharpoons$$ B + C, K1

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Among the following, the ion which will be more effective for flocculation of Fe(OH)3 solution is :

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The mole fraction of ethanol in water is 0.08. Its molality is

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5 mL of 0.1 M Pb(NO3)2 is mixed with 10 mL of 0.02 M KI. The amount of PbI2 precipitated will be about

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At 273 K temperature and 76 cm Hg pressure the density of a gas is 1.964 g L-1. The gas is

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Equal masses of ethane and hydrogen are mixed in an empty container at 298 K. The fraction of total pressure exerted by

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An ideal gas expands adiabatically against vacuum. Which of the following is correct for the given process?

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Kf (water) = 1.86 K kg mol-1. The temperature at which ice begins to separate from a mixture of 10 mass % ethylene glyco

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The radius of the first Bohr orbit of a hydrogen atom is 0.53 $$\times {10^-8}$$ cm. The velocity of the electron in the

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Which of the following statements is not true for the reaction, 2F2 + 2H2O $$ \to $$ 4HF + O2 ?

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The number of unpaired electrons in the uranium (92U) atom is

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How and why does the density of liquid water change on prolonged electrolysis?

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The difference between orbital angular momentum of an electron in a 4f -orbital and another electron in a 4s-orbital is

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Which of the following has the largest number of atoms?

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Indicate the correct IUPAC name of the coordination compound shown in the figure.

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What will be the mass of one atom of 12C?

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Bond order of He2, $$He_2^ + $$ and $$He_2^{2 + }$$ are respectively

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To a solution of a colourless efflorescent sodium salt, when dilute acid is added, a colourless gas is evolved along wit

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The reaction for obtaining the metal (M) from its oxide (M2O3) ore is given by$${M_2}{O_3}(s) + 2Al(l)\buildrel {Heat} \

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In the extraction of Ca by electro reduction of molten CaCl2 some CaF2 is added to the electrolyte for the following rea

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The total number of alkyl bromides (including stereoisomers) formed in the reaction $$M{e_3}C - CH = C{H_2} + HBr \to $$

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The product in the above reaction is

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Which of the following compounds is asymmetric?

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For a reaction 2A + B $$ \to $$ P, when concentration of B alone is doubled, t1/2 does not change and when concentration

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A solution is saturated with SrCO3 and SrF2. The $$[CO_3^{2 - }]$$ is found to be 1.2 $$ \times $$ 10-3 M. The concentra

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A homonuclear diatomic gas molecule shows 2-electron magnetic moment. The one-electron and two-electron reduced species

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$$C{H_3} - O - C{H_2} - Cl\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_\Delta ^{aq{.^\Theta }OH}} C{H_3} - O - C{H_

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Which of the following reactions give(s) a meso-compound as the main product?

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For spontaneous polymerisation, which of the following is (are) correct?

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Which of the following statement(s) is/are incorrect?

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SiO2 is attacked by which one/ones of the following?

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$$Me - C \equiv C - Me\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_{EtOH, - 33^\circ C}^{Na/N{H_3}(liq.)}} \underli

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For the following carbocations, the correct order of stability is I. $$^ \oplus C{H_2} - COC{H_3}$$II. $$^ \oplus C{H_2}

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## Mathematics

Let cos$$^{ - 1}\left( {{y \over b}} \right) = \log {\left( {{x \over n}} \right)^n}$$. Then

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Let $$\phi (x) = f(x) + f(1 - x)$$ and $$f(x) < 0$$ in [0, 1], then

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$$\int {{{f(x)\phi '(x) + \phi (x)f'(x)} \over {(f(x)\phi (x) + 1)\sqrt {f(x)\phi (x) - 1} }}dx = } $$

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The value of $$\sum\limits_{n = 1}^{10} {} \int\limits_{ - 2n - 1}^{ - 2n} {{{\sin }^{27}}} x\,dx + \sum\limits_{n = 1}^

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$$\int\limits_0^2 {[{x^2}]} \,dx$$ is equal to

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If the tangent to the curve y2 = x3 at (m2, m3) is also a normal to the curve at (m2, m3), then the value of mM is

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If $${x^2} + {y^2} = {a^2}$$, then $$\int\limits_0^a {\sqrt {1 + {{\left( {{{dy} \over {dx}}} \right)}^2}} dx = } $$

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Let f, be a continuous function in [0, 1], then $$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{j = 0}^n {{1 \over

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Let f be a differentiable function with $$\mathop {\lim }\limits_{x \to \infty } f(x) = 0.$$ If $$y' + yf'(x) - f(x)f'(x

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If $$x\sin \left( {{y \over x}} \right)dy = \left[ {y\sin \left( {{y \over x}} \right) - x} \right]dx,\,x > 0$$ and $

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Let $$f(x) = 1 - \sqrt {({x^2})} $$, where the square root is to be taken positive, then

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If the function $$f(x) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1$$ [a > 0] attains its maximum and minimum at p and q respect

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If a and b are arbitrary positive real numbers, then the least possible value of $${{6a} \over {5b}} + {{10b} \over {3a}

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If 2 log(x + 1) $$ - $$ log(x2 $$ - $$ 1) = log 2, then x =

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The number of complex numbers p such that $$\left| p \right| = 1$$ and imaginary part of p4 is 0, is

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The equation $$z\bar z + (2 - 3i)z + (2 + 3i)\bar z + 4 = 0$$ represents a circle of radius

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The expression ax2 + bx + c (a, b and c are real) has the same sign as that of a for all x if

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In a 12 storied building, 3 persons enter a lift cabin. It is known that they will leave the lift at different floors. I

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If the total number of m-element subsets of the set A = {a1, a2, ..., an} is k times the number of m element subsets con

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Let I(n) = nn, J(n) = 13.5 ......... (2n $$ - $$ 1) for all (n > 1), n $$ \in $$ N, then

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If c0, c1, c2, ......, c15 are the binomial coefficients in the expansion of (1 + x)15, then the value of $${{{c_1}} \ov

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Let A = $$\left( {\matrix{
{3 - t} \cr
{ - 1} \cr
0 \cr
} \matrix{
{} \cr
{} \cr
{} \cr

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Let $$A = \left[ {\matrix{
{12} & {24} & 5 \cr
x & 6 & 2 \cr
{ - 1} & { - 2} & 3 \

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Let $$A = \left( {\matrix{
a & b \cr
c & d \cr
} } \right)$$ be a 2 $$ \times $$ 2 real matrix with

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If $$\left| {\matrix{
{{a^2}} & {bc} & {{c^2} + ac} \cr
{{a^2} + ab} & {{b^2}} & {ca} \cr
{

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If f : S $$ \to $$ R, where S is the set of all non-singular matrices of order 2 over R and $$f\left[ {\left( {\matrix{

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Let the relation p be defined on R by a p b holds if and only if a $$ - $$ b is zero or irrational, then

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The unit vector in ZOX plane, making angles $$45^\circ $$ and $$60^\circ $$ respectively with $$\alpha = 2\widehat i +

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Four persons A, B, C and D throw an unbiased die, turn by turn, in succession till one gets an even number and win the g

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A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of rounds he must fire

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$$\cos (2x + 7) = a(2 - \sin x)$$ can have a real solution for

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The differential equation of the family of curves y = ex (A cos x + B sin x) where, A, B are arbitrary constants is

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The equation $$r\,\cos \left( {\theta - {\pi \over 3}} \right) = 2$$ represents

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The locus of the centre of the circles which touch both the circles x2 + y2 = a2 and x2 + y2 = 4ax externally is

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Let each of the equations x2 + 2xy + ay2 = 0 and ax2 + 2xy + y2 = 0 represent two straight lines passing through the ori

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A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at P and Q respectively. Th

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Area in the first quadrant between the ellipses x2 + 2y2 = a2 and 2x2 + y2 = a2 is

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The equation of circle of radius $$\sqrt {17} $$ unit, with centre on the positive side of X-axis and through the point

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The length of the chord of the parabola y2 = 4ax(a > 0) which passes through the vertex and makes an acute angle $$\a

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A double ordinate PQ of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ is such that $$\Delta OP

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If B and B' are the ends of minor axis and S and S' are the foci of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over

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The equation of the latusrectum of a parabola is x + y = 8 and the equation of the tangent at the vertex is x + y = 12.

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The equation of the plane through the point $$(2, - 1, - 3)$$ and parallel to the lines$${{x - 1} \over 2} = {{y + 2} \o

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The sine of the angle between the straight line $${{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}$$ and the pl

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Let f(x) = sin x + cos ax be periodic function. Then,

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The domain of $$f(x) = \sqrt {\left( {{1 \over {\sqrt x }} - \sqrt {x + 1} } \right)} $$ is

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Let $$y = f(x) = 2{x^2} - 3x + 2$$. The differential of y when x changes from 2 to 1.99 is

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If $$\mathop {\lim }\limits_{x \to 0} {\left( {{{1 + cx} \over {1 - cx}}} \right)^{{1 \over x}}} = 4$$, then $$\mathop {

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Let f : R $$ \to $$ R be twice continuously differentiable (or f" exists and is continuous) such that f(0) = f(1) = f'(0

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Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 12$$.Then

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The area of the region$$\{ (x,y):{x^2} + {y^2} \le 1 \le x + y\} $$ is

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In open interval $$\left( {0,\,{\pi \over 2}} \right)$$

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If the line y = x is a tangent to the parabola y = ax2 + bx + c at the point (1, 1) and the curve passes through ($$ - $

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If the vectors $$\alpha = \widehat i + a\widehat j + {a^2}\widehat k,\,\beta = \widehat i + b\widehat j + {b^2}\wideha

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Let z1 and z2 be two imaginary roots of z2 + pz + q = 0, where p and q are real. The points z1, z2 and origin form an eq

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If P(x) = ax2 + bx + c and Q(x) = $$ - $$ax2 + dx + c, where ac $$ \ne $$ 0 [a, b, c, d are all real], then P(x).Q(x) =

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Let $$A = \{ x \in R: - 1 \le x \le 1\} $$ and $$f:A \to A$$ be a mapping defined by $$f(x) = x\left| x \right|$$. Then

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Let $$f(x) = \sqrt {{x^2} - 3x + 2} $$ and $$g(x) = \sqrt x $$ be two given functions. If S be the domain of fog and T b

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Let p1 and p2 be two equivalence relations defined on a non-void set S. Then

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Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. The portion of the tangent at any point of

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Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. The portion of the tangent at any point of

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A line cuts the X-axis at A(7, 0) and the Y-axis at B(0, $$ - $$5). A variable line PQ is drawn perpendicular to AB cutt

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Let $$0 < \alpha < \beta < 1$$. Then, $$\mathop {\lim }\limits_{n \to \infty } \int\limits_{1/(k + \beta )}^{

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$$\mathop {\lim }\limits_{x \to 1} \left( {{1 \over {1nx}} - {1 \over {(x - 1)}}} \right)$$

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Let $$y = {1 \over {1 + x + lnx}}$$, then

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Consider the curve $$y = b{e^{ - x/a}}$$, where a and b are non-zero real numbers. Then

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The area of the figure bounded by the parabola $$x = - 2{y^2},\,x = 1 - 3{y^2}$$ is

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A particle is projected vertically upwards. If it has to stay above the ground for 12 sec, then

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The equation $${x^{{{(\log 3x)}^2}}} - {9 \over 2}\log 3\,x + 5 = 3\sqrt 3 $$ has

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In a certain test, there are n questions. In this test 2n-i students gave wrong answers to at least i questions, where i

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A and B are independent events. The probability that both A and B occur is $${1 \over {20}}$$ and the probability that n

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The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose su

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Consider a tangent to the ellipse $${{{x^2}} \over 2} + {{{y^2}} \over 1} = 1$$ at any point. The locus of the mid-point

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Let $$y = {{{x^2}} \over {{{(x + 1)}^2}(x + 2)}}$$. Then $${{{d^2}y} \over {d{x^2}}}$$ is

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Let $$f(x) = {1 \over 3}x\sin x - (1 - \cos \,x)$$. The smallest positive integer k such that $$\mathop {\lim }\limits_{

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Tangent is drawn at any point P(x, y) on a curve, which passes through (1, 1). The tangent cuts X-axis and Y-axis at A a

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## Physics

The intensity of light emerging from one of the slits in a Young's double slit experiment is found to be 1.5 times the i

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In a Fraunhofer diffraction experiment, a single slit of width 0.5 mm is illuminated by a monochromatic light of wavelen

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If R is the Rydberg constant in cm-1, then hydrogen atom does not emit any radiation of wavelength in the range of

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A nucleus X emits a $$\beta $$-particle to produce a nucleus Y. If their atomic masses are Mx and My respectively, then

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For nuclei with mass number close to 119 and 238, the binding energies per nucleon are approximately 7.6 MeV and 8.6 MeV

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A common emitter transistor amplifier is connected with a load resistance of 6 k$$\Omega $$
. When a small AC signal of

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In the circuit shown, the value of $$\beta $$ of the transistor is 48. If the supplied base current is 200 $$\mu $$A, wh

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The frequency v of the radiation emitted by an atom when an electron jumps from one orbit to another is given by v = k$$

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Consider the vectors $$A = \hat i + \hat j - \hat k$$
,$$B = 2\hat i - \hat j + \hat k$$ and $$C = {1 \over {\sqrt 5 }}\

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A fighter plane, flying horizontally with a speed 360 km/h at an altitude of 500 m drops a bomb for a target straight ah

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A block of mass m rests on a horizontal table with a coefficient of static friction $$\mu $$. What minimum force must be

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A tennis ball hits the floor with a speed v at an angle $$\theta $$ with the normal to the floor. If the collision is in

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The bob of a swinging second pendulum (one whose time period is 2 s) has a small speed v0 at its lowest point. It height

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A steel and a brass wire, each of length 50 cm and cross-sectional area 0.005 cm2 hang from a ceiling and are 15 cm apar

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Which of the following diagrams correctly shows the relation between the terminal velocity vT of a spherical body fallin

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An ideal gas undergoes the cyclic process abca as shown in the given p - V diagramIt rejects 50J of heat during ab and a

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A container AB in the shape of a rectangular parallelopiped of length 5 m is divided internally by a movable partition P

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When 100 g of boiling water at 100$$^\circ $$
C is added into a calorimeter containing 300 g of cold water at 10$$^\circ

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As shown in the figure, a point charge q1 = + 1 $$ \times $$ 10-6 C is placed at the origin in xy-plane and another poin

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Four identical point masses, each of mass m and carrying charge + q are placed at the corners of a square of sides a on

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A very long charged solid cylinder of radius a contains a uniform charge density p. Dielectric constant of the material

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A galvanometer can be converted to a voltmeter of full scale deflection V0 by connecting a series resistance R1 and can

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As shown in the figure, a single conducting wire is bent to form a loop in the form of a circle of radius r concentrical

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As shown in the figure, a wire is bent to form a D-shaped closed loop, carrying current I, where the curved part is a se

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What will be the equivalent resistance between the terminals A and B of the infinite resistive network shown in the figu

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When a DC voltage is applied at the two ends of a circuit kept in a closed box, it is observed that the current graduall

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Consider the circuit shown.If all the cells have negligible internal resistance, what will be the current through the 2$

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Consider a conducting wire of length L bent in the form of a circle of radius R and another conductor of length a (a <

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An object, is placed 60 cm in front of a convex mirror of focal length 30 cm. A plane mirror is now placed facing the ob

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A thin convex lens is placed just above an empty vessel of depth 80 cm. The image of a coin kept at the bottom of the ve

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A conducting circular loop of resistance 20$$\Omega $$
and cross-sectional area 20 $$ \times $$ 10-2 m2 is placed perpe

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A pair of parallel metal plates are kept with a separation d. One plate is at a potential + V and the other is at ground

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A metallic block of mass 20 kg is dragged with a uniform velocity of 0.5 ms-1 on a horizontal table for 2.1 s. The coeff

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Consider an engine that absorbs 130 cal of heat from a hot reservoir and delivers 30 cal heat to a cold reservoir in eac

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Two pith balls, each carrying charge + q are hung from a hook by two springs. It is found that when each charge is tripl

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A point source of light is used in an experiment of photoelectric effects. If the distance between the source and the ph

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Two metallic spheres of equal outer radii are found to have same moment of inertia about their respective diameters. The

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A simple pendulum of length l is displaced, so that its taught string is horizontal and then released. A uniform bar piv

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A 400$$\Omega $$ resistor, a 250 mH inductor and a 2.5 $$\mu $$F capacitor are connected in series with an AC source of

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A charged particle moves with constant velocity in a region, where no effect of gravity is felt but an electrostatic fie

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