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

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

View Question The correct order of acidity for the following compounds is :

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

View Question What is the major product of the following reaction?

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

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

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

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

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

View Question 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

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

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

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

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

View Question 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

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

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

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

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

View Question Which of the following has the largest number of atoms?

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

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

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

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

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

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

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

View Question The product in the above reaction is

View Question Which of the following compounds is asymmetric?

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

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

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

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

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

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

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

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

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

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

View Question ## Mathematics

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

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

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

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

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

View Question 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

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

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

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

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

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

View Question 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

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

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

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

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

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

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

View Question 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

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

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

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

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

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

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

View Question 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{

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

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

View Question 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

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

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

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

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

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

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

View Question 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

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

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

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

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

View Question 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

View Question 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.

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

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

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

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

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

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

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

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

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

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

View Question 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 ($$ - $

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

View Question 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

View Question 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) =

View Question 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

View Question 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

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

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

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

View Question 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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question 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

View Question ## 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

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

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

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

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

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

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

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

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

View Question 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

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

View Question 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

View Question 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

View Question 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

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

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

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

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

View Question 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

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

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

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

View Question 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

View Question 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

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

View Question 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

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

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

View Question 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

View Question 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

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

View Question 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

View Question 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

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

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

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

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

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

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

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

View Question