WB JEE 2021

Paper was held on
Sat, Jul 17, 2021 4:30 AM

## Chemistry

The exact order of boiling points of the compounds n-pentane, isopentane, butanone and 1-butanol is

View Question
The maximum number of atoms that can be in one plane in the molecule p-nitrobenzonitrile are

View Question
Cyclo [18] carbon is an allotrope of carbon with molecular formula C18. It is a ring of 18 carbon atoms, connected by si

View Question
p-nitro-N, N-dimethylaniline cannot be represented by the resonating structures.

View Question
The relationship between the pair of compounds shown above are respectively

View Question
The exact order of acidity of the compounds p-nitrophenol, acetic acid, acetylene and ethanol is

View Question
The dipeptides which may be obtained from the amino acids glycine, and alanine are

View Question
The compounds A and B above are respectively.

View Question
For a spontaneous reaction at all temperatures which of the following is correct?

View Question
A given amount of Fe2+ is oxidised by x mol of $$MnO_4^ - $$ in acidic medium. The number of moles of $$C{r_2}O_7^{2 - }

View Question
An element crystallises in a body centered cubic lattice. The edge length of the unit cell is 200 pm and the density of

View Question
Molecular velocities of two gases at the same temperature (T) are u1 and u2. Their masses are m1 and m2 respectively. Wh

View Question
When 20 g of naphthoic acid (C11H8O2) is dissolved in 50 g of benzene, a freezing point depression of 2K is observed. Th

View Question
The equilibrium constant for the reaction N2(g) + O2(g) $$\rightleftharpoons$$ 2NO(g) is 4 $$\times$$ 10$$-$$4 at 2000 K

View Question
Under the same reaction conditions, initial concentration of 1.386 mol dm$$-$$3 of a substance becomes half in 40 s and

View Question
Which of the following solutions will have highest conductivity?

View Question
Indicate the products (X) and (Y) in the following reactionsNa2S + nS(n = 1 $$-$$ 8) $$\to$$ (X)Na2SO3 + S $$\to$$ (Y)

View Question
2.5 mL 0.4 M weak monoacidic base (Kb = 1 $$\times$$ 10$$-$$12 at 25$$^\circ$$C) is titrated with 2/15 M HCl in water at

View Question
Solubility products (Ksp) of the salts of types MX, MX2 and M3X at temperature T are 4.0 $$\times$$ 10$$-$$8, 3.2 $$\tim

View Question
The reduction potential of hydrogen half-cell will be negative if

View Question
A saturated solution of BaSO4 at 25$$^\circ$$C is 4 $$\times$$ 10$$-$$5 M. The solubility of BaSO4 in 0.1 M Na2SO4 at th

View Question
A solution is made by a concentrated solution of Co(NO3)2 with a concentrated solution of NaNO2 is 50% acetic acid. A so

View Question
Extraction of a metal (M) from its sulphide ore (M2S) involves the following chemical reactions$$2{M_2}S + 3{O_2}\buildr

View Question
The white precipitate (Y), obtained on passing colorless and odourless gas (X) through an ammoniacal solution of NaCl, l

View Question
Which structure has delocalised $$\pi$$-electrons?

View Question
The H3O+ ions has the following shape

View Question
For the reaction $$_7^{14}N(\alpha ,p)\,{}^{17}O$$, 1.16 MeV (Mass equivalent = 0.00124 amu) of energy is absorbed. Mass

View Question
A solution of NaNO3, when treated with a mixture of Zn dust and 'A' yields ammonia. 'A' can be

View Question
Indicate the number of unpaired electrons in K3[Fe(CN)6] and K4[Fe(CN)6].

View Question
Which of the following compounds have magnetic moment identical with [Cr(H2O)6]3+ ?

View Question
Among the following chlorides the compounds which will be hydrolysed most easily and most slowly in aqueous NaOH solutio

View Question
The products X and Y which are formed in the following sequence of reactions are respectively.

View Question
The atomic masses of helium and neon are 4.0 and 20.0 amu respectively. The value of the de-Broglie wavelength of helium

View Question
The mole fraction of a solute in a binary solution is 0.1 at 298 K, molarity of this solution is same as its molality. D

View Question
5.75 mg of sodium vapour is converted to sodium ion. If the ionisation energy of sodium is 490 kJ mol$$-$$1 and atomic w

View Question
The product(s) in the following sequence of reactions will be

View Question
The compounds X and Y are respectively

View Question
Aqueous solution of HNO3, KOH, CH3COOH and CH3COONa of identical concentration are provided. The pair(s) of solutions wh

View Question
Reaction of silver nitrate solution with phosphorus acid produces

View Question
N2H4 and H2O2 show similarity in

View Question
## Mathematics

If $$I = \mathop {\lim }\limits_{x \to 0} sin\left( {{{{e^x} - x - 1 - {{{x^2}} \over 2}} \over {{x^2}}}} \right)$$, the

View Question
Let f : R $$\to$$ R be such that f(0) = 0 and $$\left| {f'(x)} \right| \le 5$$ for all x. Then f(1) is in

View Question
If $$\int {{{\sin 2x} \over {{{(a + b\cos x)}^2}}}dx} = \alpha \left[ {{{\log }_e}\left| {a + b\cos x} \right| + {a \ov

View Question
Let $$g(x) = \int\limits_x^{2x} {{{f(t)} \over t}dt} $$ where x > 0 and f be continuous function and f(2x) = f(x), then

View Question
$$\int\limits_1^3 {{{\left| {x - 1} \right|} \over {\left| {x - 2} \right| + \left| {x - 3} \right|}}dx} $$ is equal to

View Question
The value of the integral $$\int\limits_{ - {1 \over 2}}^{{1 \over 2}} {{{\left\{ {{{\left( {{{x + 1} \over {x - 1}}} \r

View Question
If $$\int\limits_{{{\log }_e}2}^x {{{({e^x} - 1)}^{ - 1}}dx = {{\log }_e}{3 \over 2}} $$, then the value of x is

View Question
The normal to a curve at P(x, y) meets the X-axis at G. If the distance of G from the origin is twice the abscissa of P

View Question
The differential equation of all the ellipses centred at the origin and have axes as the co-ordinate axes is where $$y^{

View Question
If $$x{{dy} \over {dx}} + y = {{xf(xy)} \over {f'(xy)'}}$$, then | f(xy) | is equal to (where k is an arbitrary positive

View Question
The straight the through the origin which divides the area formed by the curves y = 2x $$-$$ x2, y = 0 and x = 1 into tw

View Question
The value of $$\int\limits_0^5 {\max \{ {x^2},6x - 8\} \,dx} $$ is

View Question
A bulb is placed at the centre of a circular track of radius 10 m. A vertical wall is erected touching the track at a po

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

View Question
let $$\alpha$$, $$\beta$$, $$\gamma$$ be three non-zero vectors which are pairwise non-collinear. if $$\alpha$$ + 3$$\be

View Question
Let f : R $$\to$$ R be given by f(x) = | x2 $$-$$ 1 |, x$$\in$$R. Then,

View Question
Let a, b, c be real numbers, each greater than 1, such that $${2 \over 3}{\log _b}a + {3 \over 5}{\log _c}b + {5 \over 2

View Question
Consider the real valued function h : {0, 1, 2, ...... 100} $$\to$$ R such that h(0) = 5, h(100) = 20 and satisfying h(p

View Question
If |z| = 1 and z $$\ne$$ $$\pm$$ 1, then all the points representing $${z \over {1 - {z^2}}}$$ lie on

View Question
Let C denote the set of all complex numbers. Define A = {(z, w) | z, w$$\in$$C and |z| = |w|}, B = {z, w} | z, w$$\in$$C

View Question
Let $$\alpha$$, $$\beta$$ be the roots of the equation x2 $$-$$ 6x $$-$$ 2 = 0 with $$\alpha$$ > $$\beta$$. If an = $$\a

View Question
For x$$\in$$R, x $$\ne$$ $$-$$1, if $${(1 + x)^{2016}} + x{(1 + x)^{2015}} + {x^2}{(1 + x)^{2014}} + ..... + {x^{2016}}

View Question
Five letter words, having distinct letters, are to be constructed using the letters of the word 'EQUATION' so that each

View Question
What is the number of ways in which an examiner can assign 10 marks to 4 questions, giving not less than 2 marks to any

View Question
The digit in the unit's place of the number 1! + 2! + 3! + .... + 99! is

View Question
If M is a 3 $$\times$$ 3 matrix such that (0, 1, 2) M = (1 0 0), (3, 4 5) M = (0, 1, 0), then (6 7 8) M is equal to

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

View Question
Let A and B two non singular skew symmetric matrices such that AB = BA, then A2B2(ATB)$$-$$1(AB$$-$$1)T is equal to

View Question
If an (> 0) be the nth term of a G.P. then$$\left| {\matrix{
{\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}}

View Question
Let A, B, C be three non-void subsets of set S. Let (A $$\cap$$ C) $$\cup$$ (B $$\cap$$ C') = $$\phi$$ where C' denote t

View Question
Let T and U be the set of all orthogonal matrices of order 3 over R and the set of all non-singular matrices of order 3

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

View Question
The mean and variance of a binomial distribution are 4 and 2 respectively. Then the probability of exactly two successes

View Question
Let $${S_n} = {\cot ^{ - 1}}2 + {\cot ^{ - 1}}8 + {\cot ^{ - 1}}18 + {\cot ^{ - 1}}32 + ....$$ to nth term. Then $$\math

View Question
If a > 0, b > 0 then the maximum area of the parallelogram whose three vertices are O(0, 0), A(a cos$$\theta$$, b sin$$\

View Question
Let A be the fixed point (0, 4) and B be a moving point on X-axis. Let M be the midpoint of AB and let the perpendicular

View Question
A moving line intersects the lines x + y = 0 and x $$-$$ y = 0 at the points A, B respectively such that the area of the

View Question
The locus of the vertices of the family of parabolas $$6y = 2{a^3}{x^2} + 3{a^2}x - 12a$$ is

View Question
A ray of light along $$x + \sqrt 3 y = \sqrt 3 $$ gets reflected upon reaching X-axis, the equation of the reflected ray

View Question
Two tangents to the circle x2 + y2 = 4 at the points A and B meet at M($$-$$4, 0). The area of the quadrilateral MAOB, w

View Question
From a point (d, 0) three normal are drawn to the parabola y2 = x, then

View Question
If from a point P(a, b, c), perpendicular PA and PB are drawn to YZ and ZX-planes respectively, then the equation of the

View Question
The co-ordinate of a point on the auxiliary circle of the ellipse x2 + 2y2 = 4 corresponding to the point on the ellipse

View Question
The locus of the centre of a variable circle which always touches two given circles externally is

View Question
A line with positive direction cosines passes through the point P(2, $$-$$1, 2) and makes equal angle with co-ordinate a

View Question
For $$y = {\sin ^{ - 1}}\left\{ {{{5x + 12\sqrt {1 - {x^2}} } \over {13}}} \right\};\left| x \right| \le 1$$, if $$a(1 -

View Question
f(x) is real valued function such that 2f(x) + 3f($$-$$x) = 15 $$-$$ 4x for all x$$\in$$R. Then f(2) =

View Question
Consider the functions f1(x) = x, f2(x) = 2 + loge x, x > 0. The graphs of the functions intersect

View Question
The equation 6x + 8x = 10x has

View Question
Let f : D $$\to$$ R where D = [$$-$$0, 1] $$\cup$$ [2, 4] be defined by $$f(x) = \left\{ {\matrix{
{x,} & {if} & {x \

View Question
Let f(x) be continuous periodic function with period T. Let $$I = \int\limits_a^{a + T} {f(x)\,dx} $$. Then

View Question
If $$b = \int\limits_0^1 {{{{e^t}} \over {t + 1}}dt} $$, then $$\int\limits_{a - 1}^a {{{{e^{ - t}}} \over {t - a - 1}}}

View Question
The differential of $$f(x) = {\log _e}(1 + {e^{10x}}) - {\tan ^{ - 1}}({e^{5x}})$$ at x = 0 and for dx = 0.2 is

View Question
Given that f : S $$\to$$ R is said to have a fixed point at c of S if f(c) = c. Let f : [1, $$\infty$$) $$\to$$ R be def

View Question
The $$\mathop {\lim }\limits_{x \to \infty } {\left( {{{3x - 1} \over {3x + 1}}} \right)^{4x}}$$ equals

View Question
The area bounded by the parabolas $$y = 4{x^2},y = {{{x^2}} \over 9}$$ and the straight line y = 2 is

View Question
If a($$\alpha$$ $$\times$$ $$\beta$$) + b($$\beta$$ $$\times$$ $$\gamma$$) + c($$\gamma$$ + $$\alpha$$) = 0, where a, b,

View Question
If the tangent at the point P with co-ordinates (h, k) on the curve y2 = 2x3 is perpendicular to the straight line 4x =

View Question
The coefficient of a3b4c5 in the expansion of (bc + ca + ab)6 is

View Question
Three unequal positive numbers a, b, c are such that a, b, c are in G.P. while $$\log \left( {{{5c} \over {2a}}} \right)

View Question
The determinant $$\left| {\matrix{
{{a^2} + 10} & {ab} & {ac} \cr
{ab} & {{b^2} + 10} & {bc} \cr
{ac} & {bc

View Question
Let R be the real line. Let the relations S and T or R be defined by $$S = \{ (x,y):y = x + 1,0

View Question
The plane lx + my = 0 is rotated about its line of intersection with the plane z = 0 through an angle $$\alpha$$. The eq

View Question
The points of intersection of two ellipses $${x^2} + 2{y^2} - 6x - 12y + 20 = 0$$ and $$2{x^2} + {y^2} - 10x - 6y + 15 =

View Question
Let $$I = \int_{\pi /4}^{\pi /3} {{{\sin x} \over x}dx} $$. Then

View Question
If $$\left| {z + i} \right| - \left| {z - 1} \right| = \left| z \right| - 2 = 0$$ for a complex number z, then z is equa

View Question
$$\left| {\matrix{
x & {3x + 2} & {2x - 1} \cr
{2x - 1} & {4x} & {3x + 1} \cr
{7x - 2} & {17x + 6} & {12x -

View Question
The remainder when $${7^{{7^{{7^{{{..}^7}}}}}}}$$ (22 time 7) is divided by 48 is

View Question
Whichever of the following is/are correct?

View Question
A plane meets the co-ordinate axes t the points A, B, C respectively such a way that the centroid of $$\Delta$$ABC is (1

View Question
Let P be a variable point on a circle C and Q be a fixed point outside C. If R is the midpoint of the line segment PQ, t

View Question
$$\mathop {\lim }\limits_{n \to \infty } \left\{ {{{\sqrt n } \over {\sqrt {{n^3}} }} + {{\sqrt n } \over {\sqrt {{{(n +

View Question
Let $$f(x) = \left\{ {\matrix{
{0,} & {if} & { - 1 \le x \le 0} \cr
{1,} & {if} & {x = 0} \cr
{2,} & {if} &

View Question
The greatest and least value of $$f(x) = {\tan ^{ - 1}} - {1 \over 2}\,ln \,x\,on\,\left[ {{1 \over {\sqrt 3 }},\sqrt 3

View Question
Let f and g be periodic functions with the periods T1 and T2 respectively. Then f + g is

View Question
## Physics

A spherical convex surface of power 5 D separates object and image space of refractive indices 1.0 and $$4\over3$$ , res

View Question
In Young's double slit experiment, light of wavelength $$\lambda$$ passes through the double slit and forms interference

View Question
A 12.5 eV electron beam is used to bombard gaseous hydrogen at ground state. The energy level upto which the hydrogen at

View Question
Let r, v, E be the radius of orbit, speed of electron and total energy of electron respectively in H-atom. Which of the

View Question
What is the value of current through the diode in the circuit given?

View Question
For the given logic circuit, the output Y for inputs (A = 0, B = 1) and (A = 0, B = 0) respectively are

View Question
From dimensional analysis, the Rydberg constant can be expressed in terms of electric charge (e), mass (m) and Planck co

View Question
Three blocks are pushed with a force F across a frictionless table as shown in figure above. Let N1 be the contact force

View Question
A block of mass m slides with speed v on a frictionless table towards another stationary block of mass m. A massless spr

View Question
The acceleration versus distance graph for a particle moving with initial velocity 5 m/s is shown in the figure. The vel

View Question
A simple pendulum, consisting of a small ball of mass m attached to a massless string hanging vertically from the ceilin

View Question
In case of projectile motion, which one of the following figures represent variation of horizontal component of velocity

View Question
A uniform thin rod of length L, mass m is lying on a smooth horizontal table. A horizontal impulse P is suddenly applied

View Question
Centre of mass (CM) of three particles of masses 1 kg, 2 kg and 3 kg lies at the point (1, 2, 3) and CM of another syste

View Question
A body of density 1.2 $$\times$$ 103 kg/m3 is dropped from rest from a height 1 m into a liquid to density 2.4 $$\times$

View Question
Two solid spheres S1 and S2 of same uniform density fall from rest under gravity in a viscous medium and after sometime,

View Question
In the given figure, 1 represents isobaric, 2 represents isothermal and 3 represents adiabatic processes of an ideal gas

View Question
If pressure of real gas O2, in a container is given by $$p = {{RT} \over {2V - b}} - {a \over {4{b^2}}}$$, then the mass

View Question
300 g of water at 25$$^\circ$$C is added to 100 g of ice at 0$$^\circ$$C. The final temperature of the mixture is

View Question
The variation of electric field along the Z-axis due to a uniformly charged circular ring of radius a in XY-plane as sho

View Question
A metal sphere of radius R carrying charge q is surrounded by a thick concentric metal shell of inner and outer radii a

View Question
Three infinite plane sheets carrying uniform charge densities $$-$$ $$\sigma$$, 2$$\sigma$$, 4$$\sigma$$ are placed para

View Question
Two point charges +q1 and +q2 are placed a finite distance d apart. It is desired to put a third charge q3 in between th

View Question
Consider two infinitely long wires parallel to Z-axis carrying same current I in the positive z-direction. One wire pass

View Question
A thin charged rod is bent into the shape of a small circle of radius R, the charge per unit length of the rod being $$\

View Question
For two types of magnetic materials A and B, variation of $$1\over\chi$$ ($$\chi$$ : susceptibility) versus temperature

View Question
The rms value of potential difference V shown in the figure is

View Question
The carbon resistor with colour code is shown in the figure. There is no fourth band in the resistor. The value of the r

View Question
Consider a pure inductive AC circuit as shown in the figure. If the average power consumed is P, then

View Question
The cross-section of a reflecting surface is represented by the equation x2 + y2 = R2 as shown in the figure. A ray trav

View Question
For a plane electromagnetic wave, the electric field is given by$$ \overrightarrow{E} = 90\sin (0.5 \times {10^3}x + 1.5

View Question
Two metal wires of identical dimensions are connected in series. If $$\sigma$$1 and $$\sigma$$2 are the electrical condu

View Question
A uniform rod of length L pivoted at one end P is freely rotated in a horizontal plane with an angular velocity $$\omega

View Question
An ideal gas of molar mass M is contained in a very tall vertical cylindrical column in the uniform gravitational field.

View Question
Under isothermal conditions, two soap bubbles of radii a and b coalesce to form a single bubble of radius c. If the exte

View Question
A small bar magnet of dipole moment M is moving with speed v along x-direction towards a small closed circular conductin

View Question
Electric field component of an EM radiation varies with time as E = a (cos$$\omega$$0t + sin$$\omega$$t cos$$\omega$$0t)

View Question
Consider the p - V diagram for 1 mole of an ideal monatomic gas shown in the figure. Which of the following statements i

View Question
The potential energy of a particle of mass 0.02 kg moving along X-axis is given by V = Ax (x $$-$$ 4) J, where x is in m

View Question
A particle of mass m and charge q moving with velocity v enters region-b from region-a along the normal to the boundary

View Question