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WB JEE 2021

Exam Held on Sat Jul 17 2021 04:30:00 GMT+0000 (Coordinated Universal Time)
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Chemistry

The exact order of boiling points of the compounds n-pentane, isopentane, butano...
The maximum number of atoms that can be in one plane in the molecule p-nitrobenz...
Cyclo [18] carbon is an allotrope of carbon with molecular formula C<sub>18</sub...
p-nitro-N, N-dimethylaniline cannot be represented by the resonating structures....
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzwq96np/3cde18...
The exact order of acidity of the compounds p-nitrophenol, acetic acid, acetylen...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzwqjii3/142d1a...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzwqx5yy/df40b8...
For a spontaneous reaction at all temperatures which of the following is correct...
A given amount of Fe<sup>2+</sup> is oxidised by x mol of $$MnO_4^ - $$ in acidi...
An element crystallises in a body centered cubic lattice. The edge length of the...
Molecular velocities of two gases at the same temperature (T) are u<sub>1</sub> ...
When 20 g of naphthoic acid (C<sub>11</sub>H<sub>8</sub>O<sub>2</sub>) is dissol...
The equilibrium constant for the reaction <br/><br/>N<sub>2</sub>(g) + O<sub>2</...
Under the same reaction conditions, initial concentration of 1.386 mol dm<sup>$$...
Which of the following solutions will have highest conductivity?
Indicate the products (X) and (Y) in the following reactions<br/><br/>Na<sub>2</...
2.5 mL 0.4 M weak monoacidic base (K<sub>b</sub> = 1 $$\times$$ 10<sup>$$-$$12</...
Solubility products (K<sub>sp</sub>) of the salts of types MX, MX<sub>2</sub> an...
The reduction potential of hydrogen half-cell will be negative if
A saturated solution of BaSO<sub>4</sub> at 25$$^\circ$$C is 4 $$\times$$ 10<sup...
A solution is made by a concentrated solution of Co(NO<sub>3</sub>)<sub>2</sub> ...
Extraction of a metal (M) from its sulphide ore (M<sub>2</sub>S) involves the fo...
The white precipitate (Y), obtained on passing colorless and odourless gas (X) t...
Which structure has delocalised $$\pi$$-electrons?
The H<sub>3</sub>O<sup>+</sup> ions has the following shape
For the reaction $$_7^{14}N(\alpha ,p)\,{}^{17}O$$, 1.16 MeV (Mass equivalent = ...
A solution of NaNO<sub>3</sub>, when treated with a mixture of Zn dust and 'A' y...
Indicate the number of unpaired electrons in K<sub>3</sub>[Fe(CN)<sub>6</sub>] a...
Which of the following compounds have magnetic moment identical with [Cr(H<sub>2...
Among the following chlorides the compounds which will be hydrolysed most easily...
The products X and Y which are formed in the following sequence of reactions ar...
The atomic masses of helium and neon are 4.0 and 20.0 amu respectively. The valu...
The mole fraction of a solute in a binary solution is 0.1 at 298 K, molarity of ...
5.75 mg of sodium vapour is converted to sodium ion. If the ionisation energy of...
The product(s) in the following sequence of reactions will be<br/> <img src="htt...
The compounds X and Y are respectively<br/><br/> <img src="https://app-content.c...
Aqueous solution of HNO<sub>3</sub>, KOH, CH<sub>3</sub>COOH and CH<sub>3</sub>C...
Reaction of silver nitrate solution with phosphorus acid produces
N<sub>2</sub>H<sub>4</sub> and H<sub>2</sub>O<sub>2</sub> show similarity in

Mathematics

If $$I = \mathop {\lim }\limits_{x \to 0} sin\left( {{{{e^x} - x - 1 - {{{x^2}} ...
Let f : R $$\to$$ R be such that f(0) = 0 and $$\left| {f'(x)} \right| \le 5$$ f...
If $$\int {{{\sin 2x} \over {{{(a + b\cos x)}^2}}}dx} = \alpha \left[ {{{\log }...
Let $$g(x) = \int\limits_x^{2x} {{{f(t)} \over t}dt} $$ where x > 0 and f be con...
$$\int\limits_1^3 {{{\left| {x - 1} \right|} \over {\left| {x - 2} \right| + \le...
The value of the integral $$\int\limits_{ - {1 \over 2}}^{{1 \over 2}} {{{\left\...
If $$\int\limits_{{{\log }_e}2}^x {{{({e^x} - 1)}^{ - 1}}dx = {{\log }_e}{3 \ove...
The normal to a curve at P(x, y) meets the X-axis at G. If the distance of G fro...
The differential equation of all the ellipses centred at the origin and have axe...
If $$x{{dy} \over {dx}} + y = {{xf(xy)} \over {f'(xy)'}}$$, then | f(xy) | is eq...
The straight the through the origin which divides the area formed by the curves ...
The value of $$\int\limits_0^5 {\max \{ {x^2},6x - 8\} \,dx} $$ is
A bulb is placed at the centre of a circular track of radius 10 m. A vertical wa...
Two particles A and B move from rest along a straight line with constant acceler...
let $$\alpha$$, $$\beta$$, $$\gamma$$ be three non-zero vectors which are pairwi...
Let f : R $$\to$$ R be given by f(x) = | x<sup>2</sup> $$-$$ 1 |, x$$\in$$R. The...
Let a, b, c be real numbers, each greater than 1, such that $${2 \over 3}{\log _...
Consider the real valued function h : {0, 1, 2, ...... 100} $$\to$$ R such that ...
If |z| = 1 and z $$\ne$$ $$\pm$$ 1, then all the points representing $${z \over ...
Let C denote the set of all complex numbers. Define A = {(z, w) | z, w$$\in$$C a...
Let $$\alpha$$, $$\beta$$ be the roots of the equation x<sup>2</sup> $$-$$ 6x $$...
For x$$\in$$R, x $$\ne$$ $$-$$1, if $${(1 + x)^{2016}} + x{(1 + x)^{2015}} + {x^...
Five letter words, having distinct letters, are to be constructed using the lett...
What is the number of ways in which an examiner can assign 10 marks to 4 questio...
The digit in the unit's place of the number 1! + 2! + 3! + .... + 99! is
If M is a 3 $$\times$$ 3 matrix such that (0, 1, 2) M = (1 0 0), (3, 4 5) M = (0...
Let $$A = \left( {\matrix{ 1 & 0 & 0 \cr 0 & {\cos t} & {\sin t} \cr ...
Let A and B two non singular skew symmetric matrices such that AB = BA, then A<s...
If a<sub>n</sub> (> 0) be the n<sup>th</sup> term of a G.P. then<br/><br/>$$\lef...
Let A, B, C be three non-void subsets of set S. Let (A $$\cap$$ C) $$\cup$$ (B $...
Let T and U be the set of all orthogonal matrices of order 3 over R and the set ...
Four persons A, B, C and D throw and unbiased die, turn by turn, in succession t...
The mean and variance of a binomial distribution are 4 and 2 respectively. Then ...
Let $${S_n} = {\cot ^{ - 1}}2 + {\cot ^{ - 1}}8 + {\cot ^{ - 1}}18 + {\cot ^{ - ...
If a > 0, b > 0 then the maximum area of the parallelogram whose three vertices ...
Let A be the fixed point (0, 4) and B be a moving point on X-axis. Let M be the ...
A moving line intersects the lines x + y = 0 and x $$-$$ y = 0 at the points A, ...
The locus of the vertices of the family of parabolas $$6y = 2{a^3}{x^2} + 3{a^2}...
A ray of light along $$x + \sqrt 3 y = \sqrt 3 $$ gets reflected upon reaching X...
Two tangents to the circle x<sup>2</sup> + y<sup>2</sup> = 4 at the points A and...
From a point (d, 0) three normal are drawn to the parabola y<sup>2</sup> = x, th...
If from a point P(a, b, c), perpendicular PA and PB are drawn to YZ and ZX-plane...
The co-ordinate of a point on the auxiliary circle of the ellipse x<sup>2</sup> ...
The locus of the centre of a variable circle which always touches two given circ...
A line with positive direction cosines passes through the point P(2, $$-$$1, 2) ...
For $$y = {\sin ^{ - 1}}\left\{ {{{5x + 12\sqrt {1 - {x^2}} } \over {13}}} \righ...
f(x) is real valued function such that 2f(x) + 3f($$-$$x) = 15 $$-$$ 4x for all ...
Consider the functions f<sub>1</sub>(x) = x, f<sub>2</sub>(x) = 2 + log<sub>e</s...
The equation 6<sup>x</sup> + 8<sup>x</sup> = 10<sup>x</sup> has
Let f : D $$\to$$ R where D = [$$-$$0, 1] $$\cup$$ [2, 4] be defined by <br/><br...
Let f(x) be continuous periodic function with period T. Let $$I = \int\limits_a^...
If $$b = \int\limits_0^1 {{{{e^t}} \over {t + 1}}dt} $$, then $$\int\limits_{a -...
The differential of $$f(x) = {\log _e}(1 + {e^{10x}}) - {\tan ^{ - 1}}({e^{5x}})...
Given that f : S $$\to$$ R is said to have a fixed point at c of S if f(c) = c. ...
The $$\mathop {\lim }\limits_{x \to \infty } {\left( {{{3x - 1} \over {3x + 1}}}...
The area bounded by the parabolas $$y = 4{x^2},y = {{{x^2}} \over 9}$$ and the s...
If a($$\alpha$$ $$\times$$ $$\beta$$) + b($$\beta$$ $$\times$$ $$\gamma$$) + c($...
If the tangent at the point P with co-ordinates (h, k) on the curve y<sup>2</sup...
The coefficient of a<sup>3</sup>b<sup>4</sup>c<sup>5</sup> in the expansion of (...
Three unequal positive numbers a, b, c are such that a, b, c are in G.P. while $...
The determinant $$\left| {\matrix{ {{a^2} + 10} & {ab} & {ac} \cr {ab} &...
Let R be the real line. Let the relations S and T or R be defined by <br/><br/>$...
The plane lx + my = 0 is rotated about its line of intersection with the plane z...
The points of intersection of two ellipses $${x^2} + 2{y^2} - 6x - 12y + 20 = 0$...
Let $$I = \int_{\pi /4}^{\pi /3} {{{\sin x} \over x}dx} $$. Then
If $$\left| {z + i} \right| - \left| {z - 1} \right| = \left| z \right| - 2 = 0$...
$$\left| {\matrix{ x & {3x + 2} & {2x - 1} \cr {2x - 1} & {4x} & {3x + 1...
The remainder when $${7^{{7^{{7^{{{..}^7}}}}}}}$$ (22 time 7) is divided by 48 i...
Whichever of the following is/are correct?
A plane meets the co-ordinate axes t the points A, B, C respectively such a way ...
Let P be a variable point on a circle C and Q be a fixed point outside C. If R i...
$$\mathop {\lim }\limits_{n \to \infty } \left\{ {{{\sqrt n } \over {\sqrt {{n^3...
Let $$f(x) = \left\{ {\matrix{ {0,} & {if} & { - 1 \le x \le 0} \cr {1,}...
The greatest and least value of $$f(x) = {\tan ^{ - 1}} - {1 \over 2}\,ln \,x\,o...
Let f and g be periodic functions with the periods T<sub>1</sub> and T<sub>2</su...

Physics

A spherical convex surface of power 5 D separates object and image space of refr...
In Young's double slit experiment, light of wavelength $$\lambda$$ passes throug...
A 12.5 eV electron beam is used to bombard gaseous hydrogen at ground state. The...
Let r, v, E be the radius of orbit, speed of electron and total energy of electr...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv8rvf2/33fa0b...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv8u179/14bdc3...
From dimensional analysis, the Rydberg constant can be expressed in terms of ele...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv8y9ot/d95f82...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv8zzn9/627c74...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv92eyn/edfda0...
A simple pendulum, consisting of a small ball of mass m attached to a massless s...
In case of projectile motion, which one of the following figures represent varia...
A uniform thin rod of length L, mass m is lying on a smooth horizontal table. A ...
Centre of mass (CM) of three particles of masses 1 kg, 2 kg and 3 kg lies at the...
A body of density 1.2 $$\times$$ 10<sup>3</sup> kg/m<sup>3</sup> is dropped from...
Two solid spheres S<sub>1</sub> and S<sub>2</sub> of same uniform density fall f...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv99lmq/c1fbe9...
If pressure of real gas O<sub>2</sub>, in a container is given by $$p = {{RT} \o...
300 g of water at 25$$^\circ$$C is added to 100 g of ice at 0$$^\circ$$C. The fi...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv9b617/f6f174...
A metal sphere of radius R carrying charge q is surrounded by a thick concentric...
Three infinite plane sheets carrying uniform charge densities $$-$$ $$\sigma$$, ...
Two point charges +q<sub>1</sub> and +q<sub>2</sub> are placed a finite distance...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv9e713/e85513...
A thin charged rod is bent into the shape of a small circle of radius R, the cha...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv9g0jq/ccb068...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv9hbla/8943f6...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv9iz9n/a5e973...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv9l03g/6019fc...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv9mcti/6f9e3a...
For a plane electromagnetic wave, the electric field is given by<br><br>$$ \over...
Two metal wires of identical dimensions are connected in series. If $$\sigma$$<s...
A uniform rod of length L pivoted at one end P is freely rotated in a horizontal...
An ideal gas of molar mass M is contained in a very tall vertical cylindrical co...
Under isothermal conditions, two soap bubbles of radii a and b coalesce to form ...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv9o8ep/ca6c2c...
Electric field component of an EM radiation varies with time as E = a (cos$$\ome...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv9qdxc/f82dfd...
The potential energy of a particle of mass 0.02 kg moving along X-axis is given ...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kzv9tj8o/e91d82...

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