Chemistry

1.
For the above three esters, the order of rates of alkaline hydrolysis is
2.
Ph$$ - $$
CDO$$\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_{Warm}^{50\% aq.NaOH}} $$
Ph$$ - $$
COO$$\mathop H\limi
3.
The correct order of acidity for the following compounds is :
4.
The reduction product of ethyl 3-oxobutanoate by NaBH4 in methanol is
5.
What is the major product of the following reaction?
6.
The maximum number of electrons in an atom in which the last electron filled has the quantum numbers n = 3, l = 2 and m
7.
In the face centered cubic lattice structure of gold the closest distance between gold atoms is ('a' being the edge leng
8.
The equilibrium constant for the following reactions are given at 25$$^\circ $$C$$2A$$ $$\rightleftharpoons$$ B + C, K1
9.
Among the following, the ion which will be more effective for flocculation of Fe(OH)3 solution is :
10.
The mole fraction of ethanol in water is 0.08. Its molality is
11.
5 mL of 0.1 M Pb(NO3)2 is mixed with 10 mL of 0.02 M KI. The amount of PbI2 precipitated will be about
12.
At 273 K temperature and 76 cm Hg pressure the density of a gas is 1.964 g L-1. The gas is
13.
Equal masses of ethane and hydrogen are mixed in an empty container at 298 K. The fraction of total pressure exerted by
14.
An ideal gas expands adiabatically against vacuum. Which of the following is correct for the given process?
15.
Kf (water) = 1.86 K kg mol-1. The temperature at which ice begins to separate from a mixture of 10 mass % ethylene glyco
16.
The radius of the first Bohr orbit of a hydrogen atom is 0.53 $$\times {10^-8}$$ cm. The velocity of the electron in the
17.
Which of the following statements is not true for the reaction, 2F2 + 2H2O $$ \to $$ 4HF + O2 ?
18.
The number of unpaired electrons in the uranium (92U) atom is
19.
How and why does the density of liquid water change on prolonged electrolysis?
20.
The difference between orbital angular momentum of an electron in a 4f -orbital and another electron in a 4s-orbital is
21.
Which of the following has the largest number of atoms?
22.
Indicate the correct IUPAC name of the coordination compound shown in the figure.
23.
What will be the mass of one atom of 12C?
24.
Bond order of He2, $$He_2^ + $$ and $$He_2^{2 + }$$ are respectively
25.
To a solution of a colourless efflorescent sodium salt, when dilute acid is added, a colourless gas is evolved along wit
26.
The reaction for obtaining the metal (M) from its oxide (M2O3) ore is given by$${M_2}{O_3}(s) + 2Al(l)\buildrel {Heat} \
27.
In the extraction of Ca by electro reduction of molten CaCl2 some CaF2 is added to the electrolyte for the following rea
28.
The total number of alkyl bromides (including stereoisomers) formed in the reaction $$M{e_3}C - CH = C{H_2} + HBr \to $$
29.
The product in the above reaction is
30.
Which of the following compounds is asymmetric?
31.
For a reaction 2A + B $$ \to $$ P, when concentration of B alone is doubled, t1/2 does not change and when concentration
32.
A solution is saturated with SrCO3 and SrF2. The $$[CO_3^{2 - }]$$ is found to be 1.2 $$ \times $$ 10-3 M. The concentra
33.
A homonuclear diatomic gas molecule shows 2-electron magnetic moment. The one-electron and two-electron reduced species
34.
$$C{H_3} - O - C{H_2} - Cl\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_\Delta ^{aq{.^\Theta }OH}} C{H_3} - O - C{H_
35.
Which of the following reactions give(s) a meso-compound as the main product?
36.
For spontaneous polymerisation, which of the following is (are) correct?
37.
Which of the following statement(s) is/are incorrect?
38.
SiO2 is attacked by which one/ones of the following?
39.
$$Me - C \equiv C - Me\mathrel{\mathop{\kern0pt\longrightarrow}
\limits_{EtOH, - 33^\circ C}^{Na/N{H_3}(liq.)}} \underli
40.
For the following carbocations, the correct order of stability is I. $$^ \oplus C{H_2} - COC{H_3}$$II. $$^ \oplus C{H_2}

Mathematics

1.
Let cos$$^{ - 1}\left( {{y \over b}} \right) = \log {\left( {{x \over n}} \right)^n}$$. Then
2.
Let $$\phi (x) = f(x) + f(1 - x)$$ and $$f(x) < 0$$ in [0, 1], then
3.
$$\int {{{f(x)\phi '(x) + \phi (x)f'(x)} \over {(f(x)\phi (x) + 1)\sqrt {f(x)\phi (x) - 1} }}dx = } $$
4.
The value of $$\sum\limits_{n = 1}^{10} {} \int\limits_{ - 2n - 1}^{ - 2n} {{{\sin }^{27}}} x\,dx + \sum\limits_{n = 1}^
5.
$$\int\limits_0^2 {[{x^2}]} \,dx$$ is equal to
6.
If the tangent to the curve y2 = x3 at (m2, m3) is also a normal to the curve at (m2, m3), then the value of mM is
7.
If $${x^2} + {y^2} = {a^2}$$, then $$\int\limits_0^a {\sqrt {1 + {{\left( {{{dy} \over {dx}}} \right)}^2}} dx = } $$
8.
Let f, be a continuous function in [0, 1], then $$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{j = 0}^n {{1 \over
9.
Let f be a differentiable function with $$\mathop {\lim }\limits_{x \to \infty } f(x) = 0.$$ If $$y' + yf'(x) - f(x)f'(x
10.
If $$x\sin \left( {{y \over x}} \right)dy = \left[ {y\sin \left( {{y \over x}} \right) - x} \right]dx,\,x > 0$$ and $
11.
Let $$f(x) = 1 - \sqrt {({x^2})} $$, where the square root is to be taken positive, then
12.
If the function $$f(x) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1$$ [a > 0] attains its maximum and minimum at p and q respect
13.
If a and b are arbitrary positive real numbers, then the least possible value of $${{6a} \over {5b}} + {{10b} \over {3a}
14.
If 2 log(x + 1) $$ - $$ log(x2 $$ - $$ 1) = log 2, then x =
15.
The number of complex numbers p such that $$\left| p \right| = 1$$ and imaginary part of p4 is 0, is
16.
The equation $$z\bar z + (2 - 3i)z + (2 + 3i)\bar z + 4 = 0$$ represents a circle of radius
17.
The expression ax2 + bx + c (a, b and c are real) has the same sign as that of a for all x if
18.
In a 12 storied building, 3 persons enter a lift cabin. It is known that they will leave the lift at different floors. I
19.
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
20.
Let I(n) = nn, J(n) = 13.5 ......... (2n $$ - $$ 1) for all (n > 1), n $$ \in $$ N, then
21.
If c0, c1, c2, ......, c15 are the binomial coefficients in the expansion of (1 + x)15, then the value of $${{{c_1}} \ov
22.
Let A = $$\left( {\matrix{
{3 - t} \cr
{ - 1} \cr
0 \cr
} \matrix{
{} \cr
{} \cr
{} \cr
23.
Let $$A = \left[ {\matrix{
{12} & {24} & 5 \cr
x & 6 & 2 \cr
{ - 1} & { - 2} & 3 \
24.
Let $$A = \left( {\matrix{
a & b \cr
c & d \cr
} } \right)$$ be a 2 $$ \times $$ 2 real matrix with
25.
If $$\left| {\matrix{
{{a^2}} & {bc} & {{c^2} + ac} \cr
{{a^2} + ab} & {{b^2}} & {ca} \cr
{
26.
If f : S $$ \to $$ R, where S is the set of all non-singular matrices of order 2 over R and $$f\left[ {\left( {\matrix{
27.
Let the relation p be defined on R by a p b holds if and only if a $$ - $$ b is zero or irrational, then
28.
The unit vector in ZOX plane, making angles $$45^\circ $$ and $$60^\circ $$ respectively with $$\alpha = 2\widehat i +
29.
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
30.
A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of rounds he must fire
31.
$$\cos (2x + 7) = a(2 - \sin x)$$ can have a real solution for
32.
The differential equation of the family of curves y = ex (A cos x + B sin x) where, A, B are arbitrary constants is
33.
The equation $$r\,\cos \left( {\theta - {\pi \over 3}} \right) = 2$$ represents
34.
The locus of the centre of the circles which touch both the circles x2 + y2 = a2 and x2 + y2 = 4ax externally is
35.
Let each of the equations x2 + 2xy + ay2 = 0 and ax2 + 2xy + y2 = 0 represent two straight lines passing through the ori
36.
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
37.
Area in the first quadrant between the ellipses x2 + 2y2 = a2 and 2x2 + y2 = a2 is
38.
The equation of circle of radius $$\sqrt {17} $$ unit, with centre on the positive side of X-axis and through the point
39.
The length of the chord of the parabola y2 = 4ax(a > 0) which passes through the vertex and makes an acute angle $$\a
40.
A double ordinate PQ of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ is such that $$\Delta OP
41.
If B and B' are the ends of minor axis and S and S' are the foci of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over
42.
The equation of the latusrectum of a parabola is x + y = 8 and the equation of the tangent at the vertex is x + y = 12.
43.
The equation of the plane through the point $$(2, - 1, - 3)$$ and parallel to the lines$${{x - 1} \over 2} = {{y + 2} \o
44.
The sine of the angle between the straight line $${{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}$$ and the pl
45.
Let f(x) = sin x + cos ax be periodic function. Then,
46.
The domain of $$f(x) = \sqrt {\left( {{1 \over {\sqrt x }} - \sqrt {x + 1} } \right)} $$ is
47.
Let $$y = f(x) = 2{x^2} - 3x + 2$$. The differential of y when x changes from 2 to 1.99 is
48.
If $$\mathop {\lim }\limits_{x \to 0} {\left( {{{1 + cx} \over {1 - cx}}} \right)^{{1 \over x}}} = 4$$, then $$\mathop {
49.
Let f : R $$ \to $$ R be twice continuously differentiable (or f" exists and is continuous) such that f(0) = f(1) = f'(0
50.
Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 12$$.Then
51.
The area of the region$$\{ (x,y):{x^2} + {y^2} \le 1 \le x + y\} $$ is
52.
In open interval $$\left( {0,\,{\pi \over 2}} \right)$$
53.
If the line y = x is a tangent to the parabola y = ax2 + bx + c at the point (1, 1) and the curve passes through ($$ - $
54.
If the vectors $$\alpha = \widehat i + a\widehat j + {a^2}\widehat k,\,\beta = \widehat i + b\widehat j + {b^2}\wideha
55.
Let z1 and z2 be two imaginary roots of z2 + pz + q = 0, where p and q are real. The points z1, z2 and origin form an eq
56.
If P(x) = ax2 + bx + c and Q(x) = $$ - $$ax2 + dx + c, where ac $$ \ne $$ 0 [a, b, c, d are all real], then P(x).Q(x) =
57.
Let $$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|$$. Then
58.
Let $$f(x) = \sqrt {{x^2} - 3x + 2} $$ and $$g(x) = \sqrt x $$ be two given functions. If S be the domain of fog and T b
59.
Let p1 and p2 be two equivalence relations defined on a non-void set S. Then
60.
Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. The portion of the tangent at any point of
61.
Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. The portion of the tangent at any point of
62.
A line cuts the X-axis at A(7, 0) and the Y-axis at B(0, $$ - $$5). A variable line PQ is drawn perpendicular to AB cutt
63.
Let $$0 < \alpha < \beta < 1$$. Then, $$\mathop {\lim }\limits_{n \to \infty } \int\limits_{1/(k + \beta )}^{
64.
$$\mathop {\lim }\limits_{x \to 1} \left( {{1 \over {1nx}} - {1 \over {(x - 1)}}} \right)$$
65.
Let $$y = {1 \over {1 + x + lnx}}$$, then
66.
Consider the curve $$y = b{e^{ - x/a}}$$, where a and b are non-zero real numbers. Then
67.
The area of the figure bounded by the parabola $$x = - 2{y^2},\,x = 1 - 3{y^2}$$ is
68.
A particle is projected vertically upwards. If it has to stay above the ground for 12 sec, then
69.
The equation $${x^{{{(\log 3x)}^2}}} - {9 \over 2}\log 3\,x + 5 = 3\sqrt 3 $$ has
70.
In a certain test, there are n questions. In this test 2n-i students gave wrong answers to at least i questions, where i
71.
A and B are independent events. The probability that both A and B occur is $${1 \over {20}}$$ and the probability that n
72.
The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose su
73.
Consider a tangent to the ellipse $${{{x^2}} \over 2} + {{{y^2}} \over 1} = 1$$ at any point. The locus of the mid-point
74.
Let $$y = {{{x^2}} \over {{{(x + 1)}^2}(x + 2)}}$$. Then $${{{d^2}y} \over {d{x^2}}}$$ is
75.
Let $$f(x) = {1 \over 3}x\sin x - (1 - \cos \,x)$$. The smallest positive integer k such that $$\mathop {\lim }\limits_{
76.
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

Physics

1.
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
2.
In a Fraunhofer diffraction experiment, a single slit of width 0.5 mm is illuminated by a monochromatic light of wavelen
3.
If R is the Rydberg constant in cm-1, then hydrogen atom does not emit any radiation of wavelength in the range of
4.
A nucleus X emits a $$\beta $$-particle to produce a nucleus Y. If their atomic masses are Mx and My respectively, then
5.
For nuclei with mass number close to 119 and 238, the binding energies per nucleon are approximately 7.6 MeV and 8.6 MeV
6.
A common emitter transistor amplifier is connected with a load resistance of 6 k$$\Omega $$
. When a small AC signal of
7.
In the circuit shown, the value of $$\beta $$ of the transistor is 48. If the supplied base current is 200 $$\mu $$A, wh
8.
The frequency v of the radiation emitted by an atom when an electron jumps from one orbit to another is given by v = k$$
9.
Consider the vectors $$A = \hat i + \hat j - \hat k$$
,$$B = 2\hat i - \hat j + \hat k$$ and $$C = {1 \over {\sqrt 5 }}\
10.
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
11.
A block of mass m rests on a horizontal table with a coefficient of static friction $$\mu $$. What minimum force must be
12.
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
13.
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
14.
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
15.
Which of the following diagrams correctly shows the relation between the terminal velocity vT of a spherical body fallin
16.
An ideal gas undergoes the cyclic process abca as shown in the given p - V diagramIt rejects 50J of heat during ab and a
17.
A container AB in the shape of a rectangular parallelopiped of length 5 m is divided internally by a movable partition P
18.
When 100 g of boiling water at 100$$^\circ $$
C is added into a calorimeter containing 300 g of cold water at 10$$^\circ
19.
As shown in the figure, a point charge q1 = + 1 $$ \times $$ 10-6 C is placed at the origin in xy-plane and another poin
20.
Four identical point masses, each of mass m and carrying charge + q are placed at the corners of a square of sides a on
21.
A very long charged solid cylinder of radius a contains a uniform charge density p. Dielectric constant of the material
22.
A galvanometer can be converted to a voltmeter of full scale deflection V0 by connecting a series resistance R1 and can
23.
As shown in the figure, a single conducting wire is bent to form a loop in the form of a circle of radius r concentrical
24.
As shown in the figure, a wire is bent to form a D-shaped closed loop, carrying current I, where the curved part is a se
25.
What will be the equivalent resistance between the terminals A and B of the infinite resistive network shown in the figu
26.
When a DC voltage is applied at the two ends of a circuit kept in a closed box, it is observed that the current graduall
27.
Consider the circuit shown.If all the cells have negligible internal resistance, what will be the current through the 2$
28.
Consider a conducting wire of length L bent in the form of a circle of radius R and another conductor of length a (a <
29.
An object, is placed 60 cm in front of a convex mirror of focal length 30 cm. A plane mirror is now placed facing the ob
30.
A thin convex lens is placed just above an empty vessel of depth 80 cm. The image of a coin kept at the bottom of the ve
31.
A conducting circular loop of resistance 20$$\Omega $$
and cross-sectional area 20 $$ \times $$ 10-2 m2 is placed perpe
32.
A pair of parallel metal plates are kept with a separation d. One plate is at a potential + V and the other is at ground
33.
A metallic block of mass 20 kg is dragged with a uniform velocity of 0.5 ms-1 on a horizontal table for 2.1 s. The coeff
34.
Consider an engine that absorbs 130 cal of heat from a hot reservoir and delivers 30 cal heat to a cold reservoir in eac
35.
Two pith balls, each carrying charge + q are hung from a hook by two springs. It is found that when each charge is tripl
36.
A point source of light is used in an experiment of photoelectric effects. If the distance between the source and the ph
37.
Two metallic spheres of equal outer radii are found to have same moment of inertia about their respective diameters. The
38.
A simple pendulum of length l is displaced, so that its taught string is horizontal and then released. A uniform bar piv
39.
A 400$$\Omega $$ resistor, a 250 mH inductor and a 2.5 $$\mu $$F capacitor are connected in series with an AC source of
40.
A charged particle moves with constant velocity in a region, where no effect of gravity is felt but an electrostatic fie

1

WB JEE 2020

MCQ (More than One Correct Answer)

+2

-0

The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose sum is $$ - 1$$ is

A

$${x \over 2} - {y \over 3} = 1$$

B

$${x \over { - 2}} + {y \over 1} = 1$$

C

$$ - {x \over 3} + {y \over 2} = 1$$

D

$${x \over 1} - {y \over 2} = 1$$

2

WB JEE 2020

MCQ (More than One Correct Answer)

+2

-0

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

A

$${{{x^2}} \over 2} + {{{y^2}} \over 4} = 1$$

B

$${{{x^2}} \over 4} + {{{y^2}} \over 2} = 1$$

C

$${1 \over {3{x^2}}} + {1 \over {4{y^2}}} = 1$$

D

$${1 \over {2{x^2}}} + {1 \over {4{y^2}}} = 1$$

3

WB JEE 2020

MCQ (More than One Correct Answer)

+2

-0

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

A

$$2\left[ {{3 \over {{{(x + 1)}^4}}} - {3 \over {{{(x + 1)}^3}}} + {4 \over {{{(x + 2)}^3}}}} \right]$$

B

$$3\left[ {{2 \over {{{(x + 1)}^3}}} + {4 \over {{{(x + 1)}^2}}} - {5 \over {{{(x + 2)}^3}}}} \right]$$

C

$${6 \over {{{(x + 1)}^3}}} - {4 \over {{{(x + 1)}^2}}} + {3 \over {{{(x + 1)}^3}}}$$

D

$${7 \over {{{(x + 1)}^3}}} - {3 \over {{{(x + 1)}^2}}} + {2 \over {{{(x + 1)}^3}}}$$

4

WB JEE 2020

MCQ (More than One Correct Answer)

+2

-0

Let $$f(x) = {1 \over 3}x\sin x - (1 - \cos \,x)$$. The smallest positive integer k such that $$\mathop {\lim }\limits_{x \to 0} {{f(x)} \over {{x^k}}} \ne 0$$ is

A

4

B

3

C

2

D

1

Paper analysis

Total Questions

Chemistry

40

Mathematics

76

Physics

40

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