JEE Main 3 September 2020 Shift 2 Question Paper

Question 1

If the sum of the series $20 + 19\frac{3}{5} + 19\frac{1}{5} + 18\frac{4}{5} + ....$ upto $n^{th}$ term is 488 and the $n^{th}$ term is negative, then:

Accepted Answer

(C) $n^{th}$ term is $-4$

Answer

(A) $n^{th}$ term is $-4\frac{2}{5}$

Answer

(B) $n = 41$

Answer

(D) $n = 60$

Question 2

If $z_1, z_2$ are complex numbers such that $\mathrm{Re}(z_1) = |z_1 - 1|, \mathrm{Re}(z_2) = |z_2 - 1|$ and $\arg(z_1 - z_2) = \frac{\pi}{6}$, then $\mathrm{Im}(z_1 + z_2)$ is equal to:

Accepted Answer

(A) $2\sqrt{3}$

Answer

(B) $\frac{\sqrt{3}}{2}$

Answer

(C) $\frac{1}{\sqrt{3}}$

Answer

(D) $\frac{2}{\sqrt{3}}$

Question 3

Let $a, b, c \in R$ be such that $a^2 + b^2 + c^2 = 1$. If $a\cos	heta = b\cos\left(	heta + \frac{2\pi}{3}ight) = c\cos\left(	heta + \frac{4\pi}{3}ight)$, where $	heta = \frac{\pi}{9}$, then the angle between the vectors $a\hat{i} + b\hat{j} + c\hat{k}$ and $b\hat{i} + c\hat{j} + a\hat{k}$ is:

Accepted Answer

(D) $\frac{\pi}{2}$

Answer

(A) $\frac{\pi}{9}$

Answer

(B) $\frac{2\pi}{3}$

Answer

(C) $0$

Question 4

Let the latus rectum of the parabola $y^2 = 4x$ be the common chord to the circles $C_1$ and $C_2$ each of them having radius $2\sqrt{5}$. Then, the distance between the centres of the circles $C_1$ and $C_2$ is:

Accepted Answer

(C) $8$

Answer

(A) $4\sqrt{5}$

Answer

(B) $8\sqrt{5}$

Answer

(D) $12$

Question 5

Let $R_1$ and $R_2$ be two relations defined as follows:
$R_1 = \{(a,b) \in R^2 : a^2 + b^2 \in Q\}$ and
$R_2 = \{(a,b) \in R^2 : a^2 + b^2 
otin Q\}$, where $Q$ is the set of all rational numbers. Then:

Accepted Answer

(A) Neither $R_1$ nor $R_2$ is transitive.

Answer

(B) $R_1$ is transitive but $R_2$ is not transitive.

Answer

(C) $R_1$ and $R_2$ are both transitive

Answer

(D) $R_2$ is transitive but $R_1$ is not transitive.

Question 6

If the value of the integral $\int_{0}^{1/2} \frac{x^2}{\left(1 - x^2\right)^{3/2}} dx$ is $\frac{k}{6}$, then $k$ is equal to:

Accepted Answer

(C) $2\sqrt{3} - \pi$

Answer

(A) $2\sqrt{3} + \pi$

Answer

(B) $3\sqrt{2} - \pi$

Answer

(D) $3\sqrt{2} + \pi$

Question 7

If $x^3 dy + xy\, dx = x^2 dy + 2y\, dx; y(2) = e$ and $x > 1$, then $y(4)$ is equal to:

Accepted Answer

(C) $\frac{3}{2}\sqrt{e}$

Answer

(A) $\frac{\sqrt{e}}{2}$

Answer

(B) $\frac{1}{2} + \sqrt{e}$

Answer

(D) $\frac{3}{2} + \sqrt{e}$

Question 8

The probability that a randomly chosen 5 - digit number is made from exactly two digits is:

Accepted Answer

(D) $\frac{135}{10^4}$

Answer

(A) $\frac{134}{10^4}$

Answer

(B) $\frac{121}{10^4}$

Answer

(C) $\frac{150}{10^4}$

Question 9

If the surface area of a cube is increasing at a rate of 3.6 $cm^2$/sec, retaining its shape; then the rate of change of its volume (in $cm^3$/sec), when the length of a side of the cube is 10 cm, is:

Accepted Answer

(A) $9$

Answer

(B) $18$

Answer

(C) $10$

Answer

(D) $20$

Question 10

The set of all real values of $\lambda$ for which the quadratic equations, $\left(\lambda^2 + 1\right)x^2 - 4\lambda x + 2 = 0$ always have exactly one root in the interval (0, 1) is:

Accepted Answer

(D) $(1, 3]$

Answer

(A) $(0, 2)$

Answer

(B) $(2, 4]$

Answer

(C) $(-3, -1)$

Question 11

If a $\Delta ABC$ have vertices A $(-1, 7)$, B $(-7, 1)$ and C $(5, -5)$, then its orthocenter has coordinates:

Accepted Answer

(B) $(-3, 3)$

Answer

(A) $\left( \frac{3}{5}, -\frac{3}{5} \right)$

Answer

(C) $(3, -3)$

Answer

(D) $\left( -\frac{3}{5}, \frac{3}{5} \right)$

Question 12

Let p, q, r be three statements such that the truth value of $\left( p \wedge q \right) \rightarrow \left( \sim q \vee r \right)$ is F. Then the truth values of p, q,r are respectively:

Accepted Answer

(B) T, T, F

Answer

(A) T, F, T

Answer

(C) F, T, F

Answer

(D) T, T, T

Question 13

The plane which bisects the line joining the points $(4, -2, 3)$ and $(2, 4, -1)$ at right angles also passes through the point:

Accepted Answer

(C) $(4, 0, -1)$

Answer

(A) $(0, -1, 1)$

Answer

(B) $(4, 0, 1)$

Answer

(D) $(0, 1, -1)$

Question 14

Let $e_1$ and $e_2$ be the eccentricities of the ellipse, $\frac{x^2}{25} + \frac{y^2}{b^2} = 1 \left( b < 5 \right)$ and the hyperbola, $\frac{x^2}{16} - \frac{y^2}{b^2} = 1$ respectively satisfying $e_1 e_2 = 1$. If $\alpha$ and $\beta$ are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair $\left( \alpha, \beta \right)$ is equal to :

Accepted Answer

(A) $(8, 10)$

Answer

(B) $\left( \frac{24}{5}, 10 \right)$

Answer

(C) $\left( \frac{20}{3}, 12 \right)$

Answer

(D) $(8, 12)$

Question 15

Let A be a $3 	imes 3$ matrix such that $\mathrm{adj}\,A = \begin{bmatrix} 2 & -1 & 1 \ -1 & 0 & 2 \ 1 & -2 & -1 \end{bmatrix}$ and $B = \mathrm{adj}\left( \mathrm{adj}\,A ight)$. If $\left| A ight| = \lambda$ and $\left| \left( B^{-1} ight)^{T} ight| = \mu$, then the ordered pair, $\left( \left| \lambda ight| . \mu ight)$ is equal to:

Accepted Answer

(D) $\left( 3, \frac{1}{81} \right)$

Answer

(A) $\left( 9, \frac{1}{9} \right)$

Answer

(B) $(3, 81)$

Answer

(C) $\left( 9, \frac{1}{81} \right)$

Question 16

If $\int \sin^{-1} \left( \sqrt{\frac{x}{1+x}} ight) dx = A(x) 	an^{-1} \left( \sqrt{x} ight) + B(x) + C,$ where C is a constant of integration, then the ordered pair $\left( A(x), B(x) ight)$ can be:

Accepted Answer

(C) $\left( x + 1, -\sqrt{x} \right)$

Answer

(A) $\left( x - 1, -\sqrt{x} \right)$

Answer

(B) $\left( x - 1, \sqrt{x} \right)$

Answer

(D) $\left( x + 1, \sqrt{x} \right)$

Question 17

Let $x_i \left( 1 \le i \le 10 ight)$ be ten observations of a random variable X. If $\sum_{i=1}^{10} \left( x_i - p ight) = 3$ and $\sum_{i=1}^{10} \left( x_i - p ight)^2 = 9$ where $0 
e p \in R$, then the standard deviation of these observations is:

Accepted Answer

(D) $\frac{9}{10}$

Answer

(A) $\sqrt{\frac{3}{5}}$

Answer

(B) $\frac{4}{5}$

Answer

(C) $\frac{7}{10}$

Question 18

If the term independent of x in the expansion of $\left( \frac{3}{2} x^2 - \frac{1}{3x} \right)^9$ is k, then 18k is equal to:

Accepted Answer

(C) 7

Answer

(A) 9

Answer

(B) 5

Answer

(D) 11

Question 19

Suppose $f(x)$ is a polynomial of degree four, having critical points at $-1, 0, 1$. If $T = \left\{ x \in R \,\middle|\, f(x) = f(0) \right\}$, then the sum of squares of all the elements of T is:

Accepted Answer

(D) 4

Answer

(A) 8

Answer

(B) 6

Answer

(C) 2

Question 20

$\lim_{x 	o a} \frac{\left( a + 2x ight)^{\frac{1}{3}} - \left( 3x ight)^{\frac{1}{3}}}{\left( 3a + x ight)^{\frac{1}{3}} - \left( 4x ight)^{\frac{1}{3}}} \left( a 
e 0 ight)$ is equal to:

Accepted Answer

(D) $\left( \frac{2}{3} \right) \left( \frac{2}{9} \right)^{\frac{1}{3}}$

Answer

(A) $\left( \frac{2}{3} \right)^{\frac{4}{3}}$

Answer

(B) $\left( \frac{2}{9} \right)^{\frac{4}{3}}$

Answer

(C) $\left( \frac{2}{9} \right) \left( \frac{2}{3} \right)^{\frac{1}{3}}$

Question 21

If the tangent to the curve, $y = e^x$ at a point $\left( c, e^c \right)$ and the normal to the parabola, $y^2 = 4x$ at the point $(1, 2)$ intersect at the same point on the x $-$ axis, then the value of c is __________.

Accepted Answer

04.00

Question 22

The total number of 3 $-$ digit numbers, whose sum of digits is 10, is ____________.

Accepted Answer

54.00

Question 23

Let S be the set of all integer solutions, (x, y, z), of the system of equation
$x - 2y + 5z = 0$
$-2x + 4y + z = 0$
$-7x + 14y + 9z = 0$
such that $15 \le x^2 + y^2 + z^2 \le 150$. Then, the number of elements in the set S is equal to _______.

Accepted Answer

08.00

Question 24

Let a plane P contain two lines $\vec{r} = \hat{i} + \lambda \left( \hat{i} + \hat{j} \right), \lambda \in R$ and $\vec{r} = -\hat{j} + \mu \left( \hat{j} - \hat{k} \right), \mu \in R$. If $Q\left( \alpha, \beta, \gamma \right)$ is the foot of the perpendicular drawn from the point M $(1, 0, 1)$ to P, then $3 \left( \alpha + \beta + \gamma \right)$ equals ____________ .

Accepted Answer

05.00

Question 25

If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that $4^{th}$ A.M. is equal to $2^{nd}$ G.M., then m is equal to ________________.

Accepted Answer

39.00

Question 26

The electric field of a plane electromagnetic wave propagating along the x direction in vacuum is $\vec{E} = E_0\hat{j}\cos(\omega t - kx)$. The magnetic field $\vec{B}$, at the moment t = 0 is:

Accepted Answer

(B) $\vec{B} = E_0\sqrt{\mu_0 \epsilon_0}\,\cos(kx)\,\hat{k}$

Answer

(A) $\vec{B} = E_0\sqrt{\mu_0 \epsilon_0}\,\cos(kx)\,\hat{j}$

Answer

(C) $\vec{B} = \dfrac{E_0}{\sqrt{\mu_0 \epsilon_0}}\cos(kx)\,\hat{k}$

Answer

(D) $\vec{B} = \dfrac{E_0}{\sqrt{\mu_0 \epsilon_0}}\cos(kx)\,\hat{j}$

Question 27

A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m/s in the horizontal direction just before the combined system strikes the floor, is
[Take g = 10 m/s$^{2}$. Assume there is no rotational motion and loss of energy after the collision is negligible.]

Accepted Answer

(A) 21 J

Answer

(B) 20 J

Answer

(C) 23 J

Answer

(D) 19 J

Question 28

Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to:

Accepted Answer

(D) 2 : 1

Answer

(A) 1 : 2

Answer

(B) 10 : 7

Answer

(C) 5 : 7

Question 29

A uniform rod of length 'l' is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed ω the rod makes an angle θ with it (see figure). To find θ equate the rate of change of angular momentum (direction going into the paper) $\dfrac{ml^{2}}{12}\omega^{2}\sin	heta\cos	heta$ about the centre of mass (CM) to the torque provided by the horizontal and vertical forces $F_H$ and $F_V$ about the CM. The value of θ is then such that:

Accepted Answer

(C) $\cos	heta = \dfrac{3g}{2l\omega^{2}}$

Answer

(A) $\cos	heta = \dfrac{g}{l\omega^{2}}$

Answer

(B) $\cos	heta = \dfrac{2g}{3l\omega^{2}}$

Answer

(D) $\cos	heta = \dfrac{g}{2l\omega^{2}}$

Question 30

Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is:

Accepted Answer

(C) $ML^{0}T^{-3}$

Answer

(A) $M^{2}L^{0}T^{-1}$

Answer

(B) $ML^{2}T^{-2}$

Answer

(D) $MLT^{-2}$

Question 31

A calorimeter of water equivalent 20 g contains 180 g of water at $25^{\circ}C$, 'm' grams of steam at $100^{\circ}C$ is mixed in it till the temperature of the mixture is $31^{\circ}C$. The value of 'm' is close to (Latent heat of water = 540 cal g$^{-1}$, specific heat of water $= 1\,\mathrm{cal}\,g^{-1}\,^{\circ}C^{-1}$)

Accepted Answer

(C) 2

Answer

(A) 2.6

Answer

(B) 4

Answer

(D) 3.2

Question 32

Two sources of light emit X − rays of wavelength 1 nm and visible light of wavelength 500 nm, respectively. Both the sources emit light of the same power 200 W. The ratio of the number density of photons of X − rays to the number density of photons of the visible light of the given wavelengths is:

Accepted Answer

(A) $\dfrac{1}{500}$

Answer

(B) 500

Answer

(C) 250

Answer

(D) $\dfrac{1}{250}$

Question 33

Concentric metallic hollow spheres of radii R and 4R hold charges $Q_1$ and $Q_2$ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V (R) − V (4R) is:

Accepted Answer

(C) $\dfrac{3Q_1}{16\pi \epsilon_0 R}$

Answer

(A) $\dfrac{3Q_2}{4\pi \epsilon_0 R}$

Answer

(B) $\dfrac{Q_2}{4\pi \epsilon_0 R}$

Answer

(D) $\dfrac{3Q_1}{4\pi \epsilon_0 R}$

Question 34

A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become $fA$. The value of f is:

Accepted Answer

(B) $\dfrac{1}{\sqrt{2}}$

Answer

(A) $\dfrac{1}{2}$

Answer

(C) $\sqrt{2}$

Answer

(D) 1

Question 35

Two light waves having the same wavelength λ in vacuum are in phase initially. Then the first wave travels path $L_1$ through a medium of refractive index $n_1$ while the second wave travels a path of length $L_2$ through a medium of refractive index $n_2$. After this the phase difference between the two waves is:

Accepted Answer

(C) $\dfrac{2\pi}{\lambda}\left(n_1L_1 - n_2L_2\right)$

Answer

(A) $\dfrac{2\pi}{\lambda}\left(\dfrac{L_2}{n_1} - \dfrac{L_1}{n_2}\right)$

Answer

(B) $\dfrac{2\pi}{\lambda}\left(\dfrac{L_1}{n_1} - \dfrac{L_2}{n_2}\right)$

Answer

(D) $\dfrac{2\pi}{\lambda}\left(n_2L_1 - n_1L_2\right)$

Question 36

A metallic sphere cools from $50^{\circ}C$ to $40^{\circ}$ in 300s. If atmospheric temperature around is $20^{\circ}C$, then the sphere's temperature after the next 5 minutes will be close to:

Accepted Answer

(C) $33^{\circ}C$

Answer

(A) $35^{\circ}C$

Answer

(B) $31^{\circ}C$

Answer

(D) $28^{\circ}C$

Question 37

If a semiconductor photodiode can detect a photon with a maximum wavelength of 400 nm, then its band gap energy is:
Planck's constant $h = 6.63 	imes 10^{-34}$ J.s.
Speed of light $c = 3 	imes 10^{8}$ m / s

Accepted Answer

(A) 3.1eV

Answer

(B) 1.5eV

Answer

(C) 2.0eV

Answer

(D) 1.1eV

Question 38

To raise the temperature of a certain mass of gas by $50^{\circ}$ C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by $100^{\circ}C$ at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

Accepted Answer

(D) 6

Answer

(A) 7

Answer

(B) 5

Answer

(C) 3

Question 39

A perfectly diamagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field $\vec{B}$. Then the field inside the paramagnetic substance is:

Accepted Answer

(A) zero

Answer

(B) much large than $\left|\vec{B}\right|$ but opposite to $\vec{B}$

Answer

(C) $\vec{B}$

Answer

(D) much large than $\left|\vec{B}\right|$ and parallel to $\vec{B}$

Question 40

The radius R of a nucleus of mass number A can be estimated by the formula $R=\left(1.3	imes 10^{-15}ight)A^{1/3}m$. It follows that the mass density of a nucleus is of the order of: $\left(M_{prot}=M_{neut.}\simeq 1.67	imes 10^{-27}\,kgight)$

Accepted Answer

(B) $10^{17}\,kg\ m^{-3}$

Answer

(A) $10^{3}kg\ m^{-3}$

Answer

(C) $10^{10}\,kg\ m^{-3}$

Answer

(D) $10^{24}\,kg\ m^{-3}$

Question 41

The mass density of a planet of radius R varies with the distance r from its centre as $\rho\left(r\right)=\rho_{0}\left(1-\frac{r^{2}}{R^{2}}\right)$. Then the gravitational field is maximum at:

Accepted Answer

(C) $r=\sqrt{\frac{5}{9}}R$

Answer

(A) $r=\frac{1}{\sqrt{3}}R$

Answer

(B) $r=R$

Answer

(D) $r=\sqrt{\frac{3}{4}}R$

Question 42

A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate $\frac{dB}{dt}=0.032\,Ts^{-1}$. The induced current in the loop is close to (Resistivity of the metal wire is $1.23	imes 10^{-8}\,\Omega m$ )

Accepted Answer

(A) $0.61A$

Answer

(B) $0.43\,A$

Answer

(C) $0.53\,A$

Answer

(D) $0.34\,A$

Question 43

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement(s) – time (t) graph that describes the motion of the particle is (graph are drawn schematically and are not to scale):

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 44

Two resistors 400Ω and 800Ω are connected in series across a 6 V battery. The potential difference measured by a voltmeter of 10kΩ across 400Ω resistor is close to:

Accepted Answer

(C) 1.95 V

Answer

(A) 2 V

Answer

(B) 2.05V

Answer

(D) 1.8 V

Question 45

A block starts moving up an inclined plane of inclination $30^{\circ}$ with an initial velocity of $v_{0}$.
It comes back to its initial position with velocity $\frac{v_{0}}{2}$. The value of the coefficient f kinetic friction between the block and the inclined plane is close to $\frac{I}{1000}$, The nearest integer to I is

Accepted Answer

346.00

Question 46

A galvanometer coil has 500 turns and each turn has an average are of $3	imes 10^{-4}m^{2}$. If a torque of 1.5 Nm is required to keep this coil parallel to a magnetic field when a current of 0.5 A is flowing through it, the strength of the field (in T) is __________.

Accepted Answer

20.00

Question 47

If minimum possible work is done by a refrigerator in converting 100 grams of water at $0^{\circ}C$ to ice, how much heat (in calories) is released to the surroundings at temperature $27^{\circ}C$ (Latent heat of ice = 80 Cal/gram) to the nearest integer?

Accepted Answer

8791

Question 48

A massless equilateral triangle EFG of side ‘a’ (As shown in figure) has three particles of mass m situated at its vertices. The moment of inertia of the system about the line EX perpendicular to EG in the plane of EFG is $\frac{N}{20}ma^{2}$ where N is an integer. The value of N is __________.

Accepted Answer

25.00

Question 49

When an object is kept at a distance of 30 cm from a concave mirror, the image is formed at a distance of 10 cm from the mirror. If the object is moved with a speed of 9 cm $s^{-1}$, the speed (in cm $s^{-1}$) with which image moves at that instant is _______________.

Accepted Answer

1.00

Question 50

Consider the following reaction:

The product ‘P’ gives positive ceric ammonium nitrate test. This is because of the presence of which of these – OH group(s)?

Accepted Answer

(C) (b) only

Answer

(A) (d) only

Answer

(B) (b) and (d)

Answer

(D) (c) and (d)

Question 51

An ionic micelles is formed on the addition of:

Accepted Answer

(A) (A)

Answer

(B) sodium stearate to pure toluene

Answer

(C) liquid diethyl ether to aqueous NaCl solution

Answer

(D) (D)

Question 52

The five successive ionization enthalpies of an element are 800, 2427, 3658, 25024 and 32824 kJ mol$^{-1}$. The number of valence electrons in the element is:

Accepted Answer

(D) 3

Answer

(A) 4

Answer

(B) 2

Answer

(C) 5

Question 53

The compound A in the following reactions is:

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 54

Consider the hypothetical situation where the azimuthal quantum number, l, takes values 0, 1, 2,…….n + 1, where n is the principal quantum number. Then, the element with atomic number:

Accepted Answer

(B) 8 is the first noble gas

Answer

(A) 9 is the first alkali metal

Answer

(C) 13 has a half – filled valence subshell

Answer

(D) 6 has a 2p – valence subshell

Question 55

The strengths of 5.6 volume hydrogen peroxide (of density 1 g/mL) in terms of mass percentage and molarity (M), respectively, are:
(Take molar mass of hydrogen peroxide as 34 g/mol)

Accepted Answer

(C) 1.7 and 0.5

Answer

(A) 0.85 and 0.25

Answer

(B) 0.85 and 0.5

Answer

(D) 1.7 and 0.25

Question 56

100 mL of 0.1 M HCl is taken in a beaker and to it 100 mL of 0.1 M NaOH is added in steps of 2 mL and the pH is continuously measured. Which of the following graphs correctly depicts the change in pH?

Accepted Answer

(D) (D)

Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Question 57

The incorrect statement(s) among (a) – (d) regarding acid rain is (are):
(a) It can corrode water pipes.
(b) It can damage structures made up of stone.
(c) It cannot cause respiratory ailments in animals
(d) It is not harmful for trees

Accepted Answer

(B) (c) and (d)

Answer

(A) (a), (b) and (d)

Answer

(C) (a), (c) and (d)

Answer

(D) (c) only

Question 58

Complex A has a composition of H$_{12}$O$_{6}$Cl$_{3}$Cr. If the complex on treatment with conc. H$_{2}$SO$_{4}$ loses 13.5% of its original mass, the correct molecular formula of A is:
[Given : atomic mass of Cr = 52 amu and Cl = 35 amu]

Accepted Answer

(A) $\left[\mathrm{Cr}(\mathrm{H}_{2}\mathrm{O})_{4}\mathrm{Cl}_{2}\right]\mathrm{Cl}\cdot 2\mathrm{H}_{2}\mathrm{O}$

Answer

(B) $\left[\mathrm{Cr}(\mathrm{H}_{2}\mathrm{O})_{6}\right]\mathrm{Cl}_{3}$

Answer

(C) $\left[\mathrm{Cr}(\mathrm{H}_{2}\mathrm{O})_{5}\mathrm{Cl}\right]\mathrm{Cl}_{2}\cdot\mathrm{H}_{2}\mathrm{O}$

Answer

(D) $\left[\mathrm{Cr}(\mathrm{H}_{2}\mathrm{O})_{3}\mathrm{Cl}_{3}\right]\cdot 3\mathrm{H}_{2}\mathrm{O}$

Question 59

The incorrect statement is

Accepted Answer

(C) Manganate and permanganate ions are paramagnetic

Answer

(A) In manganate and permanganateions, the π - bounding takes place by overlap of p –orbitals of oxygen and d – orbitals of manganese

Answer

(B) Manganate ion is green in colour and permanganateion is purple in colour

Answer

(D) Manganate and permanganate ions are tetrahedral

Question 60

The decreasing order or reactivity of the following compounds towards nucleophilic substitution (S$_{N}$2) is:

Accepted Answer

(C) (II) > (III) > (IV) > (I)

Answer

(A) (II) > (III) > (I) > (IV)

Answer

(B) (III) > (II) > (IV) > (I)

Answer

(D) (IV) > (II) > (III) > (I)

Question 61

A mixture of one mole each of H$_{2}$, He and O$_{2}$ each are enclosed in a cylinder of volume V at temperature T. If the partial pressure of H$_{2}$ is 2 atm, the total pressure of the gases in the cylinder is:

Accepted Answer

(B) 6 atm

Answer

(A) 14 atm

Answer

(C) 22 atm

Answer

(D) 38 atm

Question 62

Among the statements (I – IV), the correct ones are:
(I) Be has smaller atomic radius compared to Mg.
(II) Be has higher ionization enthalpy than Al.
(III) Charge/radius ratio of Be is greater than that of Al.
(IV) Both Be and Al form mainly covalent compounds.

Accepted Answer

(D) (I), (II) and (IV)

Answer

(A) (I), (III) and (IV)

Answer

(B) (II), (III) and (IV)

Answer

(C) (I), (II) and (III)

Question 63

Three isomers A, B and C (mol. formula C$_{8}$H$_{11}$N) give the following results:
R has lower boiling point than S
B $\xrightarrow{	ext{C}_{6}	ext{H}_{5}	ext{SO}_{2}	ext{Cl}}$ alkali – insoluble product
A, B and C, respectively are:

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 64

For the reaction $2A + 3B + \frac{3}{2}C \rightarrow 3P$, which statement is correct?

Accepted Answer

(D) $\frac{dn_{A}}{dt} = \frac{2}{3}\frac{dn_{B}}{dt} = \frac{4}{3}\frac{dn_{C}}{dt}$

Answer

(A) $\frac{dn_{A}}{dt} = \frac{2}{3}\frac{dn_{B}}{dt} = \frac{3}{4}\frac{dn_{C}}{dt}$

Answer

(B) $\frac{dn_{A}}{dt} = \frac{dn_{B}}{dt} = \frac{dn_{C}}{dt}$

Answer

(C) $\frac{dn_{A}}{dt} = \frac{3}{2}\frac{dn_{B}}{dt} = \frac{3}{4}\frac{dn_{C}}{dt}$

Column-I	Column-II
(i).Ranitidine	(a).Antidepressant
(ii).Nardil (Phenelzine)	(b).Antibiolic
(iii).Chloramphenicol	(c).Antihistamine
(iv).Dimetane (Brompheniramine)	(d).Antacid
	(e).Analgesic

JEE Main 3 September 2020 Shift 2 Question Paper with Answers

Physics — JEE Main 3 September 2020 Shift 2

Chemistry — JEE Main 3 September 2020 Shift 2

Mathematics — JEE Main 3 September 2020 Shift 2

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