JEE Mains 2021 Mar 16 Shift 2

Arrange the following metal complex/compounds in the increasing order of spin only magnetic moment. Presume all the three, high spin system.
[Atomic numbers

Ce = 58, Gd = 64

Eu = 63

]
(a)

(NH_{4})_{2} [Ce (NO_{3})_{6}]

(b)

Gd (NO_{3})_{3}

and
(c)

Eu (NO_{3})_{3}

$(a) < (b) < (c)$
$(c) < (a) < (b)$
$(b) < (a) < (c)$
$(a) < (c) < (b)$

Topic:

The d-and f-Block Elements

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 2 solutions

Question 2

be a twice differentiable function such that

f : S \to S

where

S = (0, \infty)

f (x + 1) = x f (x)

. If

g : S \to R

be defined as

g (x) = lo g_{e} f (x)

, then the value of

∣ g^{''} (5) - g^{''} (1) ∣

is equal to :

$1$
$\frac{205}{144}$
$\frac{187}{144}$
$\frac{197}{144}$

Topic:

Relations and Functions

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 2 solutions

Question 3

Let f be a real valued function, defined on

R - {- 1, 1}

and given by

f (x) = 3 lo g_{e} ∣ ∣ \frac{x - 1}{x + 1} ∣ ∣ - \frac{2}{x - 1}

. Then in which of the following intervals, function

f (x)

is increasing ?

$(- \infty, \frac{1}{2}] - {- 1}$
$(- \infty, \infty) - {- 1, 1}$
$(- \infty, - 1) \cup ([\frac{1}{2}, \infty) - {1})$
$(- 1, \frac{1}{2}]$

Topic:

Relations and Functions

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 6 solutions

Question 4

Easy

Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass

= 500 g

, Decay constant

= 20 g / s

then how much time is required for the amplitude of the system to drop to half of its initial value?

(ln 2 = 0.693)

$0.034 s$
$17.32 s$
$15.01 s$
$34.65 s$

Topic:

Oscillations

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 3 solutions

Question 5

A mosquito is moving with a velocity

v = 0.5 t^{2} \hat{i} + 3 t \hat{j} + 9 \hat{k} m / s

and accelerating in uniform conditions. What will be the direction of mosquito after

2 s

$tan^{- 1} (\frac{2}{3})$ from y-axis
$tan^{- 1} (\frac{5}{2})$ from y-axis
$tan^{- 1} (\frac{5}{2})$ from x-axis
$tan^{- 1} (\frac{2}{3})$ from x-axis

Topic:

Physical World

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 11 solutions

Question 6

is applied on an intersection point of x=2 plane and x-axis. The magnitude of torque of this force about a point (2,3,4) is (Round off to the Nearest Integer).

A force

F = 4 \hat{i} + 3 \hat{j} + 4 \hat{k}

Topic:

Laws of motion

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 2 solutions

Question 7

is 2.7 days. The activity of

The half-life of

Au^{198}

1.50 mg

Au^{198}

if its atomic weight is

198 gmol^{- 1}

is,

(N_{A} = 6 \times 1 0^{23} / mol .)

$240 Ci$
$357 Ci$
$535 Ci$
$252 Ci$

Topic:

Nuclei

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 2 solutions

Question 8

The energy dissipated by a resistor is

10 mj

1 s

when an electric current of 2

mA

flows through it. The resistance is

Ω.

(Round off to the Nearest Integer).

Topic:

Current Electricity

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 2 solutions

Question 9

a = \hat{i} + 2 \hat{j} - 3 \hat{k}

b = 2 \hat{i} - 3 \hat{j} + 5 \hat{k}

. If

r \times a = b \times r, r

(α \hat{i} + 2 \hat{j} + \hat{k}) = 3

r \cdot (2 \hat{i} + 5 \hat{j} - α \hat{k}) = - 1, α \in

R

, then the value of

α + ∣ r ∣^{2}

is equal to:

Topic:

Vector Algebra

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 3 solutions

Question 10

distance in the magnetic field

A charge Q is moving

d l

B .

Find the value of work done by

B .

Infinite
1
$- 1$
Zero

Topic:

Moving Charges and Magnetism

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 5 solutions

Question 11

A solid disc of radius ' a ' and mass ' m ' rolls down without slipping on an inclined plane making an angle

θ

with the horizontal. The acceleration of the disc will be

\frac{2}{b} g sin θ

. where b is (Round off to the Nearest Integer) ( g= acceleration due to gravity,

θ

angle as shown in figure).

Topic:

System of Particles and Rotational Motion

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 2 solutions

Question 12

Easy

In a parallel plate capacitor set up, the plate area of capacitor is

2 m^{2}

and the plates are separated by

1 m

. If the space between the plates are filled with a dielectric material of thickness

0.5 m

and area

2 m^{2}

( see fig) the capacitance of the set-up will be

ε 0.

(Dielectric constant of the
material =3.2 ) (Round off the Nearest Integer)
.

Topic:

Electrostatic Potential and Capacitance

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 4 solutions

Question 13

A and B decompose via first order kinetics with half-lives

54.0 min

respectively. Starting from an equimolar non reactive mixture of A and B, the time taken for the concentration of A to become 16 times that of B is.............. min. (Round off to the Nearest Integer).

18.0 min

Topic:

Chemical Kinetics

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 12 solutions

Question 14

. It starts from rest and was at the origin initially. After

A body of mass

2 kg

moves under a force of

(2 \hat{i} + 3 \hat{j} + 5 \hat{k}) N

4 s

, its new coordinates are

(8, b, 20)

. The value of

b

is (Round off to the Nearest Integer)

Topic:

Laws of motion

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 5 solutions

Question 15

Easy

Calculate the value of mean free path

(λ)

for oxygen molecules at temperature

2 7^{\circ} C

and pressure

1.01 \times 1 0^{5} Pa

. Assume the molecular diameter

0.3 nm

and the gas is ideal.

(k = 1.38 \times 1 0^{- 23} JK^{- 1})

$58 nm$
$86 nm$
$32 nm$
$102 nm$

Topic:

Kinetic Theory

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 6 solutions

Question 16

is the solution of the differential equation

y = y (x)

\frac{d y}{d x} + (tan x) y = sin x, 0 \leq x \leq \frac{π}{3}

, with

y (0) = 0

, then

y (\frac{π}{4})

equal to :

$(\frac{1}{2 2}) lo g_{e} 2$
$lo g_{e} 2$
$\frac{1}{4} lo g_{e} 2$
$\frac{1}{2} lo g_{e} 2$

Topic:

Differential Equations

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 5 solutions

Question 17

For an ideal heat engine, the temperature of the source is

12 7^{\circ} C

. In order to have

60%

efficiency the temperature of the sink sound be

^{\circ} C

. (Round off to the Nearest Integer).

Topic:

Thermodynamics

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 2 solutions

Question 18

Let A

= [a_{1} a_{2}]

matrices with real entries such that A=X B, where

B = [b_{1} b_{2}]

be two

2 \times 1

X = \frac{1}{3} [11 - 1 k]

, and

k \in R .

a_{1}^{2} + a_{2}^{2} = \frac{2}{3} (b_{1}^{2} + b_{2}^{2})

, then the value of k is _______.

(k^{2} + 1) b z^{2} \neq = - 2 b_{1} b_{2}

Topic:

Matrices

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 3 solutions

Question 19

be such that the function

α \in R

f (x) = {\frac{c o s ^{- 1} ( 1 - { x } ^{2} ) s i n ^{- 1} ( 1 - { x })}{{ x } - { x } ^{3}}, x \neq = 0 α_{1} is continuous at x = 0, x = 0

w h ere

{x} = x - [x]

[x]

is greatest integer less than or equal to x. Then :

$α = 0$
$α = \frac{π}{2}$
$α = \frac{π}{4}$
No such $α$ exists

Topic:

Continuity and Differentiability

Exam:

JEE Mains 2021 Mar 16 Shift 2

View 4 solutions

Question 20

f : R \to R