JEE Mains 2021 Sep 1 Shift 2

' dropped from a height '

A body of mass '

m

h

' reaches the ground with a speed of

0.8 gh

. The value of work done by the air - friction is :

$- 0.68 mgh$
$0.64 mgh$
$mgh$
$1.64 mgh$

Topic:

Work, Energy and Power

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 2

be a continuous function. Then

f : R \to R

lim_{x \to π /4} \frac{\frac{π}{4} \int _{2}^{s e c^{2} x} f ( x ) d x}{x ^{2} - \frac{π ^{2}}{16}}

is equal to:

$2 f (2)$
$4 f$ (2)
$f$ (2)
$2 f$ (2)

Topic:

Continuity and Differentiability

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 3

A peptide synthesized by the reactions of one molecule each of Glycine, Leucine, Aspartic acid and
Histidine will have peptide linkages.

Topic:

Polymers

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 4

A steel rod with

y = 2.0 \times 1 0^{11} Nm^{- 2}

and area of cross-section

α = 1 0^{- 5}^{\circ} C^{- 1}

of length

4 m

10 cm^{2}

is heated from

0^{\circ} C

40 0^{\circ} C

without being allowed to extend. The tension produced in the rod is

x \times 1 0^{5} N

where the value of

x

is.

Topic:

Thermal properties of Matter

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 5

Hard

be the acute angle between the tangents to the ellipse

θ

\frac{x ^{2}}{9} + \frac{y ^{2}}{1} = 1

and the circle

x^{2} + y^{2} = 3

at their point of intersection in the first quadrant. Then

tan θ

is equal to :

$\frac{5}{2 3}$
$\frac{4}{3}$
$\frac{2}{3}$
2

Topic:

Conic Sections

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 6

If the sum of the coefficients in the expansion of

(x + y)^{n}

is 4096 , then the greatest coefficient in the expansion is :

Topic:

Binomial Theorem

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 7

The width of one of the two slits in a Young's double slit experiment is three times the other slit. If the amplitude of the light coming from a slit is proportional to the slit-width, the ratio of minimum to maximum intensity in the interference pattern is

x : 4

where

x

____ is.

Topic:

Wave Optics

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 8

A 50 watt bulb emits monochromatic red light of wavelength of

795 nm

. The number of photons emitted per second by the bulb is

x \times 1 0^{20}

. The value of

x

is ____ (Nearest integer)
[Given :

h = 6.63 \times 1 0^{- 34} Js

When a body slides down from rest along a smooth incline plane making an angle of

c = 3.0 \times 1 0^{8} ms^{- 1}

]

Topic:

Structure of Atom

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 9

Hard

3 0^{\circ}

with the horizontal, it takes time

T

. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time

α T

, where

a

α

constant greater than 1. The co-efficient of friction between the body and the rough plane is

\frac{1}{x} (\frac{α ^{2} - 1}{α ^{2}})

where

x

____

Topic:

Laws of motion

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 10

All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two

R

appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word FARMER in this list is :

Topic:

Permutations and Combinations

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 11

is dissolved in deionised water to make

80 g

of copper sulphate

CuSO_{4} \cdot 5 H_{2} O

5 L

of solution. The concentration of the copper sulphate solution is

x \times 1 0^{- 3} mol L^{- 1}

. The value of

x

\dots\dots\dots\dots\dots .

[Atomic masses : Cu :

63.54 u, S : 32 u, O : 16 u, H : 1 u

]

Topic:

Some Basic Concepts of Chemistry

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 12

be a polynomial of degree 3 such that

f (x)

f (k) = - \frac{2}{k}

for

k = 2, 3, 4, 5

. Then the value of

52 - 10 f (10)

is equal to :

Topic:

Complex Number and Quadratic Equations

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 13

An empty LPG cylinder weighs

14.8 kg

. When full, it weighs

29.0 kg

and shows a pressure of

3.47 atm

. In the course of use at ambient temperature, the mass of the cylinder is reduced to

23.0 kg

. The final pressure inside the cylinder is atm. (Nearest integer) (Assume LPG to be an ideal gas)

Topic:

States of Matter

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 14

The spin-only magnetic moment value of

B_{2}^{+}

species is ____

\times 1 0^{- 2} BM

. (Nearest integer) [Given:

3 = 1.73]

Topic:

The d-and f-Block Elements

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 15

Let the points of intersections of the lines

x - y + 1 = 0, x - 2 y + 3 = 0

are the mid points of the sides of a triangle ABC. Then the area of the triangle

2 x - 5 y + 11 = 0

A BC

Topic:

Straight Lines

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 16

The average translational kinetic energy of

N_{2}

gas molecules at

^{\circ} C

becomes equal to the K.E. of an electron accelerated from rest through a potential difference of

0.1

volt.
(Given

k_{B} = 1.38 \times 1 0^{- 23} J / K

)(Fill the nearest integer)

Topic:

Kinetic Theory

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 17

Hard

Let X be a random variable with distribution :

If the mean of x is 2.3 and variance of X is σ^{2} then 100 σ^{2} is equal to

Topic:

Statistics

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 18

is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length

A mass of

5 kg

4 m

has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed?

$10 m / s^{2}$
$5 m / s^{2}$
$9.8 m / s^{2}$
$4 m / s^{2}$

Topic:

Oscillations

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 19

Consider the system of linear equations

- x + y + 2 z = 0 3 x - a y + 5 z = 1 2 x - 2 y - a z = 7

for which the system is inconsistent and

S_{1}

be the set of all

a \in R

S_{2}

be the set of all

a \in R

for which the system has infinitely many solutions. If

n (S_{1})

denote the number of elements in

n (S_{2})

S_{1}

S_{2}

respectively, then

$n (S_{1}) = 2, n (S_{2}) = 2$
$n (S_{1}) = 2, n (S_{2}) = 0$
$n (S_{1}) = 0, n (S_{2}) = 2$
$n (S_{1}) = 1, n (S_{2}) = 0$

Topic:

Determinants

Exam:

JEE Mains 2021 Sep 1 Shift 2

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Question 20