JEE Main 1 September 2021 Shift 2 Question Paper

Question 1

Let $f : \mathbb{R} 	o \mathbb{R}$ be a continuous function. Then $\lim_{x 	o \frac{\pi}{4}} \frac{\frac{\pi}{4}\int_{2}^{\sec^{2} x} f(x)\,dx}{x^{2} - \frac{\pi^{2}}{16}}$ is equal to :

Accepted Answer

(B) $2f(2)$

Answer

(A) $f(2)$

Answer

(C) $2f\left(\sqrt{2}\right)$

Answer

(D) $4f(2)$

Question 2

$\cos^{-1}(\cos(-5)) + \sin^{-1}(\sin(6)) - 	an^{-1}(	an(12))$ is equal to :
(The inverse trigonometric functions take the principal values)

Accepted Answer

(C) 4 π − 11

Answer

(A) 3π − 11

Answer

(B) 4 π − 9

Answer

(D) 3π + 1

Question 3

Consider the system of linear equations
− x + y + 2z = 0
3x − ay + 5z =1
2x − 2y − az = 7
Let $S_{1}$ be the set of all a ∈ ℝ for which the system is inconsistent and $S_{2}$ be the set of all a ∈ ℝ for which the system has infinitely many solutions. If $n(S_{1})$ and $n(S_{2})$ denote the number of elements in $S_{1}$ and $S_{2}$ respectively, then

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 4

Let the acute angle bisector of the two planes x − 2y − 2z + 1 = 0 and 2x − 3y − 6z + 1 = 0 be the plane P. Then which of the following points lies on P?

Accepted Answer

(B) $\left(-2, 0, -\frac{1}{2}\right)$

Answer

(A) $\left(3, 1, -\frac{1}{2}\right)$

Answer

(C) (0, 2, –4)

Answer

(D) (4, 0, – 2)

Question 5

Which of the following is equivalent to the Boolean expression p ∧ ~q ?

Accepted Answer

(D) ~ (p → q)

Answer

(A) ~ (q → p)

Answer

(B) ~ p → ~q

Answer

(C) ~ (p → ~q)

Question 6

Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :

Accepted Answer

(B) $\frac{1}{18}$

Answer

(A) $\frac{2}{7}$

Answer

(C) $\frac{1}{7}$

Answer

(D) $\frac{1}{9}$

Question 7

If y = y (x) is the solution curve of the differential equation $x^{2}dy + \left(y - \frac{1}{x}\right)dx = 0$ ; x > 0 and y(1) = 1, then $y\left(\frac{1}{2}\right)$ is equal to :

Accepted Answer

(D) 3 − e

Answer

(A) $\frac{3}{2} - \frac{1}{\sqrt{e}}$

Answer

(B) $3 + \frac{1}{\sqrt{e}}$

Answer

(C) 3 + e

Question 8

If n is the number of solutions of the equation $2\cos x\left(4\sin\left(\frac{\pi}{4} + x\right)\sin\left(\frac{\pi}{4} - x\right) - 1\right) = 1$, x ∈ [0, π] and S is the sum of all these solutions, then the ordered pair (n, S) is :

Accepted Answer

(A) (3, 13π / 9)

Answer

(B) (2, 2π / 3)

Answer

(C) (2, 8π / 9)

Answer

(D) (3, 5π / 3)

Question 9

The function $f(x) = x^{3} - 6x^{2} + ax + b$ is such that f(2) = f(4) = 0. Consider two statements.
(S1) there exists $x_{1}, x_{2} \in (2, 4)$, $x_{1} < x_{2}$, such that $f'(x_{1}) = -1$ and $f'(x_{2}) = 0$.
(S2) there exists $x_{3}, x_{4} \in (2, 4)$, $x_{3} < x_{4}$, such that f is decreasing in $(2, x_{4})$, increasing in $(x_{4}, 4)$ and $2f'(x_{3}) = \sqrt{3}f\left(x_{4}\right)$.
Then

Accepted Answer

(A) both (S1) and (S2) are true

Answer

(B) (S1) is false and (S2) is true

Answer

(C) both (S1) and (S2) are false

Answer

(D) (S1) is true and (S2) is false

Question 10

Let $J_{n,m} = \int_{0}^{\frac{1}{2}} \frac{x^{n}}{x^{m} - 1}dx$, ∀ n > m and n, m ∈ N . Consider a matrix $A = [a_{ij}]_{3 	imes 3}$ where $a_{ij} = \begin{cases} J_{6+i,3} - J_{i+3,3}, & i \le j \ 0, & i > j \end{cases}$. Then $\left|\mathrm{adj}A^{-1}ight|$ is :

Accepted Answer

(C) $(105)^{2} 	imes 2^{38}$

Answer

(A) $(15)^{2} 	imes 2^{42}$

Answer

(B) $(15)^{2} 	imes 2^{34}$

Answer

(D) $(105)^{2} 	imes 2^{36}$

Question 11

The area, enclosed by the curves y = sin x + cos x and $y = \left|\cos x - \sin x\right|$ and the lines x = 0, $x = \frac{\pi}{2}$, is :

Accepted Answer

(A) $2\sqrt{2}\left(\sqrt{2} - 1\right)$

Answer

(B) $2\left(\sqrt{2} + 1\right)$

Answer

(C) $4\left(\sqrt{2} - 1\right)$

Answer

(D) $2\sqrt{2}\left(\sqrt{2} + 1\right)$

Question 12

The distance of line 3y − 2z − 1 = 0 = 3x − z + 4 from the point (2, − 1, 6) is :

Accepted Answer

(C) $2\sqrt{6}$

Answer

(A) $\sqrt{26}$

Answer

(B) $2\sqrt{5}$

Answer

(D) $4\sqrt{2}$

Question 13

Consider the parabola with vertex $\left(\frac{1}{2}, \frac{3}{4}\right)$ and the directrix $y = \frac{1}{2}$ . Let P be the point where the parabola meets the line $x = -\frac{1}{2}$. If the normal to the parabola at P intersects the parabola again at the point Q, then $(PQ)^{2}$ is equal to :

Accepted Answer

(B) $\frac{125}{16}$

Answer

(A) $\frac{75}{8}$

Answer

(C) $\frac{25}{2}$

Answer

(D) $\frac{15}{2}$

Question 14

The numbers of pairs (a, b) of real numbers, such that whenever α is a root of the equation $x^{2} + ax + b = 0$ , $\alpha^{2} - 2$ is also a root of this equation, is :

Accepted Answer

(A) 6

Answer

(B) 2

Answer

(C) 4

Answer

(D) 8

Question 15

Let $S_{n} = 1 \cdot (n - 1) + 2 \cdot (n - 2) + 3 \cdot (n - 3) + \dots + (n - 1) \cdot 1$ , n ≥ 4.
The sum $\sum_{n=4}^{\infty}\left(\frac{2S_{n}}{n!} - \frac{1}{(n-2)!}\right)$ is equal to :

Accepted Answer

(A) $\frac{e-1}{3}$

Answer

(B) $\frac{e-2}{6}$

Answer

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

Answer

(D) $\frac{e}{6}$

Question 16

Let $P_{1}$, $P_{2}$, ....., $P_{15}$ be 15 points on a circle. The number of distinct triangles formed by points $P_{i}, P_{j}, P_{k}$ such that i + j + k ≠ 15, is :

Accepted Answer

(C) 443

Answer

(A) 12

Answer

(B) 419

Answer

(D) 455

Question 17

The range of the function,
$f(x) = \log_{\sqrt{5}}\left(3 + \cos\left(\frac{3\pi}{4} + x\right) + \cos\left(\frac{\pi}{4} + x\right) + \cos\left(\frac{\pi}{4} - x\right) - \cos\left(\frac{3\pi}{4} - x\right)\right)$ is :

Accepted Answer

(D) [0, 2]

Answer

(A) $\left(0, \sqrt{5}\right)$

Answer

(B) [–2, 2]

Answer

(C) $\left[\frac{1}{\sqrt{5}}, \sqrt{5}\right]$

Question 18

Let $a_{1}, a_{2}, ......., a_{21}$ be an AP such that $\sum_{n=1}^{20}\frac{1}{a_{n}a_{n+1}} = \frac{4}{9}$. If the sum of this AP is 189, then $a_{6}a_{16}$ is equal to :

Accepted Answer

(B) 72

Answer

(A) 57

Answer

(C) 48

Answer

(D) 36

Question 19

The function f(x), that satisfies the condition $f(x) = x + \int_{0}^{\pi/2} \sin x \cdot \cos y\, f(y)dy$, is :

Accepted Answer

(D) x + (π − 2) sinx

Answer

(A) $x + \frac{2}{3}(\pi - 2)\sin x$

Answer

(B) x + (π + 2) sinx

Answer

(C) $x + \frac{\pi}{2}\sin x$

Question 20

Let θ be the acute angle between the tangents to the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{1} = 1$ and the circle $x^{2} + y^{2} = 3$ at their point of intersection in the first quadrant. Then tanθ is equal to :

Accepted Answer

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

Answer

(A) $\frac{5}{2\sqrt{3}}$

Answer

(C) $\frac{4}{\sqrt{3}}$

Answer

(D) 2

Question 21

Let X be a random variable with distribution.
If the mean of X is 2.3 and variance of X is $\sigma^{2}$, then $100\,\sigma^{2}$ is equal to ________ .

Accepted Answer

781

Question 22

Let $f(x) = x^{6} + 2x^{4} + x^{3} + 2x + 3$, x ∈ ℝ. Then the natural number n for which $\lim_{x 	o 1} \frac{x^{n} f(1) - f(x)}{x - 1} = 44$ is ________ .

Accepted Answer

7

Question 23

If for the complex numbers z satisfying |z − 2 − 2i| ≤ 1, the maximum value of |3iz + 6| is attained at a + ib, then a + b is equal to ________ .

Accepted Answer

5

Question 24

Let the points of intersections of the lines x − y + 1 = 0, x − 2y + 3 = 0 and 2x − 5y + 11 = 0 are the mid points of the sides of a triangle ABC. Then the area of the triangle ABC is ________ .

Accepted Answer

6

Question 25

Let f(x) be a polynomial of degree 3 such that $f(k) = -\frac{2}{k}$ for k = 2, 3, 4, 5. Then the value of 52 − 10 f(10) is equal to :

Accepted Answer

26

Question 26

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 ______ .

Accepted Answer

77

Question 27

If the sum of the coefficients in the expansion of $(x + y)^{n}$ is 4096, then the greatest coefficient in the expansion is ________ .

Accepted Answer

924

Question 28

Let $\vec{a} = 2\hat{i} - \hat{j} + 2\hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} - \hat{k}$. Let a vector $\vec{v}$ be in the plane containing $\vec{a}$ and $\vec{b}$. If $\vec{v}$ is perpendicular to the vector $3\hat{i} + 2\hat{j} - \hat{k}$ and its projection on $\vec{a}$ is 19 units, then $\left|2\vec{v}\right|^{2}$ is equal to ______ .

Accepted Answer

1494

Question 29

Let [t] denote the greatest integer ≤ t. The number of points where the function $f(x) = [x]\left|x^{2} - 1\right| + \sin\left(\frac{\pi}{[x] + 3}\right) - [x + 1], x \in (-2, 2)$ is not continuous is ______ .

Accepted Answer

2

Question 30

A man starts walking from the point P(−3,4), touches the x-axis at R, and then turns to reach at the point Q(0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then $50\left((PR)^{2} + (RQ)^{2}\right)$ is equal to ______ .

Accepted Answer

1250

Question 31

A cube is placed inside an electric field, $\vec{E} = 150y^{2}\hat{j}$. The side of the cube is 0.5 m and is placed in the field as shown in the given figure. The charge inside the cube is :

Accepted Answer

(B) 8.3 × 10$^{-11}$ C

Answer

(A) 3.8 × 10$^{-11}$ C

Answer

(C) 3.8 × 10$^{-12}$ C

Answer

(D) 8.3 × 10$^{-12}$ C

Question 32

A square loop of side 20 cm and resistance 1Ω is moved towards right with a constant speed v$_{0}$. The right arm of the loop is in a uniform magnetic field of 5T. The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value 4Ω. What should be the value of v$_{0}$ so that a steady current of 2 mA flows in the loop ?

Accepted Answer

(B) 1 cm/s

Answer

(A) 1 m/s

Answer

(C) 10$^{2}$ m/s

Answer

(D) 10$^{-2}$ cm/s

Question 33

The temperature of an ideal gas in 3-dimensions is 300 K. The corresponding de-Broglie wavelength of the electron approximately at 300 K, is :
[m$_{e}$ = mass of electron = 9 × 10$^{-31}$ kg
h = Planck constant = 6.6 × 10$^{-34}$ Js
k$_{B}$ = Boltzmann constant = 1.38 × 10$^{-23}$ JK$^{-1}$]

Accepted Answer

(A) 6.26 nm

Answer

(B) 8.46 nm

Answer

(C) 2.26 nm

Answer

(D) 3.25 nm

Question 34

A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of $0.8\sqrt{gh}$. The value of workdone by the air-friction is :

Accepted Answer

(A) –0.68 mgh

Answer

(B) mgh

Answer

(C) 1.64 mgh

Answer

(D) 0.64 mgh

Question 35

The ranges and heights for two projectiles projected with the same initial velocity at angles 42° and 48° with the horizontal are R$_{1}$, R$_{2}$ and H$_{1}$, H$_{2}$ respectively. Choose the correct option :

Accepted Answer

(B) R$_{1}$ = R$_{2}$ and H$_{1}$ < H$_{2}$

Answer

(A) R$_{1}$ > R$_{2}$ and H$_{1}$ = H$_{2}$

Answer

(C) R$_{1}$ < R$_{2}$ and H$_{1}$ < H$_{2}$

Answer

(D) R$_{1}$ = R$_{2}$ and H$_{1}$ = H$_{2}$

Question 36

A block of mass m slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given m = 8 kg, M = 16 kg
Assume all the surfaces shown in the figure to be frictionless.

Accepted Answer

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

Answer

(A) $\frac{4}{3}$g

Answer

(B) $\frac{6}{5}$g

Answer

(C) $\frac{3}{5}$g

Question 37

Due to cold weather a 1 m water pipe of cross–sectional area 1 cm$^{2}$ is filled with ice at −10°C. Resistive heating is used to melt the ice. Current of 0.5 A is passed through 4 kΩ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required ?
(Given latent heat of fusion for water/ice = 3.33 × 10$^{5}$ J kg$^{-1}$, specific heat of ice = 2 × 10$^{3}$ J kg$^{-1}$ and density of ice = 10$^{3}$ kg / m$^{3}$

Accepted Answer

(B) 35.3 s

Answer

(A) 0.353 s

Answer

(C) 3.53 s

Answer

(D) 70.6 s

Question 38

A student determined Young's Modulus of elasticity using the formula $Y = \frac{MgL^{3}}{4bd^{3}\delta}$. The value of g is taken to be 9.8 m/s$^{2}$, without any significant error, his observation are as following.
Then the fractional error in the measurement of Y is :

Accepted Answer

(B) 0.0155

Answer

(A) 0.0083

Answer

(C) 0.155

Answer

(D) 0.083

Question 39

Two resistors R$_{1}$ = (4 ± 0.8) Ω and R$_{2}$ = (4 ± 0.4) Ω are connected in parallel. The equivalent resistance of their parallel combination will be :

Accepted Answer

(C) (2 ± 0.3) Ω

Answer

(A) (4 ± 0.4) Ω

Answer

(B) (2 ± 0.4) Ω

Answer

(D) (4 ± 0.3) Ω

Question 40

The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then :

Accepted Answer

(B) y– will decay faster than x.

Answer

(A) x–will decay faster than y.

Answer

(C) x and y have same decay rate initially and later on different decay rate.

Answer

(D) x and y decay at the same rate always.

Question 41

Following plots show Magnetization (M) vs Magnetising field (H) and Magnetic susceptibility ( χ ) vs temperature (T) graph :
Which of the following combination will be represented by a diamagnetic material?

Accepted Answer

(A) (a), (c)

Answer

(B) (a), (d)

Answer

(C) (b), (d)

Answer

(D) (b), (c)

Question 42

A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water (μ = 4/3) into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled ?

Accepted Answer

(B) 10 cm

Answer

(A) 11.7 cm

Answer

(C) 7.5 cm

Answer

(D) 8.75 cm

Question 43

In the given figure, each diode has a forward bias resistance of 30Ω and infinite resistance in reverse bias. The current I$_{1}$ will be :

Accepted Answer

(C) 2 A

Answer

(A) 3.75 A

Answer

(B) 2.35 A

Answer

(D) 2.73 A

Question 44

For the given circuit the current $i$ through the battery when the key in closed and the steady state has been reached is__________.

Accepted Answer

(C) 10 A

Answer

(A) 6 A

Answer

(B) 25 A

Answer

(D) 0 A

Question 45

An object of mass 'm' is being moved with a constant velocity under the action of an applied force of 2N along a frictionless surface with following surface profile.
The correct applied force vs distance graph will be:

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 46

A mass of 5 kg 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 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?

Accepted Answer

(C) 4 m/s$^{2}$

Answer

(A) 10 m/s$^{2}$

Answer

(B) 5 m/s$^{2}$

Answer

(D) 9.8 m/s$^{2}$

Question 47

A capacitor is connected to a 20 V battery through a resistance of 10Ω. It is found that the potential difference across the capacitor rises to 2 V in 1 μs. The capacitance of the capacitor is ....................μF.
Given : $\ln\left(\frac{10}{9}\right) = 0.105$

Accepted Answer

(B) 0.95

Answer

(A) 9.52

Answer

(C) 0.105

Answer

(D) 1.85

Question 48

Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is :

Accepted Answer

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

Answer

(A) $\frac{1}{2}\sqrt{\frac{GM}{R(2\sqrt{2}+1)}}$

Answer

(C) $\frac{1}{2}\sqrt{\frac{GM}{R}(2\sqrt{2}-1)}$

Answer

(D) $\sqrt{\frac{GM}{R}}$

Question 49

Electric field of plane electromagnetic wave propagating through a non–magnetic medium is given by E = 20cos(2 × 10$^{10}$ t–200x) V/m. The dielectric constant of the medium is equal to :
(Take μ$_{r}$ = 1)

Accepted Answer

(A) 9

Answer

(B) 2

Answer

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

Answer

(D) 3

Question 50

There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is 1 : 1. The magnetic field at point P is ____.

Accepted Answer

(A) $\frac{\mu_{0}I}{4\pi xy}\left[\sqrt{x^{2}+y^{2}}+(x+y)\right]$

Answer

(B) $\frac{\mu_{0}I}{4\pi xy}\left[\sqrt{x^{2}+y^{2}}-(x+y)\right]$

Answer

(C) $\frac{\mu_{0}Ixy}{4\pi}\left[\sqrt{x^{2}+y^{2}}-(x+y)\right]$

Answer

(D) $\frac{\mu_{0}Ixy}{4\pi}\left[\sqrt{x^{2}+y^{2}}+(x+y)\right]$

Question 51

The temperature of 3.00 mol of an ideal diatomic gas is increased by 40.0 °C without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is $\frac{x}{10}$. Then the value of x (round off to the nearest integer) is ________ .
(Given R = 8.31 J mol$^{-1}$ K$^{-1}$)

Accepted Answer

25

Question 52

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 ________ .

Accepted Answer

1

Question 53

Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hours respectively. The radius of the orbit of nearer satellite is 2 × 10$^{3}$ km. The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is $\frac{\pi}{x}$ rad h$^{-1}$ where x is ..........

Accepted Answer

3

Question 54

When a body slides down from rest along a smooth inclined plane making an angle of 30° 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 αT, where α is a constant greater than 1. The co-efficient of friction between the body and the rough plane is $\frac{1}{\sqrt{x}}\left(\frac{\alpha^{2}-1}{\alpha^{2}}\right)$ where x = ..........

Accepted Answer

3

Question 55

The average translational kinetic energy of N$_{2}$ gas molecules at ..........°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 × 10$^{-23}$ J/K)
(Fill the nearest integer).

Accepted Answer

500

Question 56

A uniform heating wire of resistance 36 Ω is connected across a potential difference of 240 V. The wire is then cut into half and potential difference of 240 V is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be 1 : x, where x is ..........

Accepted Answer

4

Question 57

A steel rod with y = 2.0 × 10$^{11}$ Nm$^{-2}$ and α = 10$^{-5}$ °C$^{-1}$ of length 4 m and area of cross-section 10 cm$^{2}$ is heated from 0° C to 400°C without being allowed to extend. The tension produced in the rod is x × 10$^{5}$ N where the value of x is ..........

Accepted Answer

8

Question 58

A carrier wave with amplitude of 250 V is amplitude modulated by a sinusoidal base band signal of amplitude 150 V. The ratio of minimum amplitude to maximum amplitude for the amplitude modulated wave is 50 : x, then value of x is ..........

Accepted Answer

200

Question 59

An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of 40,000 kg is moving with a speed of 72 kmh$^{-1}$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by 1.0 m. If 90% of energy of the wagon is lost due to friction, the spring constant is .......... × 10$^{5}$ N/m.

Accepted Answer

16

Question 60

Water sample is called cleanest on the basis of which one of the BOD values given below

Accepted Answer

(C) 3 ppm

Answer

(A) 11 ppm

Answer

(B) 15 ppm

Answer

(D) 21 ppm

Question 61

Calamine and Malachite, respectively, are the ores of :

Accepted Answer

(B) Zinc and Copper

Answer

(A) Nickel and Aluminium

Answer

(C) Copper and Iron

Answer

(D) Aluminium and Zinc

Question 62

Experimentally reducing a functional group cannot be done by which one of the following reagents ?

Accepted Answer

(B) Na/H$_{2}$

Answer

(A) Pt-C/H$_{2}$

Answer

(C) Pd-C/H$_{2}$

Answer

(D) Zn/H$_{2}$O

Question 63

Which one of the following given graphs represents the variation of rate constant (k) with temperature (T) for an endothermic reaction ?

Accepted Answer

(C) (3)

Answer

(A) (1)

Answer

(B) (2)

Answer

(D) (4)

Question 64

Identify A in the following reaction.

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Physical Quantity	Least count of the Equipment used for measurement	Observed value
Mass (M)	1 g	2 kg
Length of bar (L)	1 mm	1 m
Breadth of bar (b)	0.1 mm	4 cm
Thickness of bar (d)	0.01 mm	0.4 cm
Depression (δ)	0.01 mm	5 mm

List-I (Colloid Preparation Method)	List-II (Chemical Reaction)
a.Hydrolysis	i.2AuCl $_{3}$ + 3HCHO + 3H $_{2}$ O → 2Au(sol) + 3HCOOH + 6HCl
b.Reduction	ii.As $_{2}$ O $_{3}$ + 3H $_{2}$ S → As $_{2}$ S $_{3}$ (sol) + 3H $_{2}$ O
c.Oxidation	iii.SO $_{2}$ + 2H $_{2}$ S → 3S(sol) + 2H $_{2}$ O
d.Double Decomposition	iv.FeCl $_{3}$ + 3H $_{2}$ O → Fe(OH) $_{3}$ (sol) + 3HCl

JEE Main 1 September 2021 Shift 2 Question Paper with Answers

Physics — JEE Main 1 September 2021 Shift 2

Chemistry — JEE Main 1 September 2021 Shift 2

Mathematics — JEE Main 1 September 2021 Shift 2

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