JEE Main 28 July 2022 Shift 1 Question Paper

Question 1

Let the solution curve of the differential equation $xdy = \left(\sqrt{x^{2}+y^{2}} + y\right)dx$, $x > 0$, intersect the line $x = 1$ at $y = 0$ and the line $x = 2$ at $y = \alpha$. Then the value of $\alpha$ is :

Accepted Answer

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

Answer

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

Answer

(C) $-\frac{3}{2}$

Answer

(D) $\frac{5}{2}$

Question 2

Considering only the principal values of the inverse trigonometric functions, the domain of the function $f(x) = \cos^{-1}\left(\frac{x^{2}-4x+2}{x^{2}+3}\right)$ is :

Accepted Answer

(B) $\left[-\frac{1}{4}, \infty\right)$

Answer

(A) $\left(-\infty, \frac{1}{4}\right]$

Answer

(C) $\left(-\frac{1}{3}, \infty\right)$

Answer

(D) $\left(-\infty, \frac{1}{3}\right]$

Question 3

Let the vectors $\vec{a} = (1+t)\hat{i} + (1-t)\hat{j} + \hat{k}$, $\vec{b} = (1-t)\hat{i} + (1+t)\hat{j} + 2\hat{k}$ and $\vec{c} = t\hat{i} - t\hat{j} + \hat{k}$, $t \in R$ be such that for $\alpha, \beta, \gamma \in R$, $\alpha\vec{a} + \beta\vec{b} + \gamma\vec{c} = \vec{0} \Rightarrow \alpha = \beta = \gamma = 0$. Then, the set of all values of t is :

Accepted Answer

(C) equal to R − {0}

Answer

(A) a non-empty finite set

Answer

(B) equal to N

Answer

(D) equal to R

Question 4

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $\cos^{-1}(x) - 2\sin^{-1}(x) = \cos^{-1}(2x)$ is equal to :

Accepted Answer

(A) 0

Answer

(B) 1

Answer

(C) $\frac{1}{2}$

Answer

(D) $-\frac{1}{2}$

Question 5

Let the operations $*, \odot \in \{\wedge, \vee\}$. If $(p * q) \odot (p \odot \sim q)$ is a tautology, then the ordered pair $(*, \odot)$ is :

Accepted Answer

(B) $(\vee, \vee)$

Answer

(A) $(\vee, \wedge)$

Answer

(C) $(\wedge, \wedge)$

Answer

(D) $(\wedge, \vee)$

Question 6

Let a vector $\vec{a}$ has a magnitude 9. Let a vector $\vec{b}$ be such that for every $(x, y) \in R 	imes R - \{(0,0)\}$, the vector $(x\vec{a} + y\vec{b})$ is perpendicular to the vector $(6y\,\vec{a} - 18x\,\vec{b})$. Then the value of $\left|\vec{a} 	imes \vec{b}ight|$ is equal to:

Accepted Answer

(B) $27\sqrt{3}$

Answer

(A) $9\sqrt{3}$

Answer

(C) 9

Answer

(D) 81

Question 7

For $t \in (0, 2\pi)$, if ABC is an equilateral triangle with vertices A(sint, −cost), B(cost, sint) and C(a, b) such that its orthocentre lies on a circle with centre $\left(1, \frac{1}{3}\right)$, then $(a^{2} - b^{2})$ is equal to :

Accepted Answer

(B) 8

Answer

(A) $\frac{8}{3}$

Answer

(C) $\frac{77}{9}$

Answer

(D) $\frac{80}{9}$

Question 8

For $\alpha \in N$, consider a relation R on N given by $R = \{(x, y) : 3x + \alpha y 	ext{ is a multiple of } 7\}$. The relation R is an equivalence relation if and only if :

Accepted Answer

(D) 4 is the remainder when $\alpha$ is divided by 7

Answer

(A) $\alpha = 14$

Answer

(B) $\alpha$ is a multiple of 4

Answer

(C) 4 is the remainder when $\alpha$ is divided by 10

Question 9

If $y = y(x)$, $x \in \left(0, \frac{\pi}{2}\right)$ be the solution curve of the differential equation $\left(\sin^{2}2x\right)\frac{dy}{dx} + \left(8\sin^{2}2x + 2\sin 4x\right)y = 2e^{-4x}\left(2\sin 2x + \cos 2x\right)$, with $y\left(\frac{\pi}{4}\right) = e^{-\pi}$, then $y\left(\frac{\pi}{6}\right)$ is equal to :

Accepted Answer

(A) $\frac{2}{\sqrt{3}}e^{-2\pi/3}$

Answer

(B) $\frac{2}{\sqrt{3}}e^{2\pi/3}$

Answer

(C) $\frac{1}{\sqrt{3}}e^{-2\pi/3}$

Answer

(D) $\frac{1}{\sqrt{3}}e^{2\pi/3}$

Question 10

If the tangents drawn at the points P and Q on the parabola $y^{2} = 2x - 3$ intersect at the point R(0, 1), then the orthocentre of the triangle PQR is :

Accepted Answer

(B) (2, −1)

Answer

(A) (0, 1)

Answer

(C) (6, 3)

Answer

(D) (2, 1)

Question 11

Let C be the centre of the circle $x^{2} + y^{2} - x + 2y = \frac{11}{4}$ and P be a point on the circle. A line passes through the point C, makes an angle of $\frac{\pi}{4}$ with the line CP and intersects the circle at the points Q and R. Then the area of the triangle PQR (in unit$^{2}$) is :

Accepted Answer

(B) $2\sqrt{2}$

Answer

(A) 2

Answer

(C) $8\sin\left(\frac{\pi}{8}\right)$

Answer

(D) $8\cos\left(\frac{\pi}{8}\right)$

Question 12

The remainder when $7^{2022} + 3^{2022}$ is divided by 5 is:

Accepted Answer

(C) 3

Answer

(A) 0

Answer

(B) 2

Answer

(D) 4

Question 13

Let the matrix $A = \begin{bmatrix} 0 & 1 & 0 \ 0 & 0 & 1 \ 1 & 0 & 0 \end{bmatrix}$ and the matrix $B_{0} = A^{49} + 2A^{98}$. If $B_{n} = Adj(B_{n-1})$ for all $n \geq 1$, then $\det(B_{4})$ is equal to :

Accepted Answer

(C) $3^{32}$

Answer

(A) $3^{28}$

Answer

(B) $3^{30}$

Answer

(D) $3^{36}$

Question 14

Let $S_{1} = \left\{ z_{1} \in C : \left| z_{1} - 3 \right| = \frac{1}{2} \right\}$ and $S_{2} = \left\{ z_{2} \in C : \left| z_{2} - \left| z_{2} + 1 \right| \right| = \left| z_{2} + \left| z_{2} - 1 \right| \right| \right\}$. Then, for $z_{1} \in S_{1}$ and $z_{2} \in S_{2}$, the least value of $\left| z_{2} - z_{1} \right|$ is :

Accepted Answer

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

Answer

(A) 0

Answer

(B) $\frac{1}{2}$

Answer

(D) $\frac{5}{2}$

Question 15

The foot of the perpendicular from a point on the circle $x^{2} + y^{2} = 1$, $z = 0$ to the plane $2x + 3y + z = 6$ lies on which one of the following curves ?

Accepted Answer

(B) $(5x + 6y - 12)^{2} + 4(3x + 5y - 9)^{2} = 1$, $z = 6 - 2x - 3y$

Answer

(A) $(6x + 5y - 12)^{2} + 4(3x + 7y - 8)^{2} = 1$, $z = 6 - 2x - 3y$

Answer

(C) $(6x + 5y - 14)^{2} + 9(3x + 5y - 7)^{2} = 1$, $z = 6 - 2x - 3y$

Answer

(D) $(5x + 6y - 14)^{2} + 9(3x + 7y - 8)^{2} = 1$, $z = 6 - 2x - 3y$

Question 16

If the minimum value of $f(x) = \frac{5x^{2}}{2} + \frac{\alpha}{x^{5}}$, $x > 0$, is 14, then the value of $\alpha$ is equal to :

Accepted Answer

(C) 128

Answer

(A) 32

Answer

(B) 64

Answer

(D) 256

Question 17

Let $\alpha$, $\beta$ and $\gamma$ be three positive real numbers. Let $f(x) = \alpha x^{5} + \beta x^{3} + \gamma x$, $x \in R$ and $g : R 	o R$ be such that $g(f(x)) = x$ for all $x \in R$. If $a_{1}$, $a_{2}$, $a_{3}$,..., $a_{n}$ be in arithmetic progression with mean zero, then the value of $f\left( g\left( \frac{1}{n} \sum_{i=1}^{n} f\left(a_{i}ight) ight) ight)$ is equal to :

Accepted Answer

(A) 0

Answer

(B) 3

Answer

(C) 9

Answer

(D) 27

Question 18

Consider the sequence $a_{1}$, $a_{2}$, $a_{3}$, …… such that $a_{1} = 1$, $a_{2} = 2$ and $a_{n+2} = \frac{2}{a_{n+1}} + a_{n}$ for n = 1, 2, 3, … . If $\left( \frac{a_{1} + \frac{1}{a_{2}}}{a_{3}} \right) \cdot \left( \frac{a_{2} + \frac{1}{a_{3}}}{a_{4}} \right) \cdot \left( \frac{a_{3} + \frac{1}{a_{4}}}{a_{5}} \right) \cdots \left( \frac{a_{30} + \frac{1}{a_{31}}}{a_{32}} \right) = 2^{\alpha} \left( {}^{61}C_{31} \right)$, then $\alpha$ is equal to :

Accepted Answer

(C) −60

Answer

(A) −30

Answer

(B) −31

Answer

(D) −61

Question 19

The minimum value of the twice differentiable function $f(x) = \int_{0}^{x} e^{x-t} f'(t)\,dt - (x^{2} - x + 1)e^{x}$, $x \in R$, is :

Accepted Answer

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

Answer

(B) $-2\sqrt{e}$

Answer

(C) $-\sqrt{e}$

Answer

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

Question 20

Let S be the set of all passwords which are six to eight characters long, where each character is either an alphabet from {A, B, C, D, E} or a number from {1, 2, 3, 4, 5} with the repetition of characters allowed. If the number of passwords in S whose at least one character is a number from {1, 2, 3, 4, 5} is $\alpha 	imes 5^{6}$, then $\alpha$ is equal to ______.

Accepted Answer

7073

Question 21

Let P(−2, −1, 1) and $Q\left( \frac{56}{17}, \frac{43}{17}, \frac{111}{17} \right)$ be the vertices of the rhombus PRQS. If the direction ratios of the diagonal RS are $\alpha$, $-1$, $\beta$, where both $\alpha$ and $\beta$ are integers of minimum absolute values, then $\alpha^{2} + \beta^{2}$ is equal to __________.

Accepted Answer

450

Question 22

Let $f : [0, 1] 	o R$ be a twice differentiable function in (0, 1) such that f(0) = 3 and f(1) = 5. If the line y = 2x + 3 intersects the graph of f at only two distinct points in (0, 1), then the least number of points $x \in (0, 1)$, at which $f''(x) = 0$, is _______.

Accepted Answer

2

Question 23

If $\int_{0}^{\sqrt{3}} \frac{15x^{3}}{\sqrt{1 + x^{2} + \sqrt{\left(1 + x^{2}\right)^{3}}}}\,dx = \alpha\sqrt{2} + \beta\sqrt{3}$, where $\alpha$, $\beta$ are integers, then $\alpha + \beta$ is equal to ______.

Accepted Answer

10

Question 24

Let $A = \begin{bmatrix} 1 & -1 \ 2 & \alpha \end{bmatrix}$ and $B = \begin{bmatrix} \beta & 1 \ 1 & 0 \end{bmatrix}$, $\alpha, \beta \in R$. Let $\alpha_{1}$ be the value of $\alpha$ which satisfies $(A + B)^{2} = A^{2} + \begin{bmatrix} 2 & 2 \ 2 & 2 \end{bmatrix}$ and $\alpha_{2}$ be the value of $\alpha$ which satisfies $(A + B)^{2} = B^{2}$. Then $\left| \alpha_{1} - \alpha_{2} ight|$ is equal to _______.

Accepted Answer

2

Question 25

For $p, q \in R$, consider the real valued function $f(x) = (x - p)^{2} - q$, $x \in R$ and q > 0. Let $a_{1}$, $a_{2}$, $a_{3}$ and $a_{4}$ be in an arithmetic progression with mean p and positive common difference. If $\left| f\left(a_{i}\right) \right| = 500$ for all i = 1, 2, 3, 4, then the absolute difference between the roots of f(x) = 0 is ______.

Accepted Answer

50

Question 26

For the hyperbola H : $x^{2} - y^{2} = 1$ and the ellipse E : $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$, a > b > 0, let the
(1) eccentricity of E be reciprocal of the eccentricity of H, and
(2) the line $y = \sqrt{\frac{5}{2}}x + K$ be a common tangent of E and H.
Then $4(a^{2} + b^{2})$ is equal to ________.

Accepted Answer

3

Question 27

Let $x_{1}$, $x_{2}$, $x_{3}$, ….., $x_{20}$ be in geometric progression with $x_{1} = 3$ and the common ration $\frac{1}{2}$. A new data is constructed replacing each $x_{i}$ by $\left(x_{i} - i\right)^{2}$. If $\bar{x}$ is the mean of new data, then the greatest integer less than or equal to $\bar{x}$ is __________.

Accepted Answer

142

Question 28

$\lim_{x 	o 0} \left( \frac{\left(x + 2\cos xight)^{3} + 2\left(x + 2\cos xight)^{2} + 3\sin\left(x + 2\cos xight)}{\left(x + 2ight)^{3} + 2\left(x + 2ight)^{2} + 3\sin\left(x + 2ight)} ight)^{\frac{100}{x}}$ is equal to ___________.

Accepted Answer

1

Question 29

The sum of all real values of x for which $\frac{3x^{2} - 9x + 17}{x^{2} + 3x + 10} = \frac{5x^{2} - 7x + 19}{3x^{2} + 5x + 12}$ is equal to ____.

Accepted Answer

6

Question 30

The dimensions of $\left(\frac{B^{2}}{\mu_{0}}\right)$ will be :
(if μ$_{0}$ : permeability of free space and B : magnetic field)

Accepted Answer

(C) [M L$^{-1}$ T$^{-2}$]

Answer

(A) [M L$^{2}$ T$^{-2}$]

Answer

(B) [M L T$^{-2}$]

Answer

(D) [M L$^{2}$ T$^{-2}$ A$^{-1}$]

Question 31

A NCC parade is going at a uniform speed of 9 km/h under a mango tree on which a monkey is sitting at a height of 19.6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is :
(Given g = 9.8 m/s$^{2}$)

Accepted Answer

(A) 5 m

Answer

(B) 10 m

Answer

(C) 19.8 m

Answer

(D) 24.5 m

Question 32

In two different experiments, an object of mass 5 kg moving with a speed of 25 ms$^{-1}$ hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of the following :

Accepted Answer

(B) Impulse will be same for both the cases but the average force will be different.

Answer

(A) Impulse and average force acting on the object will be same for both the cases.

Answer

(C) Average force will be same for both the cases but the impulse will be different.

Answer

(D) Average force and impulse will be different for both the cases.

Question 33

A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with velocity 4.5 cm/s. If the balloon shrinks in 5 s completely. Then, the average force acting on that balloon will be (in dyne).

Accepted Answer

(B) 9

Answer

(A) 3

Answer

(C) 12

Answer

(D) 18

Question 34

If the radius of earth shrinks by 2% while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :

Accepted Answer

(D) increase by 4%

Answer

(A) decrease by 2%

Answer

(B) decrease by 4%

Answer

(C) increase by 2%

Question 35

The force required to stretch a wire of cross-section 1 cm$^{2}$ to double its length will be :
(Given Yong's modulus of the wire = 2 × 10$^{11}$ N/m$^{2}$)

Accepted Answer

(C) 2 × 10$^{7}$ N

Answer

(A) 1 × 10$^{7}$ N

Answer

(B) 1.5 × 10$^{7}$ N

Answer

(D) 2.5 × 10$^{7}$ N

Question 36

A Carnot engine has efficiency of 50%. If the temperature of sink is reduced by 40°C, its efficiency increases by 30%. The temperature of the source will be :

Accepted Answer

(C) 266.7 K

Answer

(A) 166.7 K

Answer

(B) 255.1 K

Answer

(D) 367.7 K

Question 37

Given below are two statements :
Statement I :The average momentum of a molecule in a sample of an ideal gas depends on temperature.
Statement II : The rms speed of oxygen molecules in a gas is v. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become 2v.
In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

(D) Statement I is false but Statement II is true

Answer

(A) Both Statement I and Statement II are true

Answer

(B) Both Statement I and Statement II are false

Answer

(C) Statement I is true but Statement II is false

Question 38

In the wave equation
$y = 0.5\sin\frac{2\pi}{\lambda}\left(400t - x\right)m$
the velocity of the wave will be :

Accepted Answer

(C) 400 m/s

Answer

(A) 200 m/s

Answer

(B) 200$\sqrt{2}$ m / s

Answer

(D) 400$\sqrt{2}$ m / s

Question 39

Two capacitors, each having capacitance 40 μF are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant K such that the equivalence capacitance of the system became 24 μF. The value of K will be :

Accepted Answer

(A) 1.5

Answer

(B) 2.5

Answer

(C) 1.2

Answer

(D) 3

Question 40

A wire of resistance R$_{1}$ is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is:

Accepted Answer

(A) 9 : 1

Answer

(B) 1 : 9

Answer

(C) 4 : 1

Answer

(D) 3 : 1

Question 41

The current sensitivity of a galvanometer can be increased by :
(A) decreasing the number of turns
(B) increasing the magnetic field
(C) decreasing the area of the coil
(D) decreasing the torsional constant of the spring
Choose the most appropriate answer from the options given below :

Accepted Answer

(D) (B) and (D) only

Answer

(A) (B) and (C) only

Answer

(B) (C) and (D) only

Answer

(C) (A) and (C) only

Question 42

As shown in the figure, a metallic rod of linear density 0.45 kg m$^{-1}$ is lying horizontally on a smooth incline plane which makes an angle of 45° with the horizontal. The minimum current flowing in the rod required to keep it stationary, when 0.15 T magnetic field is acting on it in the vertical upward direction, will be :
{Use g = 10 m/s$^{2}$}

Accepted Answer

(A) 30 A

Answer

(B) 15 A

Answer

(C) 10 A

Answer

(D) 3 A

Question 43

The equation of current in a purely inductive circuit is $5\sin\left(49\pi t - 30°ight)$. If the inductance is 30 mH then the equation for the voltage across the inductor, will be :
$\left\{	ext{Let } \pi = \frac{22}{7}ight\}$

Accepted Answer

(D) $23.1\sin(49\pi t + 60°)$

Answer

(A) $1.47\sin(49\pi t - 30°)$

Answer

(B) $1.47\sin(49\pi t + 60°)$

Answer

(C) $23.1\sin(49\pi t - 30°)$

Question 44

As shown in the figure, after passing through the medium 1. The speed of light v$_{2}$ in medium 2 will be :
(Given c = 3 × 10$^{8}$ ms$^{-1}$)

Accepted Answer

(A) 1.0 × 10$^{8}$ ms$^{-1}$

Answer

(B) 0.5 × 10$^{8}$ ms$^{-1}$

Answer

(C) 1.5 × 10$^{8}$ ms$^{-1}$

Answer

(D) 3.0 × 10$^{8}$ ms$^{-1}$

Question 45

In normal adjustment, for a refracting telescope, the distance between objective and eye piece is 30 cm. The focal length of the objective, when the angular magnification of the telescope is 2, will be:

Accepted Answer

(A) 20 cm

Answer

(B) 30 cm

Answer

(C) 10 cm

Answer

(D) 15 cm

Question 46

The equation $\lambda = \frac{1.227}{x}$ nm can be used to find the de-Brogli wavelength of an electron. In this equation x stands for :
Where,
m = mass of electron
P = momentum of electron
K = Kinetic energy of electron
V = Accelerating potential in volts for electron

Accepted Answer

(D) $\sqrt{V}$

Answer

(A) $\sqrt{mK}$

Answer

(B) $\sqrt{P}$

Answer

(C) $\sqrt{K}$

Question 47

The half life period of a radioactive substance is 60 days. The time taken for $\frac{7}{8}$th of its original mass to disintegrate will be :

Accepted Answer

(C) 180 days

Answer

(A) 120 days

Answer

(B) 130 days

Answer

(D) 20 days

Question 48

Identify the solar cell characteristics from the following options :

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 49

In the case of amplitude modulation to avoid distortion the modulation index (μ) should be :

Accepted Answer

(A) μ ≤ 1

Answer

(B) μ ≥ 1

Answer

(C) μ = 2

Answer

(D) μ = 0

Question 50

If the projection of $2\hat{i}+4\hat{j}-2\hat{k}$ on $\hat{i}+2\hat{j}+\alpha\hat{k}$ is zero. Then, the value of α will be

Accepted Answer

5

Question 51

A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be ________ hours.

Accepted Answer

15

Question 52

In a Young's double slit experiment, a laser light of 560 nm produces an interference pattern with consecutive bright fringes' separation of 7.2 mm. Now another light is used to produce an interference pattern with consecutive bright fringes' separation of 8.1 mm. The wavelength of second light is ________ nm.

Accepted Answer

630

Question 53

The frequencies at which the current amplitude in an LCR series circuit becomes $\frac{1}{\sqrt{2}}$ times its maximum value, are 212 rad s$^{-1}$ and 232 rad s$^{-1}$. The value of resistance in the circuit is R = 5Ω. The self inductance in the circuit is ________ mH.

Accepted Answer

250

Question 54

As shown in the figure, a potentiometer wire of resistance 20Ω and length 300 cm is connected with resistance box (R.B.) and a standard cell of emf 4 V. For a resistance 'R' of resistance box introduced into the circuit, the null point for a cell of 20 mV is found to be 60 cm. The value of 'R' is ________ Ω .

Accepted Answer

780

Question 55

Two electric dipoles of dipole moments 1.2 × 10$^{-30}$ cm and 2.4 × 10$^{-30}$ cm are placed in two difference uniform electric fields of strengths 5 × 10$^{4}$ NC$^{-1}$ and 15 × 10$^{4}$ NC$^{-1}$ respectively. The ratio of maximum torque experienced by the electric dipoles will be $\frac{1}{x}$. The value of x is ________.

Accepted Answer

6

Question 56

The frequency of echo will be ________ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km/h towards a hill from which an echo is heard by the train driver. Velocity of sound in air is 330 m/s.

Accepted Answer

340

Question 57

The diameter of an air bubble which was initially 2 mm, rises steadily through a solution of density 1750 kg m$^{-3}$ at the rate of 0.35 cms$^{-1}$. The coefficient of viscosity of the solution is ________ poise (in nearest integer). (the density of air is negligible).

Accepted Answer

11

Question 58

A block of mass 'm' (as shown in figure) moving with kinetic energy E compresses a spring through a distance 25 cm when, its speed is halved. The value of spring constant of used spring will be nE Nm$^{-1}$ for n = ________.

Accepted Answer

24

Question 59

Four identical discs each of mass 'M' and diameter 'a' are arranged in a small plane as shown in figure. If the moment of inertia of the system about OO' is $\frac{x}{4}$Ma$^{2}$. Then, the value of x will be ________.

Accepted Answer

3

Question 60

Identify the incorrect statement from the following.

Accepted Answer

(D) Atomic orbital is characterised by the quantum numbers n and $l$ only

Answer

(A) A circular path around the nucleus in which an electron moves is proposed as Bohr's orbit.

Answer

(B) An orbital is the one electron wave function (Ψ) in an atom.

Answer

(C) The existence of Bohr's orbits is supported by hydrogen spectrum.

Question 61

Which of the following relation is not correct ?

Accepted Answer

(A) ΔH = ΔU − PΔV

Answer

(B) ΔU = q + W

Answer

(C) ΔS$_{sys}$ + ΔS$_{surr}$ ≥ 0

Answer

(D) ΔG = ΔH − TΔS

Question 62

Match List-I with List-II.
Choose the correct answer from the options given below :

Accepted Answer

(C) (A) – (II), (B) – (I), (C) – (IV), (D) – (III)

Answer

(A) (A) – (I), (B) – (II), (C) – (III), (D) – (IV)

Answer

(B) (A) – (IV), (B) – (I), (C) – (II), (D) – (III)

Answer

(D) (A) – (II), (B) – (I), (C) – (III), (D) – (IV)

Question 63

Match List-I with List-II.
Choose the correct answer from the options given below :

Accepted Answer

(C) (A) – (III), (B) – (IV), (C) – (II), (D) – (I)

Answer

(A) (A) – (II), (B) – (III), (C) – (I), (D) – (IV)

Answer

(B) (A) – (III), (B) – (II), (C) – (I), (D) – (IV)

Answer

(D) (A) – (III), (B) – (II), (C) – (IV), (D) – (I)

Question 64

In which of the following pairs, electron gain enthalpies of constituent elements are nearly the same or identical ?
(A) Rb and Cs
(B) Na and K
(C) Ar and Kr
(D) I and At
Choose the correct answer from the options given below :

Accepted Answer

(C) (A) and (C) only

Answer

(A) (A) and (B) only

Answer

(B) (B) and (C) only

Answer

(D) (C) and (D) only

List-I	List-II
A.Cd(s) + 2Ni(OH) $_3$ (s) → CdO(s) + 2Ni(OH) $_2$ (s) + H $_2$ O( $l$ )	I.Primary battery
B.Zn(Hg) + HgO(s) → ZnO(s) + Hg( $l$ )	II.Discharging of secondary battery
C.2PbSO $_4$ (s) + 2H $_2$ O( $l$ ) → Pb(s) + PbO $_2$ (s) + 2H $_2$ SO $_4$ (aq)	III.Fuel cell
D.2H $_2$ (g) + O $_2$ (g) → 2H $_2$ O( $l$ )	IV.Charging of secondary battery

List-I (Reaction)	List-II (Catalyst)
A.4NH $_3$ (g) + 5O $_2$ (g) → 4NO(g) + 6H $_2$ O(g)	I.NO(g)
B.N $_2$ (g) + 3H $_2$ (g) → 2NH $_3$ (g)	II.H $_2$ SO $_4$ ( $l$ )
C.C $_{12}$ H $_{22}$ O $_{11}$ (aq) + H $_2$ O( $l$ ) → C $_6$ H $_{12}$ O $_6$ (Glucose) + C $_6$ H $_{12}$ O $_6$ (Fructose)	III.Pt(s)
D.2SO $_2$ (g) + O $_2$ (g) → 2SO $_3$ (g)	IV.Fe(s)

List-I	List-II
A.(NH $_4$ ) $_2$ Cr $_2$ O $_7$ $\xrightarrow{\Delta}$	I.H $_2$
B.KMnO $_4$ + HCl →	II.N $_2$
C.Al + NaOH + H $_2$ O →	III.O $_2$
D.NaNO $_3$ $\xrightarrow{\Delta}$	IV.Cl $_2$

JEE Main 28 July 2022 Shift 1 Question Paper with Answers

Physics — JEE Main 28 July 2022 Shift 1

Chemistry — JEE Main 28 July 2022 Shift 1

Mathematics — JEE Main 28 July 2022 Shift 1

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