NTA JEE Main 29th July 2022 Shift 1 - Physics

NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 1

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Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R)
Assertion (A): Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is $$\rho$$ and radius of the drop is $$r$$, then $$T = K\sqrt{\frac{\rho r^3}{S^{3/2}}}$$ is dimensionally correct, where K is dimensionless.
Reason (R): Using dimensional analysis we get R.H.S. having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.

A

Both (A) and (R) are true and (R) is the correct explanation of (A)

B

Both (A) and (R) are true but (R) is not the correct explanation of (A)

C

(A) is true but (R) is false

D

(A) is false but (R) is true

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 2

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A ball is thrown up vertically with a certain velocity so that it reaches a maximum height h. Find the ratio of the times in which it is at height $$\frac{h}{3}$$ while going up and coming down respectively.

A

$$\frac{\sqrt{2}-1}{\sqrt{2}+1}$$

B

$$\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$$

C

$$\frac{\sqrt{3}-1}{\sqrt{3}+1}$$

D

$$\frac{1}{3}$$

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 3

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If $$t = \sqrt{x} + 4$$, then $$\left(\frac{dx}{dt}\right)_{t=4}$$ is:

A

4

B

Zero

C

8

D

16

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 4

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A ball is projected with kinetic energy E, at an angle of $$60^\circ$$ to the horizontal. The kinetic energy of this ball at the highest point of its flight will become:

A

Zero

B

$$\frac{E}{2}$$

C

$$\frac{E}{4}$$

D

E

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 5

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A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v. Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N) and speed of the block (v)?

A

B

C

D

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 6

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Two bodies of mass 1 kg and 3 kg have position vectors $$\hat{i} + 2\hat{j} + \hat{k}$$ and $$-3\hat{i} - 2\hat{j} + \hat{k}$$ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector:

A

$$\hat{i} - 2\hat{j} + \hat{k}$$

B

$$-3\hat{i} - 2\hat{j} + \hat{k}$$

C

$$-2\hat{i} + 2\hat{k}$$

D

$$-2\hat{i} - \hat{j} + 2\hat{k}$$

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 7

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If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will:

A

Remain same

B

Become 8 times its initial value

C

Become $$\frac{1^{th}}{4}$$ of its initial value

D

Become 4 times its initial value

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 8

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Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Clothes containing oil or grease stains cannot be cleaned by water wash.
Reason (R): Because the angle of contact between the oil/grease and water is obtuse.
In the light of the above statements, choose the correct answer from the option given below.

A

Both (A) and (R) are true and (R) is the correct explanation of (A)

B

Both (A) and (R) are true but (R) is not the correct explanation of (A)

C

(A) is true but (R) is false

D

(A) is true but (R) is true

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 9

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Two metallic wires of identical dimensions are connected in series. If $$\sigma_1$$ and $$\sigma_2$$ are the conductivities of these wires respectively, the effective conductivity of the combination is:

A

$$\frac{\sigma_1\sigma_2}{\sigma_1+\sigma_2}$$

B

$$\frac{2\sigma_1\sigma_2}{\sigma_1+\sigma_2}$$

C

$$\frac{\sigma_1+\sigma_2}{2\sigma_1\sigma_2}$$

D

$$\frac{\sigma_1+\sigma_2}{\sigma_1\sigma_2}$$

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 10

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The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination $$\alpha$$, is given by:

A

$$2\pi\sqrt{\frac{L}{g\cos\alpha}}$$

B

$$2\pi\sqrt{\frac{L}{g\sin\alpha}}$$

C

$$2\pi\sqrt{\frac{L}{g}}$$

D

$$2\pi\sqrt{\frac{L}{g\tan\alpha}}$$

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 11

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A spherically symmetric charge distribution is considered with charge density varying as $$\rho(r) = \begin{cases} \rho_0\left(\frac{3}{4} - \frac{r}{R}\right) & \text{for } r \leq R \\ 0 & \text{for } r > R \end{cases}$$
Where, $$r(r < R)$$ is the distance from the centre O (as shown in figure). The electric field at point P will be:

A

$$\frac{\rho_0 r}{4\varepsilon_0}\left(\frac{3}{4} - \frac{r}{R}\right)$$

B

$$\frac{\rho_0 r}{3\varepsilon_0}\left(\frac{3}{4} - \frac{r}{R}\right)$$

C

$$\frac{\rho_0 r}{4\varepsilon_0}\left(1 - \frac{r}{R}\right)$$

D

$$\frac{\rho_0 r}{5\varepsilon_0}\left(1 - \frac{r}{R}\right)$$

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 12

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Given below are two statements.
Statement I: Electric potential is constant within and at the surface of each conductor.
Statement II: Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.
In the light of the above statements, choose the most appropriate answer from the options given below.

A

Both statement I and statement II are correct

B

Both statement I and statement II are incorrect

C

Statement I is correct but statement II is incorrect

D

Statement I is incorrect but statement II is correct

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 13

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An alternating emf $$E = 440\sin 100\pi t$$ is applied to a circuit containing an inductance of $$\frac{\sqrt{2}}{\pi}$$ H. If an a.c. ammeter is connected in the circuit, its reading will be:

A

4.4 A

B

1.55 A

C

2.2 A

D

3.11 A

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 14

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A coil of inductance 1 H and resistance 100 $$\Omega$$ is connected to a battery of 6 V. Determine approximately:
(a) The time elapsed before the current acquires half of its steady-state value
(b) The energy stored in the magnetic field associated with the coil at an instant 15 ms after the circuit is switched on.
(Given $$\ln 2 = 0.693$$, $$e^{-3/2} = 0.25$$)

A

$$t = 10$$ ms; $$U = 2$$ mJ

B

$$t = 10$$ ms; $$U = 1$$ mJ

C

$$t = 7$$ ms; $$U = 1$$ mJ

D

$$t = 7$$ ms; $$U = 2$$ mJ

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 15

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Match List-I with List-II

List-I	List-II
(a) UV rays	(i) Diagnostic tool in medicine
(b) X-rays	(ii) Water purification
(c) Microwave	(iii) Communication, Radar
(d) Infrared wave	(iv) Improving visibility in foggy days

Choose the correct answer from the options given below :

A

(a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)

B

(a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)

C

(a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)

D

(a)-(iii), (b)-(i), (c)-(ii), (d)-(iv)

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 16

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The kinetic energy of emitted electron is E when the light incident on the metal has wavelength $$\lambda$$. To double the kinetic energy, the incident light must have wavelength:

A

$$\frac{hc}{E\lambda - hc}$$

B

$$\frac{hc\lambda}{E\lambda + hc}$$

C

$$\frac{h\lambda}{E\lambda + hc}$$

D

$$\frac{hc\lambda}{E\lambda - hc}$$

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 17

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Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.

A

3 : 4

B

4 : 3

C

1 : 4

D

4 : 1

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 18

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Find the modulation index of an AM wave having 8 V variation where maximum amplitude of the AM wave is 9 V.

A

0.8

B

0.5

C

0.2

D

0.1

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 19

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A travelling microscope has 20 divisions per cm on the main scale while its Vernier scale has total 50 divisions and 25 Vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope?

A

0.001 cm

B

0.002 mm

C

0.002 cm

D

0.005 cm

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 20

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In an experiment to find out the diameter of wire using screw gauge, the following observation were noted:
(a) Screw moves 0.5 mm on main scale in one complete rotation
(b) Total divisions on circular scale = 50
(c) Main scale reading is 2.5 mm
(d) 45th division of circular scale is in the pitch line
(e) Instrument has 0.03 mm negative error
Then the diameter of wire is:

A

2.92 mm

B

2.54 mm

C

2.98 mm

D

3.45 mm

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 21

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An object is projected in the air with initial velocity u at an angle $$\theta$$. The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be _____ degree.

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 22

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If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth $$\alpha h$$ ($$ h \ll R_E$$) from the earth surface. The value of $$\alpha$$ will be _____. (use $$R_E = 6400$$ km)

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 23

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The pressure $$P_1$$ and density $$d_1$$ of diatomic gas $$(\gamma = \frac{7}{5})$$ changes suddenly to $$P_2(> P_1)$$ and $$d_2$$ respectively during an adiabatic process. The temperature of the gas increases and becomes _____ times of its initial temperature. (Given $$\frac{d_2}{d_1} = 32$$)

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 24

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One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $$\frac{\alpha^2}{4}R$$ J mol$$^{-1}$$ K$$^{-1}$$; then the value of $$\alpha$$ will be _____. (Assume that the given diatomic gas has no vibrational mode.)

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 25

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Two light beams of intensities 4I and 9I interfere on a screen. The phase difference between these beams on the screen at point A is zero and at point B is $$\pi$$. The difference of resultant intensities, at the point A and B, will be _____ I.

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 26

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The current I flowing through the given circuit will be _____ A.

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 27

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A closely wound circular coil of radius 5 cm produces a magnetic field of $$37.68 \times 10^{-4}$$ T at its center. The current through the coil is _____ A. [Given, number of turns in the coil is 100 and $$\pi = 3.14$$]

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 28

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A wire of length 314 cm carrying current of 14 A is bent to form a circle. The magnetic moment of the coil is _____ A-m$$^2$$. [Given $$\pi = 3.14$$]

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 29

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The X-Y plane be taken as the boundary between two transparent media $$M_1$$ and $$M_2$$. $$M_1$$ in $$Z \geq 0$$ has a refractive index of $$\sqrt{2}$$ and $$M_2$$ with $$Z < 0$$ has a refractive index of $$\sqrt{3}$$. A ray of light travelling in $$M_1$$ along the direction given by the vector $$\vec{A} = 4\sqrt{3}\hat{i} - 3\sqrt{3}\hat{j} - 5\hat{k}$$, is incident on the plane of separation. The value of difference between the angle of incident in $$M_1$$ and the angle of refraction in $$M_2$$ will be _____ degree.

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NTA JEE Main 29th July 2022 Shift 1 - Physics - Question 30

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If the potential barrier across a p-n junction is 0.6 V. Then the electric field intensity, in the depletion region having the width of $$6 \times 10^{-6}$$ m, will be _____ $$\times 10^5$$ N C$$^{-1}$$

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