NTA JEE Main 9th April 2019 Shift 1 - Physics

NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 1

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In the density measurement of a cube, the mass and edge length are measured as $$(10.00 \pm 0.10)$$ kg and $$(0.10 \pm 0.01)$$ m, respectively. The error in the measurement of density is:

A

0.31

B

0.10

C

0.07

D

0.01

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 2

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A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum-height (p-h) diagram is:

A

B

C

D

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 3

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The stream of a river is flowing with a speed of 2 km h$$^{-1}$$. A swimmer can swim at a speed of 4 km h$$^{-1}$$. The direction of the swimmer with respect to the flow of the river, to cross the river straight, is:

A

150°

B

90°

C

120°

D

60°

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 4

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A uniform cable of mass $$M$$ and length $$L$$ is placed on a horizontal surface such that its $$\left(\frac{1}{n}\right)^{th}$$ part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be:

A

$$\frac{MgL}{2n^2}$$

B

$$\frac{MgL}{n^2}$$

C

$$nMgL$$

D

$$\frac{2MgL}{n^2}$$

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 5

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A body of mass 2 kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body?

A

1.8 kg

B

1.2 kg

C

1.0 kg

D

1.5 kg

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 6

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A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of $$\theta$$, where $$\theta$$ is the angle by which it has rotated, is given as $$k\theta^2$$. If its moment of inertia is I then the angular acceleration of the disc is:

A

$$\frac{2k}{I}\theta$$

B

$$\frac{k}{2I}\theta$$

C

$$\frac{k}{4I}\theta$$

D

$$\frac{k}{I}\theta$$

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 7

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The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane: (i) a ring of radius R, (ii) a solid cylinder of radius $$\frac{R}{2}$$ and (iii) a solid sphere of radius $$\frac{R}{4}$$. If, in each case, the speed of the center of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is:

A

2 : 3 : 4

B

20 : 15 : 14

C

4 : 3 : 2

D

14 : 15 : 20

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 8

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A solid sphere of mass M and radius a is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance 3a from the centre will be:

A

$$\frac{GM}{9a^2}$$

B

$$\frac{GM}{3a^2}$$

C

$$\frac{2GM}{3a^2}$$

D

$$\frac{2GM}{9a^2}$$

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 9

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If 'M' is the mass of water that rises in a capillary tube of radius 'r', then mass of water which will rise in a capillary tube of radius '2r' is:

A

4 M

B

2 M

C

$$\frac{M}{2}$$

D

M

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 10

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Following figure shows two processes A and B for a gas. If $$\Delta Q_A$$ and $$\Delta Q_B$$ are the amount of heat absorbed by the system in two cases, and $$\Delta U_A$$ and $$\Delta U_B$$ are changes in internal energies, respectively, then:

A

$$\Delta Q_A < \Delta Q_B; \; \Delta U_A < \Delta U_B$$

B

$$\Delta Q_A = \Delta Q_B; \; \Delta U_A = \Delta U_B$$

C

$$\Delta Q_A > \Delta Q_B; \; \Delta U_A = \Delta U_B$$

D

$$\Delta Q_A > \Delta Q_B; \; \Delta U_A > \Delta U_B$$

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 11

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For given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127°C. At 2 atm pressure and at 227°C, the rms speed of the molecules will be:

A

100 m/s

B

80 m/s

C

$$80\sqrt{5}$$ m/s

D

$$100\sqrt{5}$$ m/s

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 12

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An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is $$\bar{v}$$, m is its mass and k$$_B$$ is Boltzmann's constant, then its temperature will be:

A

$$\frac{m\bar{v}^2}{5k_B}$$

B

$$\frac{m\bar{v}^2}{6k_B}$$

C

$$\frac{m\bar{v}^2}{3k_B}$$

D

$$\frac{m\bar{v}^2}{7k_B}$$

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 13

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A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is $$\frac{1}{16}$$th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:

A

$$2T\sqrt{\frac{1}{10}}$$

B

$$2T\sqrt{\frac{1}{14}}$$

C

$$4T\sqrt{\frac{1}{15}}$$

D

$$4T\sqrt{\frac{1}{14}}$$

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 14

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A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is $$y = 0.3 \sin(0.157x) \cos(200\pi t)$$. The length of the string is: (All quantities are in SI units.)

A

20 m

B

60 m

C

40 m

D

80 m

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 15

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The pressure wave, $$P = 0.01 \sin[1000t - 3x]$$ N m$$^{-2}$$, corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is 0°C. On some other day when temperature is T, the speed of sound produced by the same blade and at the same frequency is found to be 336 m s$$^{-1}$$. Approximate value of T is:

A

12°C

B

15°C

C

4°C

D

11°C

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 16

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A system of three charges are placed as shown in the figure:

If $$D >> d$$, the potential energy of the system is best given by:

A

$$\frac{1}{4\pi\varepsilon_0}\left[-\frac{q^2}{d} - \frac{qQd}{D^2}\right]$$

B

$$\frac{1}{4\pi\varepsilon_0}\left[+\frac{q^2}{d} + \frac{qQd}{D^2}\right]$$

C

$$\frac{1}{4\pi\varepsilon_0}\left[-\frac{q^2}{d} - \frac{qQd}{2D^2}\right]$$

D

$$\frac{1}{4\pi\varepsilon_0}\left[-\frac{q^2}{d} + \frac{2qQd}{D^2}\right]$$

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 17

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A capacitor with capacitance 5 $$\mu$$F is charged to 5 $$\mu$$C. If the plates are pulled apart to reduce the capacitance to 2 $$\mu$$F, how much work is done?

A

$$6.25 \times 10^{-6}$$ J

B

$$2.55 \times 10^{-6}$$ J

C

$$2.16 \times 10^{-6}$$ J

D

$$3.75 \times 10^{-6}$$ J

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 18

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A wire of resistance R is bent to form a square ABCD as shown in the figure. The effective resistance between E and C is: (E is mid-point of arm CD)

A

R

B

$$\frac{7}{64}R$$

C

$$\frac{1}{16}R$$

D

$$\frac{3}{4}R$$

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 19

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Determine the charge on the capacitor in the following circuit:

A

2 $$\mu$$C

B

60 $$\mu$$C

C

10 $$\mu$$C

D

200 $$\mu$$C

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 20

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A moving coil galvanometer has resistance 50 $$\Omega$$ and it indicates full deflection at 4 mA current. A voltmeter is made using this galvanometer and a 5 k$$\Omega$$ resistance. The maximum voltage, that can be measured using this voltmeter, will be close to:

A

40 V

B

15 V

C

20 V

D

10 V

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 21

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A rigid square loop of side 'a' and carrying current $$I_2$$ is lying on a horizontal surface near a long current $$I_1$$ carrying wire in the same plane as shown in figure. The net force on the loop due to the wire will be:

A

Attractive and equal to $$\frac{\mu_0 I_1 I_2}{3\pi}$$

B

Repulsive and equal to $$\frac{\mu_0 I_1 I_2}{4\pi}$$

C

Repulsive and equal to $$\frac{\mu_0 I_1 I_2}{2\pi}$$

D

Zero

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 22

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A rectangular coil (Dimension 5 cm $$\times$$ 2.5 cm) with 100 turns, carrying a current of 3 A in the clock-wise direction, is kept centered at the origin and in the X-Z plane. A magnetic field of 1 T is applied along X-axis. If the coil is tilted through 45° about Z-axis, then the torque on the coil is:

A

0.42 N m

B

0.55 N m

C

0.38 N m

D

0.27 N m

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 23

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The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to:

A

L

B

$$\frac{1}{L^2}$$

C

$$\frac{1}{L}$$

D

$$L^2$$

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 24

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The magnetic field of a plane electromagnetic wave is given by $$\vec{B} = B_0[\hat{i}\cos(kz - \omega t)] + B_1[\hat{j}\cos(kz + \omega t)]$$, where $$B_0 = 3 \times 10^{-5}$$ T and $$B_1 = 2 \times 10^{-6}$$ T. The RMS value of the force experienced by a stationary charge $$Q = 10^{-4}$$ C at z = 0 is closest to:

A

0.1 N

B

0.9 N

C

$$3 \times 10^{-2}$$ N

D

0.6 N

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 25

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A concave mirror for face viewing has a focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:

A

1.60 m

B

0.16 m

C

0.32 m

D

0.24 m

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 26

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The figure shows a Young's double slit experimental setup. It is observed that when a thin transparent sheet of thickness t and refractive index $$\mu$$ is put in front of one of the slits, the central maximum gets shifted by a distance equal to n fringe width. If the wavelength of light used is $$\lambda$$ then t will be:

A

$$\frac{D\lambda}{a(\mu - 1)}$$

B

$$\frac{n\lambda}{(\mu - 1)}$$

C

$$\frac{2n\lambda}{(\mu - 1)}$$

D

$$\frac{2D\lambda}{a(\mu - 1)}$$

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 27

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The electric field of light wave is given as $$\vec{E} = 10^{-3} \cos\left(\frac{2\pi x}{5 \times 10^{-7}} - 2\pi \times 6 \times 10^{14}t\right) \hat{x} \frac{N}{C}$$. This light falls on a metal plate of work function 2 eV. The stopping potential of the photo-electrons is: Given, E (in eV) = $$\frac{12375}{\lambda(\text{in } \mathring{A})}$$

A

0.72 V

B

2.0 V

C

2.48 V

D

0.48 V

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 28

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Taking the wavelength of first Balmer line in hydrogen spectrum (n = 3 to n = 2) as 660 nm, the wavelength of the 2nd Balmer line (n = 4 to n = 2) will be:

A

889.2 nm

B

488.9 nm

C

388.9 nm

D

642.7 nm

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 29

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An NPN transistor is used in common emitter configuration as an amplifier with 1 k$$\Omega$$ load resistance. Signal voltage of 10 mV is applied across the base-emitter. This produces a 3 mA change in the collector current and 15 $$\mu$$A change in the base current of the amplifier. The input resistance and voltage gain are:

A

0.33 k$$\Omega$$, 1.5

B

0.67 k$$\Omega$$, 300

C

0.67 k$$\Omega$$, 200

D

0.33 k$$\Omega$$, 300

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NTA JEE Main 9th April 2019 Shift 1 - Physics - Question 30

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A signal A cos$$\omega$$t is transmitted using $$v_0 \sin\omega_0 t$$ as carrier wave. The correct amplitude modulated (AM) signal is:

A

$$v_0 \sin[\omega_0(1 + 0.01A\sin\omega t)t]$$

B

$$(v_0 + A)\cos\omega t \sin\omega_0 t$$

C

$$v_0 \sin\omega_0 t + A\cos\omega t$$

D

$$v_0 \sin\omega_0 t + \frac{A}{2}\sin(\omega_0 - \omega)t + \frac{A}{2}\sin(\omega_0 + \omega)t$$

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