NTA JEE Main 26th August 2021 Shift 2 - Physics

NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 1

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If the length of the pendulum in pendulum clock increases by 0.1%, then the error in time per day is:

A

43.2 s

B

8.64 s

C

86.4 s

D

4.32 s

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 2

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The angle between vector $$\left(\vec{A}\right)$$ and $$\left(\vec{A} - \vec{B}\right)$$ is:

A

$$\tan^{-1}\left(\frac{B\cos\theta}{A - B\sin\theta}\right)$$

B

$$\tan^{-1}\left(\frac{\sqrt{3}B}{2A - B}\right)$$

C

$$\tan^{-1}\left(\frac{-\frac{B}{2}}{A - B\frac{\sqrt{3}}{2}}\right)$$

D

$$\tan^{-1}\left(\frac{A}{0.7B}\right)$$

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 3

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Match List - I with List - II:
        List - I                                    List - II
a. Magnetic induction        i.   $$ML^2T^{-2}A^{-1}$$
b. Magnetic flux                  ii.  $$M^0L^{-1}A$$
c. Magnetic permeability   iii. $$MT^{-2}A^{-1}$$
d. Magnetization                 iv.  $$MLT^{-2}A^{-2}$$
Choose the most appropriate answer from the options given below:

A

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

B

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

C

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

D

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

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 4

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A particle of mass $$m$$ is suspended from a ceiling through a string of length $$L$$. The particle moves in a horizontal circle of radius $$r$$ such that $$r = \frac{L}{\sqrt{2}}$$. The speed of particle will be:

A

$$\sqrt{rg}$$

B

$$\sqrt{2rg}$$

C

$$\sqrt{\frac{rg}{2}}$$

D

$$2\sqrt{rg}$$

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 5

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A bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a:

A

straight line vertically down the plane

B

parabola in a direction opposite to the motion of plane

C

parabola in the direction of motion of plane

D

hyperbola

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 6

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The solid cylinder of length 80 cm and mass $$M$$ has a radius of 20 cm. Calculate the density of the material used if the moment of inertia of the cylinder about an axis $$CD$$ parallel to $$AB$$ as shown in figure is 2.7 kg m$$^2$$.

A

$$1.49 \times 10^2$$ kg m$$^{-3}$$

B

$$7.5 \times 10^1$$ kg m$$^{-3}$$

C

14.9 kg m$$^{-3}$$

D

$$7.5 \times 10^2$$ kg m$$^{-3}$$

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 7

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Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $$\frac{24}{\pi} \times 10^2$$ N m$$^{-2}$$. What is the minimum radius of the wire?

(take g = 10 m s$$^{-2}$$)

A

1250 cm

B

1.25 cm

C

125 cm

D

12.5 cm

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 8

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The temperature of equal masses of three different liquids $$x$$, $$y$$ and $$z$$ are 10°C, 20°C and 30°C respectively. The temperature of mixture when $$x$$ is mixed with $$y$$ is 16°C and that when $$y$$ is mixed with $$z$$ is 26°C. The temperature of mixture when $$x$$ and $$z$$ are mixed will be:

A

25.62°C

B

20.28°C

C

28.32°C

D

23.84°C

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 9

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A refrigerator consumes an average 35 W power to operate between temperature -10°C to 25°C. If there is no loss of energy then how much average heat per second does it transfer?

A

350 J s$$^{-1}$$

B

298 J s$$^{-1}$$

C

263 J s$$^{-1}$$

D

35 J s$$^{-1}$$

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 10

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A cylindrical container of volume $$4.0 \times 10^{-3}$$ m$$^3$$ contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K. The pressure of the mixture of gases is:
[Take gas constant as 8.3 J mol$$^{-1}$$ K$$^{-1}$$]

A

$$24.9 \times 10^3$$ Pa

B

$$249 \times 10^1$$ Pa

C

$$24.9 \times 10^5$$ Pa

D

24.9 Pa

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 11

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The two thin coaxial rings, each of radius $$a$$ and having charges $$+Q$$ and $$-Q$$ respectively are separated by a distance of $$s$$. The potential difference between the centres of the two rings is:

A

$$\frac{Q}{2\pi\varepsilon_0}\left[\frac{1}{a} - \frac{1}{\sqrt{s^2 + a^2}}\right]$$

B

$$\frac{Q}{4\pi\varepsilon_0}\left[\frac{1}{a} - \frac{1}{\sqrt{s^2 + a^2}}\right]$$

C

$$\frac{Q}{4\pi\varepsilon_0}\left[\frac{1}{a} + \frac{1}{\sqrt{s^2 + a^2}}\right]$$

D

$$\frac{Q}{2\pi\varepsilon_0}\left[\frac{1}{a} + \frac{1}{\sqrt{s^2 + a^2}}\right]$$

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 12

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A parallel-plate capacitor with plate area $$A$$ has separation $$d$$ between the plates. Two dielectric slabs of dielectric constant $$K_1$$ and $$K_2$$ of same area $$\frac{A}{2}$$ and thickness $$\frac{d}{2}$$ are inserted in the space between the plates. The capacitance of the capacitor will be given by:

A

$$\frac{\varepsilon_0 A}{d}\left(\frac{1}{2} + \frac{K_1 K_2}{K_1 + K_2}\right)$$

B

$$\frac{\varepsilon_0 A}{d}\left(\frac{1}{2} + \frac{2(K_1 + K_2)}{K_1 K_2}\right)$$

C

$$\frac{\varepsilon_0 A}{d}\left(\frac{1}{2} + \frac{K_1 + K_2}{K_1 K_2}\right)$$

D

$$\frac{\varepsilon_0 A}{d}\left(\frac{1}{2} + \frac{K_1 K_2}{2(K_1 + K_2)}\right)$$

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 13

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An electric bulb of 500 W at 100 V is used in a circuit having a 200 V supply. Calculate the resistance $$R$$ to be connected in series with the bulb so that the power delivered by the bulb is 500 W.

A

30 $$\Omega$$

B

5 $$\Omega$$

C

20 $$\Omega$$

D

10 $$\Omega$$

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 14

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If you are provided a set of resistances, 2 $$\Omega$$, 4 $$\Omega$$, 6 $$\Omega$$ and 8 $$\Omega$$. Connect these resistances to obtain an equivalent resistance of $$\frac{46}{3}$$ $$\Omega$$.

A

2 $$\Omega$$ and 6 $$\Omega$$ are in parallel with 4 $$\Omega$$ and 8 $$\Omega$$ in series

B

4 $$\Omega$$ and 6 $$\Omega$$ are in parallel with 2 $$\Omega$$ and 8 $$\Omega$$ in series

C

2 $$\Omega$$ and 4 $$\Omega$$ are in parallel with 6 $$\Omega$$ and 8 $$\Omega$$ in series

D

6 $$\Omega$$ and 8 $$\Omega$$ are in parallel with 2 $$\Omega$$ and 4 $$\Omega$$ in series

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 15

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In the given circuit the AC source has $$\omega = 100$$ rad s$$^{-1}$$. Considering the inductor and capacitor to be ideal, what will be the current $$I$$ flowing through the circuit?

A

5.9 A

B

6 A

C

0.94 A

D

3.16 A

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 16

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A light beam is described by $$E = 800 \sin\omega\left(t - \frac{x}{c}\right)$$. An electron is allowed to move normal to the propagation of light beam with a speed of $$3 \times 10^7$$ m s$$^{-1}$$. What is the maximum magnetic force exerted on the electron?

A

$$1.28 \times 10^{-21}$$ N

B

$$12.8 \times 10^{-18}$$ N

C

$$1.28 \times 10^{-18}$$ N

D

$$12.8 \times 10^{-17}$$ N

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 17

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The de-Broglie wavelength of a particle having kinetic energy $$E$$ is $$\lambda$$. How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to 75% of the initial value?

A

$$E$$

B

$$\frac{7E}{9}$$

C

$$\frac{16E}{9}$$

D

$$\frac{E}{9}$$

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 18

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At time $$t = 0$$, a material is composed of two radioactive atoms $$A$$ and $$B$$, where $$N_A(0) = 2N_B(0)$$. The decay constant of both kind of radioactive atoms is $$\lambda$$. However, $$A$$ disintegrates to $$B$$ and $$B$$ disintegrates to $$C$$. Which of the following figures represents the evolution of $$\frac{N_B(t)}{N_B(0)}$$ with respect to time $$t$$?

A

B

C

D

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 19

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Four NOR gates are connected as shown in figure. The truth table for the given figure is:

A

B

C

D

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 20

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A transmitting antenna at top of a tower has a height of 50 m, and the height of receiving antenna is 80 m. What is the range of communication for the line of sight (LOS) mode?
[use radius of the earth = 6400 km]

A

80.2 km

B

144.1 km

C

57.28 km

D

45.5 km

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 21

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The acceleration due to gravity is found up to an accuracy of 4% on a planet. The energy supplied to a simple pendulum of known mass $$m$$ to undertake oscillations of time period $$T$$ is being estimated. If time period is measured to an accuracy of 3%, the accuracy to which $$E$$ is known is _________ %

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 22

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The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is _________ N (take $$g = 10$$ m s$$^{-2}$$)

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 23

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Two simple harmonic motions are represented by the equations $$x_1 = 5\sin\left(2\pi t + \frac{\pi}{4}\right)$$ and $$x_2 = 5\sqrt{2}(\sin 2\pi t + \cos 2\pi t)$$. The amplitude of the second motion is _________ times the amplitude in the first motion.

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 24

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Two waves are simultaneously passing through a string and their equations are:
$$y_1 = A_1 \sin k(x - vt)$$, $$y_2 = A_2 \sin k(x - vt + x_0)$$. Given amplitudes $$A_1 = 12$$ mm and $$A_2 = 5$$ mm, $$x_0 = 3.5$$ cm and wave number $$k = 6.28$$ cm$$^{-1}$$. The amplitude of resulting wave will be _________ mm.

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 25

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If the maximum value of accelerating potential provided by a radio frequency oscillator is 12 kV. The number of revolution made by a proton in a cyclotron to achieve one sixth the speed of light is:
[$$m_p = 1.67 \times 10^{-27}$$ kg, $$e = 1.6 \times 10^{-19}$$ C, Speed of light = $$3 \times 10^8$$ m s$$^{-1}$$]

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 26

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A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field 20 mT. The torque acting on the coil when a current of 0.2 A is passed through it and its plane becomes parallel to the magnetic field will be $$\sqrt{x} \times 10^{-5}$$ Nm. The value of $$x$$ is _________

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 27

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A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s$$^{-1}$$ in a uniform horizontal magnetic field of $$3.0 \times 10^{-2}$$ T. The maximum emf induced in the coil will be _________ $$\times 10^{-2}$$ volt (rounded off to the nearest integer).

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 28

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An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on another side of the lens at 8 cm as shown in the figure. The image of the object coincides with the object.

When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be _________ cm

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 29

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A source of light is placed in front of a screen. The intensity of light on the screen is $$I$$. Two Polaroids $$P_1$$ and $$P_2$$ are so placed in between the source of light and screen that the intensity of light on the screen is $$\frac{I}{2}$$. Then the $$P_2$$, should be rotated by an angle of _________ (degrees) so that the intensity of light on the screen becomes $$\frac{3I}{8}$$.

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NTA JEE Main 26th August 2021 Shift 2 - Physics - Question 30

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For the given circuit, the power across zener diode is _________ mW.

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