NTA JEE Main 2025 April 7th Shift 1 - Physics

NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 26

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Two harmonic waves moving in the same direction superimpose to form a wave $$x = a \cos(1.5t) \cos(50.5t)$$ where t is in seconds. Find the period with which they beat (close to nearest integer)

A

6 s

B

4 s

C

1 s

D

2 s

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 27

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Two plane polarized light waves combine at a certain point whose electric field components are $$E_1 = E_0 \sin \omega t$$ and $$E_2 = E_0 \sin(\omega t + \frac{\pi}{3})$$. Find the amplitude of the resultant wave.

A

0.9 E

B

$$E_0$$

C

1.7 $$E_0$$

D

3.4 $$E_0$$

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 28

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A wire of resistance R is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points A and B is R/n. The value of n is :

A

16

B

14

C

10

D

12

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 29

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Uniform magnetic fields of different strengths ($$B_1$$ and $$B_2$$), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q, at the interface at an instant, moves into the region 2 with velocity v and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface?

(Consider the velocity of the particle to be normal to the magnetic field and $$B_2 > B_1$$)

A

$$\frac{mv}{qB_1}\left(1 - \frac{B_2}{B_1}\right) \times 2$$

B

$$\frac{mv}{qB_1}\left(1 - \frac{B_1}{B_2}\right)$$

C

$$\frac{mv}{qB_1}\left(1 - \frac{B_2}{B_1}\right)$$

D

$$\frac{mv}{qB_1}\left(1 - \frac{B_1}{B_2}\right) \times 2$$

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 30

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If $$\epsilon_0$$ denotes the permittivity of free space and $$\Phi_E$$ is the flux of the electric field through the area bounded by the closed surface, then dimension of $$\left(\epsilon_0 \frac{d\Phi_E}{dt}\right)$$ are that of :

A

Electric field

B

Electric potential

C

Electric charge

D

Electric current

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 31

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A rod of length 5L is bent right angle keeping one side length as 2L.

The position of the centre of mass of the system: (Consider L = 10 cm)

A

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

B

$$3\hat{i} + 7\hat{j}$$

C

$$5\hat{i} + 8\hat{j}$$

D

$$4\hat{i} + 9\hat{j}$$

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 32

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The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility $$\chi_{mg} = 1.2 \times 10^{-5}$$) is :

A

$$\frac{6}{5} \times 10^{-3} \%$$

B

$$\frac{5}{6} \times 10^{-5} \%$$

C

$$\frac{5}{6} \times 10^{-4} \%$$

D

$$\frac{5}{3} \times 10^{-5} \%$$

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 33

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A lens having refractive index 1.6 has focal length of 12 cm, when it is in air. Find the focal length of the lens when it is placed in water. (Take refractive index of water as 1.28)

A

355 mm

B

288 mm

C

555 mm

D

655 mm

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 34

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An ac current is represented as $$i = 5\sqrt{2} + 10\cos\left(650\pi t + \frac{\pi}{6}\right)$$ Amp. The r.m.s value of the current is :

A

50 Amp

B

100 Amp

C

10 Amp

D

$$5\sqrt{2}$$ Amp

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 35

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Two thin convex lenses of focal lengths 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is :

A

5 D

B

1 D

C

20 D

D

10 D

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 36

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In the following circuit, the reading of the ammeter will be (Take Zener breakdown voltage = 4 V)

A

24 mA

B

80 mA

C

10 mA

D

60 mA

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 37

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Two projectiles are fired from ground with same initial speeds from same point at angles $$(45^\circ + \alpha)$$ and $$(45^\circ - \alpha)$$ with horizontal direction. The ratio of their times of flights is

A

1

B

$$\frac{1 - \tan\alpha}{1 + \tan\alpha}$$

C

$$\frac{1 + \sin 2\alpha}{1 - \sin 2\alpha}$$

D

$$\frac{1 + \tan\alpha}{1 - \tan\alpha}$$

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 38

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Match the List-I with List-II.

Choose the correct answer from the options given below : 

A

A-III, B-IV, C-I, D-II

B

A-III, B-II, C-IV, D-I

C

A-II, B-IV, C-I, D-II

D

A-IV, B-II, C-III, D-I

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 39

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A cubic block of mass m is sliding down on an inclined plane at $$60^{\circ}$$ with an acceleration of $$\frac{g}{2}$$, the value of coefficient of kinetic friction is

A

$$\sqrt{3} - 1$$

B

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

C

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

D

$$1 - \frac{\sqrt{3}}{2}$$

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 40

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In a hydrogen like ion, the energy difference between the 2nd excitation energy state and ground state is 108.8 eV. The atomic number of the ion is

A

4

B

2

C

1

D

3

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 41

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For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is

A

5 : 36

B

5 : 27

C

3 : 4

D

27 : 5

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 42

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A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius(r). Which of the following curves represents the variation of r with E?

A

B

C

D

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 43

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An object of mass 1000 g experiences a time dependent force $$\vec{F} = (2t\hat{i} + 3t^2\hat{j})$$ N. The power generated by the force at time t is :

A

$$(2t^2 + 3t^3)$$ W

B

$$(2t^2 + 18t^3)$$ W

C

$$(3t^3 + 5t^5)$$ W

D

$$(2t^3 + 3t^5)$$ W

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 44

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Two wires A and B are made of same material having ratio of lengths $$\frac{L_A}{L_B} = \frac{1}{3}$$ and their diameters ratio $$\frac{d_A}{d_B} = 2$$. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

A

1 : 6

B

1 : 12

C

3 : 4

D

1 : 3

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 45

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Two charges $$q_1$$ and $$q_2$$ are separated by a distance of 30 cm. A third charge $$q_3$$ initially at 'C' as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of $$q_3$$ from C to D is given by $$\frac{q_3 K}{4\pi\epsilon_0}$$, the value of K is :

A

$$8q_2$$

B

$$6q_2$$

C

$$8q_1$$

D

$$6q_1$$

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 46

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A, B and C are disc, solid sphere, and spherical shell respectively with same radii and masses. These masses are placed as shown in the figure. The moment of inertia of the given system about PQ is $$\frac{x}{15}I$$, where I is the moment of inertia of the disc about its diameter. The value of x is ______.

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 47

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For ac circuit shown in figure, R = 100 k$$\Omega$$ and C = 100 pF and the phase difference between $$V_{in}$$ and $$(V_B - V_A)$$ is $$90^{\circ}$$. The input signal frequency is $$10^x$$ rad/sec, where 'x' is ______.

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 48

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A container contains a liquid with refractive index of 1.2 up to a height of 60 cm and another liquid having refractive index 1.6 is added to height H above first liquid. If viewed from above, the apparent shift in the position of bottom of container is 40 cm. The value of H is ___ cm.
(Consider liquids are immisible)

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 49

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A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is 1727 degrees C and power radiated by the wire is 94.2 W. Its emissivity is $$\frac{x}{8}$$ where x = ______.
(Given $$\sigma = 6.0 \times 10^{-8}$$ W m$$^{-2}$$ K$$^{-4}$$, $$\pi = 3.14$$ and assume that the emissivity of wire material is same at all wavelength. )

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NTA JEE Main 2025 April 7th Shift 1 - Physics - Question 50

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An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is ______ $$\times 10^{-1}$$ J. (Take $$\pi = 3.14$$)

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