JEE Main 2024 question paper pdf with solutions- Download Jan 29 Shift 2 Physics Question Paper pdf

31: Two sources of light emit with a power of 200 W. The ratio of the number of photons of visible light emitted by each source having wavelengths 300 nm and 500 nm respectively, will be:

(1) 1:5
(2) 1:3
(3) 5:3
(4) 3:5

36: A stone of mass 900 g is tied to a string and moved in a vertical circle of radius 1 m making 10 rpm. The tension in the string, when the stone is at the lowest point, is:

(1) 97 N
(2) 9.8 N
(3) 8.82 N
(4) 17.8 N

37: The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 m. If it dissipates 10% of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is:

(1) 6√5 m/s
(2) 5√6 m/s
(3) 5√5 m/s
(4) 2√5 m/s

38: If the distance between an object and its two-times magnified virtual image produced by a curved mirror is 15 cm, the focal length of the mirror must be:

(1) 15 cm
(2) −12 cm
(3) −10 cm
(4) 10/3 cm

39: Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter, they enter normally in a region of uniform magnetic field and describe circular paths of radii R₁ and R₂, respectively. The mass ratio of X and Y is:

(1) (R₂/R₁)²
(2) (R₁/R₂)²
(3) R₁/R₂
(4) R₂/R₁

40: In Young’s double slit experiment, light from two identical sources is superimposing on a screen. The path difference between the two lights reaching a point on the screen is 7λ/4. The ratio of intensity of the fringe at this point with respect to the maximum intensity of the fringe is:

(1) 1/2
(2) 3/4
(3) 1/3
(4) 1/4

41: A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T, then the work done in the process will be:

(1) 8πR²T
(2) 3πR²T
(3) 1/8πR²T
(4) 4πR²T

42: A bob of mass ‘m’ is suspended by a light string of length ‘L’. It is imparted a minimum horizontal velocity at the lowest point A such that it just completes a half-circle reaching the topmost position B. The ratio of kinetic energies (K.E.)_A : (K.E.)_B is:

(1) 3:2
(2) 5:1
(3) 2:5
(4) 1:5

43: A wire of length L and radius r is clamped at one end. If its other end is pulled by a force F, its length increases by l. If the radius of the wire and the applied force are both reduced to half of their original values, keeping the original length constant, the increase in length will become:

(1) 3 times
(2) 3/2 times
(3) 4 times
(4) 2 times

44: A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from the Sun is reduced to one-fourth of the original distance, how many days will it take to complete one revolution?

(1) 25
(2) 50
(3) 100
(4) 20

45: A plane electromagnetic wave of frequency 35 MHz travels in free space along the X-direction. At a particular point (in space and time), E = 9.6 j V/m. The value of the magnetic field at this point is:

(1) 3.2×10⁻⁸ kT
(2) 3.2×10⁻⁸ iT
(3) 9.6 jT
(4) 9.6×10⁻⁸ kT

46: In the given circuit, the current in resistance R₃ is:

(1) 1 A
(2) 1.5 A
(3) 2 A
(4) 2.5 A

47: A particle is moving in a straight line. The variation of position x as a function of time t is given as x = (t³ − 6t² + 20t + 15) m. The velocity of the body when its acceleration becomes zero is:

(1) 4 m/s
(2) 8 m/s
(3) 10 m/s
(4) 6 m/s

48: N moles of a polyatomic gas (f = 6) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N is:

(1) 6
(2) 3
(3) 4
(4) 2

49: Given below are two statements:
Statement I: Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford’s model.
Statement II: An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford’s model.

(1) Both Statement I and Statement II are false
(2) Statement I is false but Statement II is true
(3) Statement I is true but Statement II is false
(4) Both Statement I and Statement II are true

50: An electric field is given by E = (6i + 5j + 3k) N/C. The electric flux through a surface area 30i m² lying in the YZ-plane (in SI units) is:

(1) 90
(2) 150
(3) 180
(4) 60

51: Two metallic wires P and Q have the same volume and are made up of the same material. If their areas of cross-section are in the ratio 4:1 and force F₁ is applied to P, an extension of Δℓ is produced. The force required to produce the same extension in Q is F₂. The value of F₁/F₂ is:

52: A horizontal straight wire 5 m long extending from east to west falls freely at a right angle to the horizontal component of Earth’s magnetic field 0.60 × 10⁻⁴ Wb/m². The instantaneous value of emf induced in the wire when its velocity is 10 m/s is:

53: Hydrogen atom is bombarded with electrons accelerated through a potential difference V, which causes excitation of hydrogen atoms. If the experiment is performed at T = 0 K, the minimum potential difference needed to observe any Balmer series lines in the emission spectra will be α/10 V, where α is:

54: A charge of 4.0 µC is moving with a velocity of 4.0 × 10⁶ m/s along the positive y-axis under a magnetic field B of strength 2k̂ T. The force acting on the charge is xî N. The value of x is:

55: A simple harmonic oscillator has an amplitude A and a time period 6π seconds. Assuming the oscillation starts from its mean position, the time required by it to travel from x = A to x = √3/2 A will be π/x seconds, where x is:

56: In the given figure, the charge stored in a 6µF capacitor, when points A and B are joined by a connecting wire, is µC:

57: In a single slit diffraction pattern, a light of wavelength 6000 Å is used. The distance between the first and third minima in the diffraction pattern is found to be 3 mm when the screen is placed 50 cm away from the slits. The width of the slit is ×10⁻⁴ m:

58: In the given circuit, the current flowing through the resistance 20Ω is 0.3A, while the ammeter reads 0.9A. The value of R₁ is Ω:

59: A particle is moving in a circle of radius 50 cm in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at t = 0 is 4 m/s, the time taken to complete the first revolution will be 1/α [1 − e⁻²π] seconds, where α is:

60: A body of mass 5 kg moving with a uniform speed 3√2 m/s in the X-Y plane along the line y = x + 4. The angular momentum of the particle about the origin will be kg·m²/s: