Practice Questions

Q39.Given below are two statements : Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions. In the light of the above statements, choose the correct answer from the options given below. (1) Statement I is true but Statement II is false (2) Statement I is false but Statement II is true (3) Both Statement I and Statement II are false (4) Both Statement I and Statement II are true 2025 (22 Jan Shift 1) JEE Main Previous Year Paper

Q39.What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness ' h ' in terms of the angle of incidence ' i ' and angle of refraction ' r ', if the glass slab is placed in air medium? (1) h tan(i−r) (2) h sin(i−r) tan r cos r (3) h (4) h cos(i−r) sin r

Q39.A bead of mass ' m ' slides without friction on the wall of a vertical circular hoop of radius ' R ' as shown in figure. The bead moves under the combined action of gravity and a massless spring ( k ) attached to the bottom of the hoop. The equilibrium length of the spring is ' R '. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' R ', would be (spring constant is ' k ', g is accleration due to gravity) (1) √3Rg + kR2m (2) 2√gR + kR2m (3) √2Rg + kR2m (4) √2Rg + 4kR2m

Q39.A plane electromagnetic wave propagates along the +x direction in free space. The components of the electric field, →E and magnetic field, →B vectors associated with the wave in Cartesian frame are (1) Ex, By (2) Ey, Bz (3) Ez, By (4) Ey, Bx

Q39.A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is I0 . If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be (1) 2I0 (2) I0 (3) I0 (4) I0 2 √2

Q39.The kinetic energy of translation of the molecules in 50 g of CO2 gas at 17∘C is (1) 4205.5 J (2) 4102.8 J (3) 3582.7 J (4) 3986.3 J

Q39.Arrange the following in the ascending order of wavelength (λ) : (A) Microwaves (λ1) (B) Ultraviolet rays (λ2) (C) Infrared rays (λ3) (D) X-rays (λ4) Choose the most appropriate answer from the options given below : (1) λ4 < λ3 < λ2 < λ1 (2) λ3 < λ4 < λ2 < λ1 (3) λ4 < λ3 < λ1 < λ2 (4) λ4 < λ2 < λ3 < λ1

Q39.The equation of a transverse wave travelling along a string is y(x, t) = 4.0 sin [20 × 10−3x + 600t]mm , where x is in mm and t is in second. The velocity of the wave is : 2025 (23 Jan Shift 2) JEE Main Previous Year Paper (1) −60 m/s (2) −30 m/s (3) +30 m/s (4) +60 m/s

Q39.The expression given below shows the variation of velocity (v) with time (t), v = At2 + C+tBt . The dimension of ABC is : (1) [M0 L1 T−3] (2) [M0 L2 T−2] (3) [M0 L1 T−2] (4) [M0 L2 T−3]

Q40.Which of the following phenomena can not be explained by wave theory of light? 2025 (28 Jan Shift 2) JEE Main Previous Year Paper (1) Compton effect (2) Refraction of light (3) Reflection of light (4) Diffraction of light

Q40.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number A, for nuclei with mass numbers between 30 and 170. Reason (R): Nuclear force is long range. In the light of the above statements, choose the correct answer from the options given below : (1) (A) is true but (R) is false (2) (A) is false but (R) is true (3) Both (A) and (R) are true and (R) is the correct (4) Both (A) and (R) are true but (R) is NOT the explanation of (A) correct explanation of (A)

Q40.Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge, (1) [F] = [C2M−1 L−2 T2] (2) [F] = [C2M−2 L2 T2] (3) [F] = [CM−2 L−2 T−2] (4) [F] = [CM−1 L−2 T2]

Q40.A radioactive nucleus n2 has 3 times the decay constant as compared to the decay constant of another radioactive nucleus n1 . If initial number of both nuclei are the same, what is the ratio of number of nuclei of n2 to the number of nuclei of n1 , after one half-life of n1 ? (1) 1/8 (2) 8 (3) 4 (4) 1/4

Q40.A cup of coffee cools from 90∘C to 80∘C in t minutes when the room temperature is 20∘C. The time taken by the similar cup of coffee to cool from 80∘C to 60∘C at the same room temperature is : (1) 13 10 t (2) 1013 t (3) 13 5 t (4) 135 t

Q40.The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV , respectively. If we incident a light of wavelength 550 nm on these two metal surfaces, then photo-electric effect is possible for the case of (1) Both Cs and Li (2) Neither Cs nor Li (3) Cs only (4) Li only

Q40.The workdone in an adiabatic change in an ideal gas depends upon only : (1) change in its temperature (2) change in its volume (3) change in its pressure (4) change in its specific heat

Q40.Find the equivalent resistance between two ends of the following circuit (1) r (2) r 9 3 (3) r (4) r 6

Q40.The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation (1) E2 = pc2 + m2c2 (2) E2 = p2c2 + m2c2 (3) E2 = pc2 + m2c4 (4) E2 = p2c2 + m2c4

Q40.A uniform solid cylinder of mass ' m ' and radius ' r ' rolls along an inclined rough plane of inclination 45∘ . If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be (1) 1 g (2) 1 g √2 3√2 (3) √2 g (4) √2g 3

Q41.The fractional compression ( ΔVV ) of water at the depth of 2.5 km below the sea level is ______ % . Given, the Bulk modulus of water = 2 × 109 N m−2 , density of water = 103 kgm−3 , acceleration due to gravity = g = 10 m s−2 . (1) 1.25 (2) 1.0 (3) 1.75 (4) 1.5

Q41. A tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be (1) 4 m/s (2) 2 m/s (3) 6 m/s (4) 8 m/s

Q41.If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon = 27 days and gravitational attraction between the satellite and the moon is neglected. (1) 27 days (2) 1 day (3) 81 days (4) 3 days

Q41.The Young's double slit interference experiment is performed using light consisting of 480 nm and 600 nm wavelengths to form interference patterns. The least number of the bright fringes of 480 nm light that are required for the first coincidence with the bright fringes formed by 600 nm light is (1) 5 (2) 4 (3) 6 (4) 8

Q41.The temperature of a body in air falls from 40∘C to 24∘C in 4 minutes. The temperature of the air is 16∘C. The temperature of the body in the next 4 minutes will be: (1) 14 3 ∘C (2) 423 ∘C (3) 28 3 ∘C (4) 563 ∘C

Q41.A balloon and its content having mass M is moving up with an acceleration ' a '. The mass that must be released from the content so that the balloon starts moving up with an acceleration ' 3a′ will be (Take ' g ' as acceleration due to gravity) (1) 2Ma (2) 3Ma 3a+g 2a−g (3) 3Ma (4) 2Ma 2a+g 3a−g