Practice Questions

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]

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.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 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.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.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.An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density 1000 kg/m3 . If the pressure inside the bubble is 2100 N/m2 greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use g = 10 m/s2 ) (1) 0.1 (2) 0.05 (3) 0.02 (4) 0.25

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

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

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.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

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.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.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

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.Consider following statements: A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid. B. As the temperature of liquid rises, the coefficient of viscosity increases. C. As the temperature of gas increases, the coefficient of viscosity increases D. The onset of turbulence is determined by Reynold's number. E. In a steady flow two stream lines never intersect. Choose the correct answer from the options given below: 2025 (28 Jan Shift 1) JEE Main Previous Year Paper (1) C, D, E Only (2) A, D, E Only (3) B, C, D Only (4) A, B, C Only

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. Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown in figure. A point object O is placed midway, between P and B . The separation between the images of O, formed by each refracting surface is : (1) 0.214 R (2) 0.411 R (3) 0.124 R (4) 0.114 R

Q41.A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is yπ × 10−2 s, where the value of y is (Acceleration due to gravity, g = 10 m/s2 , density of water = 103 kg/m3 ) 2025 (23 Jan Shift 1) JEE Main Previous Year Paper (1) 6 (2) 2 (3) 4 (4) 1

Q41.Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K . If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding temperature to be negligible), (1) 16 E (2) E (3) 64 E (4) 256 E

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