Practice Questions

Q29.Young's double slit inteference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5 mm . The slits are illuminated by a parallel beam of light whose wavelength in air is 690 nm . The fringe-width on a screen placed behind the plane of slits at a distance of 0.72 m , will be : (1) 0.23 mm (2) 0.33 mm (3) 0.63 mm (4) 0.46 mm

Q29.An amount of ice of mass 10−3 kg and temperature −10∘C is transformed to vapour of temperature 110∘C by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice = 2100Jkg−1 K−1 , specific heat of water = 4180Jkg−1 K−1 , specific heat of steam = 1920Jkg−1 K−1 , Latent heat of ice = 3.35 × 105Jkg−1 and Latent heat of steam = 2.25 × 106 Jkg−1 ) (1) 3043 J (2) 3024 J (3) 3003 J (4) 3022 J

Q29.Two point charges −4μc and 4μc, constituting an electric dipole, are placed at (−9, 0, 0)cm and (9, 0, 0)cm in a uniform electric field of strength 104NC−1 . The work done on the dipole in rotating it from the equilibrium through 180∘ is : (1) 18.4 mJ (2) 14.4 mJ (3) 12.4 mJ (4) 16.4 mJ

Q30.Refer to the circuit diagram given in the figure. which of the following observations are correct? A. Total resistance of circuit is 6Ω B. Current in Ammeter is 1 A C. Potential across AB is 4 Volts. D. Potential across 2025 (23 Jan Shift 1) JEE Main Previous Year Paper CD is 4 Volts E. Total resistance of the circuit is 8Ω. Choose the correct answer from the options given below: (1) A, B and D Only (2) A, B and C Only (3) A, C and D Only (4) B, C and E Only

Q30.Match List - I with List - II. (1) (A)-(II), (B)-(I), (C)-(IV), (D)-(III) (2) (A)-(I), (B)-(III), (C)-(IV), (D)-(II) (3) (A)-(III), (B)-(I), (C)-(II), (D)-(IV) (4) (A)-(III), (B)-(I), (C)-(IV), (D)-(II)

Q30.For a short dipole placed at origin O, the dipole moment P is along x-axis, as shown in the figure. If the electric potential and electric field at A are V0 and E0 , respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the y-axis is given by 2025 (22 Jan Shift 2) JEE Main Previous Year Paper (1) V0 and E04 (2) zero and E016 (3) zero and E0 (4) V0 and E0 8 2 16

Q30.An electron in the ground state of the hydrogen atom has the orbital radius of 5.3 × 10−11 m while that for the electron in third excited state is 8.48 × 10−10 m . The ratio of the de Broglie wavelengths of electron in the excited state to that in the ground state is (1) 3 (2) 16 (3) 9 (4) 4

Q30.A satellite is launched into a circular orbit of radius ' R ' around the earth. A second satellite is launched into an orbit of radius 1.03 R . The time period of revolution of the second satellite is larger than the first one approximately by (1) 9% (2) 3% (3) 4.5% (4) 2.5%

Q30.A particle of mass ' m ' and charge ' q ' is fastened to one end ' A ' of a massless string having equilibrium length l, whose other end is fixed at point ' O '. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the x -axis is (1) √qEl2 m (2) √qElm (3) √qEl4 m (4) √2qElm

Q30.The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) : (1) 5π (2) 40π (3) 10π (4) zero

Q31.A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of 10πrads−1 about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim ? (π = 3.14) (1) 0.5024 V (2) V (3) 0.2512V V (4) 0.1256V V

Q31.The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have (1) high thermal conductivity and high electrical (2) low thermal conductivity and low electrical conductivity conductivity (3) high thermal conductivity and low electrical (4) low thermal conductivity and high electrical conductivity conductivity

Q31.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: In a central force field, the work done is independent of the path chosen. Reason R: Every force encountered in mechanics does not have an associated potential energy. In the light of the above statements, choose the most appropriate answer from the options given below 2025 (28 Jan Shift 1) JEE Main Previous Year Paper (1) A is false but R is true (2) Both A and R are true but R is NOT the correct explanation of A (3) A is true but R is false (4) Both A and R are true and R is the correct explanation of A

Q31.A bob of mass m is suspended at a point O by a light string of length l and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity v0 at the point ' A ', the string becomes slack when, the bob reaches at the point ' D '. The ratio of the kinetic energy of the bob at the points B and C is ______ -. (1) 1 (2) 2 (3) 4 (4) 3

Q31.A long straight wire of a circular cross-section with radius ' a ' carries a steady current I . The current I is uniformly distributed across this cross-section. The plot of magnitude of magnetic field B with distance r from the centre of the wire is given by 2025 (24 Jan Shift 2) JEE Main Previous Year Paper (1) (2) (3) (4)

Q31.A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm . [Assume that the light is incident nearly perpendicular to the glass surface.] (1) 137.5 nm (2) 275 nm (3) 94.8 nm (4) 68.7 nm

Q32.Choose the correct nuclear process from the below options [p: proton, n : neutron, e− : electron, e+ : positron, v : neutrino, ¯v : antineutrino] (1) n →p + e+ + ¯v (2) n →p + e+ + v (3) n →p + e−+ v (4) n →p + e−+ ¯v

Q32. An infinite wire has a circular bend of radius a, and carrying a current I as shown in figure. The magnitude of 2025 (28 Jan Shift 2) JEE Main Previous Year Paper magnetic field at the origin O of the arc is given by : μ0 (1) a 4π I [ π2 + 1] (2) 4πμ0 aI [ 3π2 + 2] μ0 (3) 2π a I [ π2 + 2] (4) 4πμ0 aI [ 3π2 + 1]

Q32.In photoelectric effect, the stopping potential (V0)v/s frequency (ν) curve is plotted. ( h is the Planck's constant and ϕ0 is work function of metal ) (A) V0v/sν is linear. (B) The slope of V0v/sν curve = ϕ0h (C) h constant is related to the slope of V0v/sν line. (D) The value of electric charge of electron is not required to determine h using the V0v/sν curve. (E) The work function can be estimated without knowing the value of h. Choose the correct answer from the options given below : (1) (C) and (D) only (2) (A), (C) and (E) only (3) (A), (B) and (C) only (4) (D) and (E) only

Q32.Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be (1) 2.0 cm (2) 1.5 cm (3) 1.0 cm (4) 0.5 cm

Q32.Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is P1 . The reading of the pressure gauge falls to P2 when the valve is opened. The speed of water flowing in the pipe is proportional to (1) P1 −P2 (2) (P1 −P2)4 (3) (P1 −P2)2 (4) √P1 −P2

Q33.A hemispherical vessel is completely filled with a liquid of refractive index μ. A small coin is kept at the lowest point (O) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is (1) √3 (2) √3 2 (3) 3 (4) √2 2

Q33.The electric flux is ϕ = ασ + βλ where λ and σ are linear and surface charge density, respectively. ( αβ ) represents (1) electric field (2) area (3) charge (4) displacement

Q33.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Emission of electrons in photoelectric effect can be suppressed by applying a sufficiently negative electron potential to the photoemissive substance. Reason (R) : A negative electric potential, which stops the emission of electrons from the surface of a photoemissive substance, varies linearly with frequency of incident radiation. In the light of the above statements, choose the most appropriate answer from the options given below : (1) (A) is false but (R) is true (2) (A) is true but (R) is false (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)

Q33.A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be t1 and t2 , respectively, then (1) t1 > t2 (2) t1 = t2 (3) t1 < t2 (4) t1 = 2t2