Practice Questions

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.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.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 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.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.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.Two projectiles are fired with same initial speed from same point on ground at angles of (45∘−α) and (45∘+ α), respectively, with the horizontal direction. The ratio of their maximum heights attained is : (1) 1−tan α (2) 1−sin 2α 1+tan α 1+sin 2α (3) 1+sin 2α (4) 1+sin α 1−sin 2α 1−sin α

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

Q31.An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature. A. The work done by gas during the process is zero. B. The heat added to gas is different from change in its internal energy. C. The volume of the gas is increased. D. The internal energy of the gas is increased. E. The process is isochoric (constant volume process) Choose the correct answer from the options given below: (1) E Only (2) A, B, C, D Only (3) A, D, E Only (4) A, C Only →

Q31.Water of mass m gram is slowly heated to increase the temperature from T1 to Tz The change in entropy of the water, given specific heat of water is 1Jkg−1 K−1 , is : (1) m ln ( T2T1 ) (2) zero (3) m ln ( T1T2 ) (4) m (T2 −T1)

Q32.Given is a thin convex lens of glass (refractive index μ ) and each side having radius of curvature R. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that 2025 (22 Jan Shift 1) JEE Main Previous Year Paper the image gets formed on the object itself ? (1) R/μ (2) R/(2μ −3) (3) μR (4) R/(2μ −1)

Q32. Match List - I with List - II. Choose the correct answer from the options given below : (1) (A)-(I), (B)-(III), (C)-(II), (D)-(IV) (2) (A)-(IV), (B)-(II), (C)-(III), (D)-(I) (3) (A)-(II), (B)-(IV), (C)-(I), (D)-(III) (4) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)

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.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

Q32.An electron of mass ' m ' with an initial velocity →v = v0^i (v0 > 0) enters an electric field E = −Eo^k . If the initial de Broglie wavelength is λ0 , the value after time t would be (1) λ0 (2) e2E20t2 m2v2o √1+ e2E02t2m2v02 λo√1 + (3) λ0 (4) λ0 √1−e2Eo2t2m2v2o

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.Given are statements for certain thermodynamic variables, (A) Internal energy, volume (V) and mass (M) are extensive variables. (B) Pressure (P), temperature (T) and density ( ρ ) are intensive variables. (C) Volume (V), temperature (T) and density ( ρ ) are intensive variables. (D) Mass (M), temperature (T) and internal energy are extensive variables. Choose the correct answer from the options given below : (1) (B) and (C) Only (2) (C) and (D) Only (3) (D) and (A) Only (4) (A) and (B) Only

Q33.A sand dropper drops sand of mass m(t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e. dmdt ∝√v . If P is the power delivered to run the belt at constant speed then which of the following relationship is true? 2025 (29 Jan Shift 2) JEE Main Previous Year Paper (1) P ∝√v (2) P ∝v (3) P2 ∝v5 (4) P2 ∝v3

Q33.What is the relative decrease in focal length of a lens for an increase in optical power by 0.1 D from 2.5D ? ['D' stands for dioptre] (1) 0.01 (2) 0.04 (3) 0.40 (4) 0.1

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.An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is : (1) √ πeeBh (2) √2hπeB (3) √ 2πeBh (4) √4πeBh

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

Q33.In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex refractive meniscus towards A . If an object placed at 13 cm from the vertex of the meniscus in A forms an image with a magnification of ' −2′ then the radius of curvature of meniscus is : (1) 1 3 cm (2) 43 cm (3) 1 cm (4) 23 cm