Practice Questions

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 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 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.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 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.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

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.If λ and K are de Broglie wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be 2025 (29 Jan Shift 1) JEE Main Previous Year Paper (1) (2) (3) (4)

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

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.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.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)

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

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.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.Which of the following circuits represents a forward biased diode? Choose the correct answer from the options given below : (1) (A) and (D) only (2) (B), (D) and (E) only (3) (C) and (E) only (4) (B), (C) and (E) only

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.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 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.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.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.A concave mirror of focal length f in air is dipped in a liquid of refractive index μ. Its focal length in the liquid will be: (1) μf (2) f (3) f (4) f (μ−1) μ 2025 (23 Jan Shift 2) JEE Main Previous Year Paper