Practice Questions

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. 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]

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.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.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.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.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

Q34.A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water ? (Given : density of water = 1000 kg m−3 ) (1) 1400 cm3 (2) 600 cm3 (3) 4000 cm3 (4) 400 cm3

Q34. Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance Rp = 1Ω as shown in the figure. An external resistance of Re = 2Ω is connected via the sliding contact. The electric current in the circuit is : (1) 0.9 A (2) 1.35 A (3) 0.3 A (4) 1.0 A 2025 (22 Jan Shift 1) JEE Main Previous Year Paper

Q34. Three equal masses m are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At t = 0, −−−−−−→ → → → → → they are given an initial velocity →VA = V0AC, →VB = V0BA and →VC = V0CB . Here, AC, CB and BA are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is : (1) 3amV0 (2) 32 a mV0 (3) √3 2 a mV0 (4) 12 a mV0

Q34.A force F = α + βx2 acts on an object in the x -direction. The work done by the force is 5 J when the object is displaced by 1 m . If the constant α = 1 N then β will be (1) 15 N/m2 (2) 12 N/m2 (3) 8 N/m2 (4) 10 N/m2

Q34.A small uncharged conducting sphere is placed in contact with an identical sphere but having 4 × 10−8C charge and then removed to a distance such that the force of repulsion between them is 9 × 10−3 N . The distance between them is (Take 1 as 9 × 109inSI units) 4πϵo (1) 3 cm (2) 2 cm (3) 4 cm (4) 1 cm 2025 (24 Jan Shift 2) JEE Main Previous Year Paper

Q34.A sub-atomic particle of mass 10−30 kg is moving with a velocity 2.21 × 106 m/s. Under the matter wave consideration, the particle will behave closely like (h = 6.63 × 10−34 J. s) (1) Visible radiation (2) Gamma rays (3) Infra-red radiation (4) X-rays

Q34. What is the current through the battery in the circuit shown below (1) 1.5 A (2) 0.5 A (3) 0.25 A (4) 1.0 A Q35.5 The refractive index of the material of a glass prism is √3. The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism? (1) 60∘ (2) 58∘ (3) 48∘ (4) 50∘

Q34.Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire's cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be (1) [a/4, 3a/2] (2) [a/4, 2a] (3) [a/2, 2a] (4) [a/2, 3a]

Q35.A thin plano convex lens made of glass of refractive index 1.5 is immersed in a liquid of refractive index 1.2. When the plane side of the lens is silver coated for complete reflection, the lens immersed in the liquid 2025 (24 Jan Shift 1) JEE Main Previous Year Paper behaves like a concave mirror of focal length 0.2 m . The radius of curvature of the curved surface of the lens is (1) 0.20 m (2) 0.25 m (3) 0.15 m (4) 0.10 m

Q35.At the interface between two materials having refractive indices n1 and n2 , the critical angle for reflection of an em wave is θ1C . The n2 material is replaced by another material having refractive index n3 such that the critical angle at the interface between n1 and n3 materials is θ2C . If n3 > n2 > n1; n2 = 25 and n3 sin θ2C −sin θ1C = 12 , then θ1C is (1) sin−1 ( 16 ) (2) sin−1 ( 13 ) (3) sin−1 ( −56 ) (4) sin−1 ( 23 )

Q35.The number of spectral lines emitted by atomic hydrogen that is in the 4th energy level, is (1) 3 (2) 1 (3) 6 (4) 0

Q35.Consider a moving coil galvanomenter (MCG): A. The torsional constant in moving coil galvanometer has dimentions [ML2 T−2] B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity. C. If we increase number of turns (N) to its double (2 N), then the voltage sensitivity doubles. D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer. E. Current sensitivity of MCG depends inversely on number of turns of coil. Choose the correct answer from the options given below: 2025 (23 Jan Shift 1) JEE Main Previous Year Paper (1) A, D Only (2) A, B, E Only (3) B, D, E Only (4) A, B Only

Q35.A small point of mass m is placed at a distance 2R from the centre ' O′ of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is F1 . A spherical part of radius R/3 is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be F2 . The value of ratio F1 : F2 is (1) 12 : 11 (2) 11 : 10 (3) 12 : 9 (4) 16 : 9

Q35. N equally spaced charges each of value q , are placed on a circle of radius R . The circle rotates about its axis with an angular velocity ω as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, IA −IB , for the given Amperian loops is (1) 2π N qω (2) N22π qω (3) N π qω (4) 2πN qω

Q35.Consider a long thin conducting wire carrying a uniform current I. A particle having mass " M " and charge " q " is released at a distance " a " from the wire with a speed v0 along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance x from the wire. The value of x is [ μ0 is vacuum permeability] (1) ae−4πmvoqμoI (2) a [1 − 2qμoImvo ] − 2 qμoI (3) a [1 mv ] (4) a

Q36.A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm . If D and d are the total distance and displacement covered by the particle in 12.5 s , then D is d (1) 16 (2) 10 5 (3) 15 (4) 25 4