Practice Questions

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

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 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 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. 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.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.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]

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 Carnot engine (E) is working between two temperatures 473 K and 273 K . In a new system two engines - engine E1 works between 473 K to 373 K and engine E2 works between 373 K to 273 K . If η12, η1 and η2 are the efficiencies of the engines E, E1 and E2 , respectively, then (1) η12 = η1η2 (2) η12 ≥η1 + η2 (3) η12 = η1 + η2 (4) η12 < η1 + η2

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.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.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

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

Q36.A ball of mass 100 g is projected with velocity 20 m/s at 60∘ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is (1) 5 J (2) 15 J (3) 20 J (4) zero

Q36.A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is (1) 190 g (2) 200 g (3) 300 g (4) 290 g

Q36. LIST-I LIST-II A. Pressure varies inversely with volume of an ideal gas. I. Adiabatic process B. Heat absorbed goes partly to increase internal energy and partly to do work. II. Isochoric process C. Heat is neither absorbed nor released by a system. III. Isothermal process D. No work is done on or by a gas. IV. Isobaric process (1) A-III, B-IV, C-I, D-II (2) A-I, B-IV, C-II, D-III (3) A-III, B-I, C-IV, D-II (4) A-I, B-III, C-II, D-IV

Q36.A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities ρ1 and ρ2′ , respectively. The frequency of 9th harmonic of closed tube is identical with 4th harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is ρ1 : ρ2 = 1 : 16, then the length of the open tube is : (1) 15 7 cm (2) 207 cm (3) 15 9 cm (4) 209 cm

Q36.The width of one of the two slits in Young's double slit experiment is d while that of the other slit is x d. If the ratio of the maximum to the minimum intensity in the interference pattern on the screen is 9 : 4 then what is the value of x ? (Assume that the field strength varies according to the slit width.) (1) 4 (2) 5 (3) 3 (4) 2

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

Q36.A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is Options (1) 8/9 (2) 27/32 (3) 32/27 (4) 9/8

Q36.A convex lens made of glass (refractive index = 1.5 ) has focal length 24 cm in air. When it is totally immersed in water (refractive index = 1.33 ), its focal length changes to (1) 24 cm (2) 96 cm (3) 48 cm (4) 72 cm