Practice Questions

Q23.An initially parallel cylindrical beam travels in a medium of refractive index μ(I) = μ0 + μ2I , where μ0 and μ2 are positive constants and I is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. As the beam enters the medium, it will (1) diverge (2) converge (3) diverge near the axis and converge near the (4) travel as a cylindrical beam periphery

Q28.A nucleus of mass M + Δm is at rest and decays into two daughter nuclei of equal mass M2 each. Speed of light is C. The speed of daughter nuclei is (1) c Δm (2) M+Δm c√2ΔmM (3) c√ΔmM (4) c√ M+ΔmΔm

Q11.If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time? (1) a2T 2 + 4π2v2 (2) aTx (3) aT + 2πv (4) aTv

Q15.Let P(r) = Q r be the charge density distribution for a solid sphere of radius R and total charge Q. for a πR4 point ' p ' inside the sphere at distance r1 from the centre of the sphere, the magnitude of electric field is JEE Main 2009 JEE Main Previous Year Paper (1) 0 (2) Q 4πε0r21 (3) Qr21 (4) Q21 4πε0R4 3πε0R4

Q4. A thin rod of length ' L ' is lying along the x-axis with its ends at x = 0 and x = L . Its linear density (mass/length) varies with x ask ( Lx )n , where n can be zero or any positive number. If the position xCM of the centre of mass of the rod is plotted against ' n ', which of the following graphs best approximates the dependence of xCM on n ? (1) (2) (3) (4) JEE Main 2008 JEE Main Previous Year Paper

Q19.Paragraph: Consider a block of conducting material of resistivity ' ρ ' shown in the figure. Current 'l' enters at 'A' and leaves from ' D '. We apply superposition principle to find voltage ' ΔV ' developed between ' B ' and ' JEE Main 2008 JEE Main Previous Year Paper C '. The calculation is done in the following steps: (i) Take current 'l' entering from 'A' and assume it to spread over a hemispherical surface in the block. (ii) Calculate field E(r) at distance ' r ' from A by using Ohm's law E = ρj, where j is the current per unit area at ' r '. (iii) From the ' r ' dependence of E(r), obtain the potential V (r) at r. (iv) Repeat (i), (ii) and (iii) for current 'l' leaving ' D ' and superpose results for ' A ' and ' D '. Question: ΔV measured between B and C is ρl ρl (1) ρl (2) ρl πa − π(a+b) a − (a+b) ρl ρl (3) ρl (4) 2πa − 2π(a+b) 2π(a−b)

Q30.Suppose an electron is attracted towards the origin by a force k/r where ' k ' is a constant and ' r ' is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the nth orbital of the electron is found to be ' rn ' and the kinetic energy of the electron to be Tn . Then which of the following is true? (1) Tn ∝1/n2, rn ∝n2 (2) Tn independent of n, rn ∝n (3) Tn ∝1/n, rn ∝n (4) Tn ∝1/n, rn ∝n2 JEE Main 2008 JEE Main Previous Year Paper

Q8. For the given uniform square lamina ABCD, whose centre is O, (1) √2IAC = IEF (2) IAD = 3IEF (3) IAC = IEF (4) IAC = √2IEF

Q25.A parallel plate condenser with a dielectric of dielectric constant K between the plates has a capacity C and is charged to a potential V volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is (1) 1/2( K −1)CV2 (2) CV2( K −1)/K (3) (K −1)CV2 (4) zero

Q13.Four point masses, each of value m, are placed at the corners of a square ABCD of side ℓ. The moment of inertia through A and parallel to BD is (1) mℓ2 (2) 2 mℓ2 (3) 3mℓ2 (4) 3 mℓ2

Q54.If the lattice constant of this semiconductor is decreased, then which of the following is correct? (1) All Ec, Eg, Ev decrease (2) All F F−F increase (3) Ec , and Ev increase but Eg decreases (4) Ec , and Ev , decrease Eg increases

Q6. Two points A and B move from rest along a straight line with constant acceleration f and f ' respectively. If A takes m sec. more than B and describes ' n ' units more than B in acquiring the same speed then (1) (f −f ′)m2 = ff ′n (2) (f + f ′)m2 = ff ′n (3) 2 1 (f + f ′)m = ff ′n2 (4) (f ′ −f)n = 21 ff ′m2

Q7. A and B are two like parallel forces. A couple of moment H lies in the plane of A and B and is contained with them. The resultant of A and B after combining is displaced through a distance (1) 2H (2) H A−B A+B (3) H (4) H 2(A+B) A−B

Q9. A particle is projected from a point O with velocity u at an angle of 60∘ with the horizontal. When it is moving in a direction at right angles to its direction at O , its velocity then is given by (1) u (2) u 3 2 (3) 2u (4) u 3 √3

Q11.The upper half of an inclined plane with inclination ϕ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by (1) 2 sin ϕ (2) 2 cos ϕ (3) 2 tan ϕ (4) tan ϕ

Q23.A 'T' shaped object with dimensions shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the JEE Main 2005 JEE Main Previous Year Paper location of P with respect to C (1) 2 3 ℓ (2) 23 ℓ (3) 4 ℓ (4) ℓ 3

Q11.A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to (1) x3 (2) ex (3) x (4) loge x

Q23.Suppose the gravitational force varies inversely as the nth power of distance. Then the time period planet in circular orbit of radius R around the sun will be proportional to (1) R( n+12 ) (2) R( n−12 ) (3) Rn (4) R( n−22 )

Q42.Four charges equal to −Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium the value of q is (1) −Q4 (1 + 2√2) (2) −Q2 (1 + 2√2) (3) −Q2 (1 + 2√2) (4) Q2 (1 + 2√2)

Q58.In a uniform magnetic field of induction B a wire in the form of semicircle of radius r rotates about the diameter of the circle with angular frequency ω. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is R the mean power generated per period of rotation is (1) Bπr2ω (2) (Bπr2ω)2 2R 2R (3) (Bπrω)2 (4) (Bπrω2)2 2R 8R

Q65.A plane convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of the size of the object? (1) 20 cm (2) 30 cm (3) 60 cm (4) 80 cm

Q75.For a transistor amplifier in common emitter configuration having load impedance of 1kΩ (hfe = 50 and hoe = 25 ) the current gain is (1) −5.2 (2) −15.7 (3) −24.8 (4) −48.78

Q7. Two particles start simultaneously from the same point and move along two straight lines, one with uniform → velocity →u and the other from rest with uniform acceleration f . Let α be the angle between their directions of motion. The relative velocity of the second particle w.r.t. the first is least after a time. (1) u cos α (2) u sin α f f (3) f cos α (4) u sin α. u

Q9. Two stones are projected from the top of a cliff h metres high, with the same speed u, so as to hit the ground at the same spot. If one of the stones is projected at an angle θ to the horizontal then the θ equals (1) u√2gh (2) √2ugh (3) 2 g√uh (4) 2 h√ug

Q21.A particle performing uniform circular motion has angular frequency is doubled \& its kinetic energy halved, then the new angular momentum is (1) L (2) 2 L 4 (3) 4 L (4) L2