Practice Questions

Q20.In the circuit shown below, the key K is closed at t = 0 . The current through the battery is (1) VR1R2 at t = 0 and V at t = ∞ (2) V at t = 0 and V (R1+R2) at t = ∞ √R21+R22 R2 R2 R1R2 (3) V at t = 0 and V R1R2 at t = ∞ (4) V (R1+R2) at t = 0 and V at t = ∞ R2 √R21+R22 R1R2 R2

Q21.In a series LCR circuit R = 200Ω and the voltage and the frequency of the main supply is 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by 30∘ . On taking out the inductor from the circuit the current leads the voltage by 30∘ . The power dissipated in the LCR circuit is (1) 305 W (2) 210 W (3) Zero W (4) 242 W

Q22.If a source of power 4 kW produces 1020 photons/second, the radiation belong to a part of the spectrum called (1) X-rays (2) ultraviolet rays (3) microwaves (4) γ -rays

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

Q24.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. The initial shape of the wave front of the beam is (1) convex (2) concave (3) convex near the axis and concave near the (4) planar periphery

Q25.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. The speed of light in the medium is (1) minimum on the axis of the beam (2) the same everywhere in the beam (3) directly proportional to the intensity I (4) maximum on the axis of the beam JEE Main 2010 JEE Main Previous Year Paper

Q27.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. 40. The binding energy per nucleon for the parent nucleus is E1 and that for the daughter nuclei is E2 . Then (1) E2 = 2E1 (2) E1 > E2 (3) E2 > E1 (4) E1 = 2E2

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

Q29.A radioactive nucleus (initial mass number A and atomic number Z) emits 3α-particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be (1) A−Z−8 (2) A−Z−4 Z−4 Z−8 (3) A−Z−12 (4) A−Z−4 Z−4 Z−2

Q30. The combination of gates shown below yields (1) OR gate (2) NOT gate (3) XOR gate (4) NAND gate

Q1. A particle has an initial velocity 3^i + 4^j and an acceleration of 0.4^i + 0.3^j. Its speed after 10 s is (1) 10 units (2) 7√2 units (3) 7 units (4) 8.5 units

Q3. A thin uniform rod of length ℓ and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ω. Its centre of mass rises to a maximum height of (1) 1 ℓ2ω2 (2) 1 ℓω 3 g 6 g (3) 1 ℓ2ω2 (4) 1 ℓ2ω2 2 g 6 g

Q4. The height at which the acceleration due to gravity becomes g (where g = the acceleration due to gravity on 9 the surface of the earth) in terms of R, the radius of the earth is (1) 2R (2) R √2 (3) R (4) √2R 2

Q5. Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area A and wire-2 has cross-sectional area 3A. If the length of wire 1 increases by Δx on applying force F , how much force is needed to stretch wire 2 by the same amount? (1) F (2) 4 F (3) 6 F (4) 9 F

Q7. Assuming the gas to be ideal the work done on the gas in taking it from A to B is (1) 200R (2) 300R (3) 400R (4) 500R

Q8. The work done on the gas in taking it from D to A is (1) −414R (2) +414R (3) −690R (4) +690R

Q9. The net work done on the gas in the cycle ABCDA is (1) Zero (2) 276R (3) 1076R (4) 1904R

Q10.One kg of a diatomic gas is at a pressure of 8 × 104 N/m2 . The density of the gas is 4 kg/m−3 . What is the energy of the gas due to its thermal motion? (1) 3 × 104 J (2) 5 × 104 J (3) 6 × 104 J (4) 7 × 104 J

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

Q13.Three sound waves of equal amplitudes have frequencies (v −1), v, (v + 1). They superpose to give beats. The number of beats produced per second will be (1) 4 (2) 3 (3) 2 (4) 1

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

Q16.Two points P and Q are maintained at the potentials of 10 V and −4 V respectively. The work done in moving 100 electrons from P to Q is (1) −19 × 10−17 J (2) 9.60 × 10−17 J (3) −2.24 × 10−16 J (4) 2.24 × 10−16 J

Q17.A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, then the Q/q equals (1) −2√2 (2) −1 (3) 1 (4) −1 √2

Q19.The magnitude of the magnetic field (B) due to loop ABCD at the origin (O) is (1) zero (2) μ0(b−a) 24ab (3) μ0I 4π [ b−aab ] (4) μo∣4π [2(b −a) + π3 (a + b)]

Q20.Due to the presence of the current l1 at the origin (1) The forces on AB and DC are zero (2) The forces on AD and BC are zero (3) The magnitude of the net force on the loop is (4) The magnitude of the net force on the loop is given by μ0I1 4π [2(b −a) + π3 (a + b)] given by μ0∥124ab (b −a)