Practice Questions

Q11.Two conductors have the same resistance at 0∘C but their temperature coefficients of resistance are α1 and α2 . The respective temperature coefficients of their series and parallel combinations are nearly (1) α1+α2 2 , α1 + α2 (2) α1 + α2, α1+α22 α1α2 (4) α1+α2 (3) α1 + α2, 2 , α1+α22 α1+α2

Q12.A diatomic ideal gas is used in a Car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from V to 32 V the efficiency of the engine is (1) 0.5 (2) 0.75 (3) 0.99 (4) 0.25

Q13.The equation of a wave on a string of linear mass density 0.04 kg m−1 is given by y = 0.02( m) sin [2π ( 0.04(t s) − 0.50(x m) )]. The tension in the string is (1) 4.0 N (2) 12.5 N (3) 0.5 N (4) 6.25 N

Q14.A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field →E at the centre O is (1) q ^j (2) − q ^j 4π2ε0r2 4π2ε0r2 (3) − q ^j (4) q ^j 2π2ε0r2 2π2ε0r2

Q15.Let there be a spherically symmetric charge distribution with charge density varying as ρ(r) = ρ0 ( 54 −rR ) upto r = R, and ρ(r) = 0 for r > R, where r is the distance from the origin. The electric field at a distance r(r < R) from the origin is given by (1) 4πρ0r 3ε0 ( 53 −rR ) (2) 4ε0ρ0r ( 53 −rR ) (3) 4ρ0r 3ε0 ( 54 −rR ) (4) 3ε0ρ0r ( 54 −rR ) JEE Main 2010 JEE Main Previous Year Paper

Q16.Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30∘ with each other. When suspended in a liquid of density 0.8 g cm−3 , the angle remains the same. If density of the material of the sphere is 16 g cm−3 , the dielectric constant of the liquid is (1) 4 (2) 3 (3) 2 (4) 1

Q17.Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t1 is the time taken for the energy stored in the capacitor to reduce to half its initial value and t2 is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio t1/t2 will be (1) 1 (2) 1 2 (3) 1 (4) 2 4

Q18.Two long parallel wires are at a distance 2 d apart. They carry steady equal current flowing out of the plane of the paper as shown. The variation of the magnetic field along the line XX ' is given by (1) (2) (3) (4)

Q19.A rectangular loop has a sliding connector PQ of length ℓ and resistance RΩ and it is moving with a speed v as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents I1, I2 and I are (1) I1 = −I2 = BℓvR , I = 2 BℓvR (2) I1 = I2 = Bℓv3R , I = 2 3RBℓv (3) l1 = I2 = I = BℓvR (4) I1 = I2 = Bℓv6R , I = Bℓv3R JEE Main 2010 JEE Main Previous Year Paper

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

Q26.Statement-1 : When ultraviolet light is incident on a photocell, its stopping potential is V0 and the maximum kinetic energy of the photoelectrons is Kmax . When the ultraviolet light is replaced by X− rays, both V0 and Kmax increase. Statement-2 : Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light. Of the four choices given after the statements, choose the one that best describes the two statements. (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-2 is not the correct explanation of Statement-1. Statement- 1. (3) Statement-1 is false, Statement-2 is true. (4) Statement-1 is true, Statement- 2 is false.

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

Q31.Ionisation energy of He+ is 19.6 × 10−18 Jatom−1 . The energy of the first stationary state (n = 1) of Li2+ is (1) 4.41 × 10−16 Jatom−1 (2) −4.41 × 10−17 Jatom −1 (3) −2.2 × 10−15 Jatom−1 (4) 8.82 × 10−17 Jatom −1

Q32.The correct sequence which shows decreasing order of the ionic radii of the elements is (1) Al3+ > Mg2+ > Na+ > F−> O2− (2) Na+ > Mg2+ > Al3+ > O2−> F (3) Na+ > F > Mg2+ > O2−> Al3+ (4) O2−> F > Na+ > Mg2+ > Al3+

Q33.The standard enthalpy of formation of NH3 is −46.0 kJ mol−1 . If the enthalpy of formation of H2 from its atoms is −436 kJ mol−1 and that of N2 is −712 kJ mol−1 , the average bond enthalpy of N −H bond in NH3 JEE Main 2010 JEE Main Previous Year Paper is (1) −964 kJ mol−1 (2) +352 kJ mol−1 (3) +1056 kJ mol−1 (4) −1102 kJ mol−1

Q34.The energy required to break one mole of Cl −Cl bonds in Cl2 is 242 kJ mol−1 . The longest wavelength of light capable of breaking a single Cl −Cl bond is (c = 3 × 108 ms−1 and NA = 6.02 × 1023 mol−1) (1) 594 nm (2) 640 nm (3) 700 nm (4) 494 nm

Q35.For a particular reversible reaction at temperature T, ΔH and ΔS were found to be both +ve. If Te is the temperature at equilibrium, the reaction would be spontaneous when (1) Te > T (2) T > Te (3) Te is 5 times T (4) T = Te