Practice Questions

Q19.A resistor 'R' and 2μF capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V . Calculate the value of R to make the bulb light up 5 s after the switch has been closed. (log10 2.5 = 0.4) (1) 1.7 × 105Ω (2) 2.7 × 106Ω (3) 3.3 × 107Ω (4) 1.3 × 104Ω

Q20.A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius R. The magnitude of the magnetic induction along its axis is (1) μ0I (2) μ0I 2π2R 2πR (3) μ0I (4) μ0l 4π2R π2R

Q21.A boat is moving due east in a region where the earth's magnetic field is 5.0 × 10−5NA−1 m−1 due north and horizontal. The boat carries a vertical aerial 2 m long. If the speed of the boat is 1.50 ms−1 , the magnitude of the induced emf in the wire of aerial is : (1) 0.75mV (2) 0.50mV (3) 0.15mV (4) 1mV

Q22.A fully charged capacitor C with initial charge q0 is connected to a coil of self inductance L at t = 0 . The time at which the energy is stored equally between the electric and the magnetic field is : (1) π √LC (2) 2π√LC 4 (3) √LC (4) π√LC

Q23.Let the x −z plane be the boundary between two transparent media. Medium 1 in z ≥0 has a refractive index of √2 and medium 2 with z < 0 has a refractive index of √3 . A ray of light in medium 1 given by the vector →A = 6√3^i + 8√3^j −10^k is incident on the plane of separation. The angle of refraction in medium 2 is (1) 45∘ (2) 60∘ (3) 75∘ (4) 30∘

Q24.A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is : JEE Main 2011 JEE Main Previous Year Paper (1) 1 m/s (2) 10 m/s 15 (3) 15 m/s (4) 101 m/s

Q27.Energy required for the electron excitation in Li++ from the first to the third Bohr orbit is : (1) 36.3eV (2) 108.8eV (3) 122.4eV (4) 12.1eV

Q28.The half life of a radioactive substance is 20 minutes. The approximate time interval (t2 −t1) between the time t2 when 23 of it has decayed and time t1 and 31 of it had decayed is : (1) 14 min (2) 20 min (3) 28 min (4) 7 min

Q30.A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : 0 mm Circular scale reading : 52 divisions Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above date is : (1) 0.052 cm (2) 0.026 cm (3) 0.005 cm (4) 0.52 cm

Q1. The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 × 10−3 are (1) 5, 1, 2 (2) 5, 1, 5 (3) 5, 5, 2 (4) 4, 4, 2

Q2. A particle is moving with velocity →v = K(y^i + x^j), where K is a constant. The general equation for its path is (1) y = x2+ constant (2) y2 = x+ constant (3) xy = constant (4) y2 = x2+ constant

Q3. A small particle of mass m is projected at an angle θ with the x-axis with an initial velocity v0 in the x −y plane as shown in the figure. At a time t < v0 sing θ , the angular momentum of the particle is where ^i,^j and ^k are unit vectors along x, y and z-axis respectively. (1) −mgv0 t2 cos θ^j (2) mgv0 t cos θ^k (3) −12 mgv0t2 cos θ^k (4) 21 mgv0t2 cos θ^i

Q4. Two fixed frictionless inclined plane making an angle 30∘ and 60∘ with the vertical are shown in the figure. Two block A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B ? (1) 4.9 ms−2 in horizontal direction (2) 9.8 ms−2 in vertical direction (3) zero (4) 4.9 ms−2 in vertical direction

Q5. The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x) = a − b , where a and b are constants and x is the distance between the atoms. If the dissociation x12 x6 energy of the molecule is D = [U(x = ∞) −Uat equilbrium ], D is (1) b2 (2) b2 2a 12a (3) b2 (4) b2 4a 6a

Q8. A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of ' P ' is such that it sweeps out a length s = t3 + 5 , where s is in metres and t is in seconds. The radius of the path is 20 m. The acceleration of ' P ' when t = 2 s is nearly (1) 13 m/s2 (2) 12 m/s2 (3) 7.2 m/s2 (4) 14 m/s2

Q9. For a particle in uniform circular motion the acceleration →a at a point P(R, θ) on the circle of radius R is (here θ is measured from the x-axis) (1) −v2R cos θ^i + v2R sin θ^j (2) −v2R sin θ^i + v2R cos θ^j (3) −v2R cos θ^i −v2R sin θ^j (4) v2R ^i + v2R ^j

Q10.A ball is made of a material of density ρ where ρoil < ρ < ρwater with ρoil and ρwater representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position? JEE Main 2010 JEE Main Previous Year Paper (1) (2) (3) (4)

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

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