Practice Questions

Q1. The amount of heat produced in an electric circuit depends upon the current (I), resistance (R) and time (t). If the error made in the measurements of the above quantities are 2%, 1% and 1% respectively then the maximum possible error in the total heat produced will be (1) 1% (2) 2% (3) 6% (4) 3%

Q1. The electrical resistance R of a conductor of length l and area of cross section a is given by R = ρla where ' ρ ' is the electrical resistivity. What is the dimensional formula for electrical conductivity ' σ ' which is reciprocal of resistivity? (1) [M −1L−3T 3A2] (2) [ML−3T −3A2] (3) [ML3T −3A−2] (4) [M −2L3T 2A−1]

Q2. The graph of an object's motion (along the x− axis) is shown in the figure. The instantaneous velocity of the object at points A and B are vA and vB respectively. Then (1) vA = vB = 0.5 m/s (2) vA = 0.5 m/s < vB (3) vA = 0.5 m/s > vB (4) vA = vB = 2 m/s

Q5. Two point masses of mass m1 = fM and m2 = (1 −f)M(f < 1) are in outer space (far from gravitational influence of other objects) at a distance R from each other. They move in circular orbits about their centre of mass with angular velocities ω1 for m1 and ω2 for m2 . In that case (1) (1 −f)ω1 = fω (2) ω1 = ω2 and independent of f (3) fω1 = (1 −f)ω2 (4) ω1 = ω2 and depend on f

Q5. A particle gets displaced by Δ¯r = (2^i + 3^j + 4^k)m under the action of a force →F = (7^i + 4^j + 3^k). The change in its kinetic energy is (1) 38 J (2) 70 J (3) 52.5 J (4) 126 J

Q5. Two cars of masses m1 and m2 are moving in circles of radii r1 and r2 , respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is (1) m1r1 : m2r2 (2) m1 : m2 (3) r1 : r2 (4) 1 : 1

Q7. A steel wire can sustain 100 kg weight without breaking. If the wire is cut into two equal parts, each part can sustain a weight of (1) 50 kg (2) 400 kg (3) 100 kg (4) 200 kg

Q7. A thin liquid film formed between a U-shaped wire and a light slider supports a weight of 1.5 × 10−2 N (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is (1) 0.0125 Nm−1 (2) 0.1 Nm−1 (3) 0.05 Nm−1 (4) 0.025 Nm−1

Q8. Which graph correctly presents the variation of acceleration due to gravity with the distance from the centre of the earth (radius of the earth = RE )? (1) (2) (3) (4)

Q9. The terminal velocity of a small sphere of radius a in a viscous liquid is proportional to JEE Main 2012 (26 May Online) JEE Main Previous Year Paper (1) a2 (2) a3 (3) a (4) a−1

Q9. Assuming the earth to be a sphere of uniform density, the acceleration due to gravity inside the earth at a distance of r from the centre is proportional to (1) r (2) r−1 (3) r2 (4) r−2

Q11.The pressure of an ideal gas varies with volume as P = αV , where α is a constant. One mole of the gas is allowed to undergo expansion such that its volume becomes ' m ' times its initial volume. The work done by the gas in the process is (1) αV 2 (m2 −1) (2) α2V2 2 (m2 −1) (3) α 2 (m2 −1) (4) αV2 2 (m2 −1)

Q11.A given ideal gas with γ = Cp = 1.5 at a temperature T . If the gas is compressed adiabatically to one-fourth Cv of its initial volume, the final temperature will be (1) 2√2T (2) 4T (3) 2T (4) 8T

Q13.A perfect gas at 27∘C is heated at constant pressure so as to double its volume. The final temperature of the gas will be, close to (1) 327∘C (2) 200∘C (3) 54∘C (4) 300∘C

Q15.Three positive charges of equal value q are placed at vertices of an equilateral triangle. The resulting lines of force should be sketched as in (1) (2) (3) (4)

Q17.It is preferable to measure the e.m.f. of a cell by potentiometer than by a voltmeter because of the following possible reasons. (i) In case of potentiometer, no current flows through the cell. (ii) The length of the potentiometer allows greater precision. (iii) Measurement by the potentiometer is quicker. (iv) The sensitivity of the galvanometer, when using a potentiometer is not relevant. Which of these reasons are correct? (1) (i),(iii),(iv) (2) (i),(iii),(iv) (3) (i),(ii) (4) (i),(ii),(iii),(iv)

Q17.A 6.0 volt battery is connected to two light bulbs as shown in figure. Light bulb 1 has resistance 3 ohm while light bulb 2 has resistance 6ohm. Battery has negligible internal resistance. Which bulb will glow brighter? (1) Bulb 1 will glow more first and then its (2) Bulb 1 brightness will become less than bulb 2 (3) Bulb 2 (4) Both glow equally

Q18.A generator has armature resistance of 0.1Ω and develops an induced emf of 120 V when driven at its rated speed. Its terminal voltage when a current of 50 A is being drawn is (1) 120 V (2) 5 V (3) 115 V (4) 70 V

Q18.In a sensitive meter bridge apparatus the bridge wire should possess (1) high resistivity and low temperature coefficient. (2) low resistivity and high temperature coefficient. (3) low resistivity and low temperature coefficient. (4) high resistivity and high temperature coefficient.

Q20.A bar magnet of length 6 cm has a magnetic moment of 4 J T−1 . Find the strength of magnetic field at a distance of 200 cm from the centre of the magnet along its equatorial line. (1) 4 × 10−8 tesla (2) 3.5 × 10−8 tesla (3) 5 × 10−8 tesla (4) 3 × 10−8 tesla

Q21.The velocity of certain ions that pass undeflected through crossed electric field E = 7.7kV/m and magnetic field B = 0.14 T is (1) 18 km/s (2) 77 km/s (3) 55 km/s (4) 1078 km/s

Q21.An electromagnetic wave in vacuum has the electric and magnetic fields →E and →B, which are always → perpendicular to each other. The direction of polarization is given by →X and that of wave propagation by k. Then : (1) →X∥→B and →k∥→B × →E (2) →X∥→E and →k∥→E × →B (3) →X∥→B and →k∥→E × →B (4) →X∥→E and →k∥→B × →E

Q22.A radio transmitter transmits at 830kHz. At a certain distance from the transmitter magnetic field has amplitude 4.82 × 10−11 T. The electric field and the wavelength are respectively (1) 0.014 N/C, 36 m (2) 0.14 N/C, 36 m (3) 0.14 N/C, 360 m (4) 0.014 N/C, 360 m

Q23.Which of the following processes play a part in the formation of a rainbow? (i) Refraction (ii) Total internal reflection (iii) Dispersion (iv) Interference (1) (i), (ii) and (iii) (2) (i) and (ii) (3) (i), (ii) and (iv) (4) (iii) and (iv)

Q23.The frequency of X -rays; γ -rays and ultraviolet rays are respectively a, b and c then (1) a < b; b > c (2) a > b; b > c (3) a < b < c (4) a = b = c