Practice Questions

Q12.An ideal monatomic gas with pressure P , volume V and temperature T is expanded isothermally to a volume 2V and a final pressure Pi . If the same gas is expanded adiabatically to a volume 2 V, the final pressure is Pa . The ratio Pa is Pi (1) 2−1/3 (2) 21/36 (3) 22/3 (4) 2−2/3

Q13.A ring is suspended from a point S on its rim as shown in the figure. When displaced from equilibrium, it oscillates with time period of 1 second. The radius of the ring is (take g = π2 ) (1) 0.15 m (2) 1.5 m (3) 1.0 m (4) 0.5 m

Q13.A cylindrical tube, open at both ends, has a fundamental frequency, f , in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now (1) f (2) f 2 (3) 3f (4) 2f 4

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

Q13.An air column in a pipe, which is closed at one end, will be in resonance wtih a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is (velocity of sound = 330 m/s ) (1) 125.00 (2) 93.75 (3) 62.50 (4) 187.50

Q14.A wave represented by the equation y1 = a cos (kx −ωt) is superimposed with another wave to form a stationary wave such that the point x −0 is node. The equation for the other wave is (1) a cos(kx −ωt + π) (2) a cos(kx + ωt + π) (3) a cos (kx + ωt + π2 ) (4) a cos (kx −ωt + π2 )

Q14.A uniform tube of length 60.5 cm is held vertically with its lower end dipped in water. A sound source of frequency 500 Hz sends sound waves into the tube. When the length of tube above water is 16 cm and again when it is 50 cm, the tube resonates with the source of sound. Two lowest frequencies (in Hz ), to which tube will resonate when it is taken out of water, are (approximately). (1) 281,562 (2) 281,843 (3) 276,552 (4) 272,544

Q14.The disturbance y(x, t) of a wave propagating in the positive x-direction is given by y = 1+x21 at time t = 0 and by y = 1 at t = 2 s, where x and y are in meters. The shape of the wave disturbance does not [1+(x−12)] change during the propagation. The velocity of wave in m/s is (1) 2.0 (2) 4.0 (3) 0.5 (4) 1.0 JEE Main 2012 (26 May Online) JEE Main Previous Year Paper

Q15.Following are expressions for four plane simple harmonic waves (i) y1 = A cos 2π (n1t + λ1x ) (ii) The pairs of + + − y2 = A cos 2π (iii) y3 = A cos 2π (iv) y4 = A cos 2π λ1 λ2 λ2 (n1t x + π) (n2t x ) (n2t x ) waves which will produce destructive interference and stationary waves respectively in a medium, are (1) (iii, iv), (i, ii) (2) (i, iii), (ii, iv) (3) (i, iv), (ii, iii) (4) (i, ii), (iii, iv)

Q15.A charge of total amount Q is distributed over two concentric hollow spheres of radii r and R(R > r ) such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is (1) 1 (R−r)Q (2) 1 (R+r)Q 4πε0 (R2+r2) 4πε0 2(R2+r2) (3) 1 (R+r)Q (4) 1 (R−r)Q 4πε0 (R2+r2 ) 4πε0 2(R2+r2)

Q16.Three resistors of 4Ω, 6Ω and 12Ω are connected in parallel and the combination is connected in series with a 1.5 V battery of 1Ω internal resistance. The rate of Joule heating in the 4Ω resistor is (1) 0.55 W (2) 0.33 W (3) 0.25 W (4) 0.86 W

Q16.The flat base of a hemisphere of radius a with no charge inside it lies in a horizontal plane. A uniform electric π with the vertical direction. The electric flux through the curved surface of the field →E is applied at an angle 4 JEE Main 2012 (19 May Online) JEE Main Previous Year Paper hemisphere is (1) πa2E (2) πa2E √2 (3) πa2E (4) (π+2πϕ2E 2√2 (2√22)

Q17.The capacitor of an oscillatory circuit is enclosed in a container. When the container is evacuated, the resonance frequency of the circuit is 10kHz. When the container is filled with a gas, the resonance frequency changes by 50 Hz. The dielectric constant of the gas is (1) 1.001 (2) 2.001 (3) 1.01 (4) 3.01

Q17.Two electric bulbs marked 25 W −220 V and 100 W −220 V are connected in series to a 440 V supply. Which of the bulbs will fuse? (1) both (2) 100 W (3) 25 W (4) neither

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

Q17.The electric potential V (x) in a region around the origin is given by V (x) = 4x2 volts. The electric charge enclosed in a cube of 1 m side with its centre at the origin is (in coulomb) (1) 8ε0 (2) −4ε0 (3) 0 (4) −8ε0 JEE Main 2012 (07 May Online) JEE Main Previous Year Paper

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.The resistance of a wire is R. It is bent at the middle by 180∘ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is (1) 2R (2) R/2 (3) R/4 (4) R/8

Q18.Two circuits (a) and (b) have charged capacitors of capacitance C, 2C and 3C with open switches. Charges on each of the capacitor are as shown in the figures. On closing the switches Circuit (a) Circuit (b) (1) No charge flows in (a) but charge flows from R (2) Charges flow from L to R in both (a) and (b) to L in (b) (3) Charges flow from R to L in (a) and from L to R (4) No charge flows in (a) but charge flows from L in (b) to R in (b)

Q19.In an experiment of potentiometer for measuring the internal resistance of primary cell a balancing length ℓ is obtained on the potentiometer wire when the cell is open circuit. Now the cell is short circuited by a resistance R. If R is to be equal to the internal resistance of the cell the balancing length on the potentiometer wire will be (1) ℓ (2) 2ℓ (3) ℓ/2 (4) ℓ/4 JEE Main 2012 (26 May Online) JEE Main Previous Year Paper

Q19.The magnetic force acting on charged particle of charge 2μC in magnetic field of 2T acting in y− direction, when the particle velocity is (2^i + 3^j) × 106 ms−1 is (1) 8 N in z-direction (2) 8 N in y-direction (3) 4 N in y-direction (4) 4 N in z-direction

Q19.A proton and a deuteron are both accelerated through the same potential difference and enter in a magnetic field perpendicular to the direction of the field. If the deuteron follows a path of radius R, assuming the neutron and proton masses are nearly equal, the radius of the proton's path will be (1) √2R (2) R √2 (3) R (4) R 2

Q19.Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively rp, rd and rα . Which one of the following relations is correct? (1) rα = rp = rd (2) rα = rp < rd (3) rα > rd > rp (4) rα = rd > rp

Q20.Currents of a 10 ampere and 2 ampere are passed through two parallel thin wires A and B respectively in opposite directions. Wire A is infinitely long and the length of the wire B is 2 m. The force acting on the conductor B, which is situated at 10 cm distance from A will be (1) 8 × 10−5 N (2) 5 × 10−5 N (3) 8π × 10−7 N (4) 4π × 10−7 N

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