Practice Questions

Q10.In a cylindrical water tank, there are two small holes A and B on the wall at a depth of h1 , from the surface of water and at a height of h2 from the bottom of water tank. Surface of water is at height of h2 from the bottom of water tank. Surface of water is at heigh H from the bottom of water tank. Water coming out from both holes strikes the ground at the same point S . Find the ratio of h1 and h2 (1) Depends on H (2) 1 : 1 (3) 2 : 2 (4) 1 : 2

Q11.A square hole of side length ℓ is made at a depth of h and a circular hole of radius r is made at a depth of 4 h from the surface of water in a water tank kept on a horizontal surface. If ℓ<< h, r << h and the rate of water flow from the holes is the same, then r is equal to JEE Main 2012 (07 May Online) JEE Main Previous Year Paper (1) ℓ (2) ℓ √2π √3π (3) ℓ (4) ℓ 3π 2π

Q11.A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500 K It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be (1) efficiency of Carnot engine cannot be made (2) 1200 K larger than 50% (3) 750 K (4) 600 K

Q11.The door of a working refrigerator is left open in a well insulated room. The temperature of air in the room will (1) decrease (2) increase in winters and decrease in summers (3) remain the same (4) increase

Q12.The displacement y(t) = A sin(ωt + ϕ) of a pendulum for ϕ = 2π3 is correctly represented by JEE Main 2012 (19 May Online) JEE Main Previous Year Paper (1) (2) (3) (4)

Q12.If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between t = 0s to t = τs, then τ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with ' b' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds: (1) 0.693 (2) b b (3) 1 (4) 2 b b JEE Main 2012 (Offline) JEE Main Previous Year Paper

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

Q12.The heat radiated per unit area in 1 hour by a furnace whose temperature is 3000 K is (σ = 5.7× 10−8 W m−2 K−4 ) (1) 1.7 × 1010 J (2) 1.1 × 1012 J (3) 2.8 × 108 J (4) 4.6 × 106 J

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.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

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.This question has Statement 1 and Statement 2 . Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: Bats emitting ultrasonic waves can detect the location of a prey by hearing the waves reflected from it. Statement 2: When the source and the detector are moving, the frequency of reflected waves is changed. (1) Statement 1 is false, Statement 2 is true. (2) Statement 1 is true, Statement 2 is false. (3) Statement 1 is true, Statement 2 is true, (4) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 2 is the correct explanation of Statement 1. Statement 1. JEE Main 2012 (12 May Online) JEE Main Previous Year Paper

Q14.This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: In an adiabatic process, change in internal energy of a gas is equal to work done on/ by the gas in the process. Statement 2: The temperature of a gas remains constant in an adiabatic process. (1) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1. (2) Statement 1 is true, Statement 2 is false. (3) Statement 1 is false, Statement 2 is true. (4) Statement 1 is false, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

Q14.In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as a function of distance from the centre. The graph which would correspond to the above will be (1) (2) (3) (4)

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.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.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)

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 series combination of n1 capacitors, each of capacity C1 is charged by source of potential difference 4 V . When another parallel combination of n2 capacitors each of capacity C2 is charged by a source of potential difference V , it has the same total energy stored in it as the first combination has. The value of C2 in terms of C1 is then (1) 16 n2 C1 (2) 2C1 n1 n1n2 (3) 2 n1 n2 C1 (4) 16C1n1n2

Q16.This question has Statement 1 and Statement 2 . Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: It is not possible to make a sphere of capacity 1 farad using a conducting material. Statement 2: It is possible for earth as its radius is 6.4 × 106 m. (1) Statement 1 is true, Statement 2 is true, (2) Statement 1 is false, Statement 2 is true. Statement 2 is the correct explanation of Statement 1. (3) Statement 1 is true, Statement 2 is true, (4) Statement 1 is true, Statement 2 is false. Statement 2 is not the correct explanation of Statement 1.

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)

Q16.The figure shows an experimental plot for discharging of a capacitor in an R −C circuit. The time constant τ of this circuit lies between: (1) 150 sec and 200 sec (2) 0 and 50 sec (3) 50 sec and 100 sec (4) 100 sec and 150 sec

Q16.This question has Statement 1and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: In the resonance tube experiment, if the tuning fork is replaced by another identical turning fork but with its arm having been filled, the length of the air column should be increased to obtain resonance again. Statement 2: On filling the arms, the frequency of a tuning fork increases. (1) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1. (2) Statement 1 is true, Statement 2 is false. (3) Statement 1 is false, Statement 2 is true. (4) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.

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