Practice Questions

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

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.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 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

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.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

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.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

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.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. An insulating solid sphere of radius R has a uniformly positive charge density ρ. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero. Statement 1: When a charge q is taken from the centre to the surface of the sphere, its potential energy changes by qp Statement 2 : The electric field at a distance r(r < R) from the centre of the sphere is 3ε0 ρr 3ε0 (1) Statement 1 is true, Statement 2 is true, (2) Statement 1 is true, Statement 2 is false Statement 2 is not the correct explanation for statement 1. (3) Statement 1 is false, Statement 2 is true (4) Statement 1 is true, Statement 2 is the correct explanation for statement 1 JEE Main 2012 (Offline) 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.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)

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.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.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.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.

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.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 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

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.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

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

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.