Practice Questions

Q12.When two sound waves travel in the same direction in a medium, the displacements of a particle located at ' x ' y1 = 0.05 cos(0.50πx −100πt) at time ' t ' is given by : where y1, y2 and x are in meters and t in seconds. The y2 = 0.05 cos(0.46πx −92πt) speed of sound in the medium is : (1) 92 m/s (2) 200 m/s (3) 100 m/s (4) 332 m/s

Q13.Bob of a simple pendulum of length l is made of iron. The pendulum is oscillating over a horizontal coil carrying direct current. If the time period of the pendulum is T then : JEE Main 2013 (23 Apr Online) JEE Main Previous Year Paper (1) and damping is smaller than in air alone. T < 2π√lg and damping is larger than in air alone. (2) T = 2π√lg and damping is smaller than in air alone. (3) T > 2π√lg (4) and damping is larger than in air alone. T < 2π√lg

Q13.The surface charge density of a thin charged disc of radius R is σ. The value of the electric field at the centre of the disc is σ . With respect to the field at the centre, the electric field along the axis at a distance R from 2∈0 the centre of the disc: (1) reduces by 70.7% (2) reduces by 29.3% (3) reduces by 9.7% (4) reduces by 14.6%

Q13.An engine approaches a hill with a constant speed. When it is at a distance of 0.9 km, it blows a whistle whose echo is heard by the driver after 5 seconds. If the speed of sound in air is 330 m/s , then the speed of the engine is : (1) 32 m/s (2) 27.5 m/s (3) 60 m/s (4) 30 m/s

Q13.A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is : (1) Q (2) Q ln 2 4π∈0L ln 2 4π∈0L (3) Q (4) 3Q 8π∈0L 4π∈0L

Q14.Two point dipoles of dipole moment →p1 and →p2 are at a distance x from each other and →p1||→p2 . The force between the dipoles is : (1) 1 4p1p2 (2) 1 3p1p2 4πε0 x4 4πε0 x3 (3) 1 6p1p2 (4) 1 8p1p2 4πε0 x4 4πε0 x4

Q14.The gravitational field in a region is given by: →E = (5N/kg)^i + (12N/kg)^j If the potential at the origin is taken to be zero, then the ratio of the potential at the points (12 m, 0) and (0, 5 m) is : (1) Zero (2) 1 (3) 144 (4) 25 25 144

Q14.A sonometer wire of length 114 cm is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio 1 : 3 : 4 ? (1) At 36 cm and 84 cm from one end (2) At 24 cm and 72 cm from one end (3) At 48 cm and 96 cm from one end (4) At 72 cm and 96 cm from one end

Q14.A point charge of magnitude +1μC is fixed at (0 , 0, 0). An isolated uncharged spherical conductor, is fixed with its center at (4, 0, 0). The potential and the induced electric field at the centre of the sphere is : (1) 1.8 × 105 V and −5.625 × 106 V/m (2) 0 V and 0 V/m (3) 2.25 × 105 V and −5.625 × 106 V/m (4) 2.25 × 105 V and 0 V/m

Q14.In an LCR circuit as shown below both switches are open initially. Now switch S1 is closed, S2 kept open. ( q is charge on the capacitor and τ = RC is capacitive time constant). Which of the following statement is correct? (1) At t = 2τ, q = CV (1 −e−2) (2) At t = τ2 , q = CV (1 −e−1) (3) Work done by the battery is half of the energy (4) At t = τ, q = CV/2 dissipated in the resistor

Q15.A parallel plate capacitor having a separation between the plates d, plate area A and material with dielectric constant K has capacitance C0 . Now one-third of the material is replaced by another material with dielectric constant 2 K, so that effectively there are two capacitors one with area 31 A , dielectric constant 2 K and another with area 2 3 A and dielectric constant K. If the capacitance of this new capacitor is C then C0C is (1) 1 (2) 34 (3) 2 (4) 1 3 3 JEE Main 2013 (25 Apr Online) JEE Main Previous Year Paper

Q15.Two capacitors C1 and C2 are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then: (1) 3C1 + 5C2 = 0 (2) 9C1 = 4C2 (3) 5C1 = 3C2 (4) 3C1 = 5C2 JEE Main 2013 (07 Apr) JEE Main Previous Year Paper

Q15.Two small equal point charges of magnitude q are suspended from a common point on the ceiling by insulating mass less strings of equal lengths. They come to equilibrium with each string making angle θ from the vertical. If the mass of each charge is m, then the electrostatic potential at the centre of line joining them will be 1 = ( 4π ∈0 k). (1) 2√kmg tan θ (2) √kmg tan θ (3) 4√kmg/ tan θ (4) 4√kmg/ tan θ

Q15.Two balls of same mass and carrying equal charge are hung from a fixed support of length l. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, x between the balls is proportional to : (1) l (2) l2 (3) l2/3 (4) l1/3

Q15.Consider a finite insulated, uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential : (1) less than the charged conductor and more than at infinity. (2) more than the charged conductor and less than at infinity. (3) more than the charged conductor and more than at infinity. (4) less than the charged conductor and less than at infinity.

Q16.In a metre bridge experiment null point is obtained at 40 cm from one end of the wire when resistance X is balanced against another resistance Y . If X < Y , then the new position of the null point from the same end, if one decides to balance a resistance of 3X against Y , will be close to : (1) 80 cm (2) 75 cm (3) 67 cm (4) 50 cm

Q16.To establish an instantaneous current of 2 A through a 1μF capacitor ; the potential difference across the capacitor plates should be changed at the rate of: (1) 2 × 104 V/s (2) 4 × 106 V/s (3) 2 × 106 V/s (4) 4 × 104 V/s

Q16.The supply voltage to a room is 120 V . The resistance of the lead wires is 6 Ω. A 60 W bulb is already switched on. What is the decrease of voltage across the bulb, when a 240 W heater is switched on in parallel to the bulb? (1) 13 .3 V (2) 10. 4 V (3) zero V (4) 2 .9 V

Q16.Six equal resistances are connected between points P, Q and R as shown in figure. Then net resistance will be maximum between : (1) P and R (2) P and Q (3) Q and R (4) Any two points

Q17.A parallel plate capacitor of area 60 cm2 and separation 3 mm is charged initially to 90μC. If the medium between the plate gets slightly conducting and the plate loses the charge initially at the rate of 2.5 × 10−8C/s, then what is the magnetic field between the plates ? (1) 2.5 × 10−8 T (2) 2.0 × 10−7 T (3) 1.63 × 10−11 T (4) Zero

Q17.A letter ′A′ is constructed of a uniform wire with resistance 1.0Ω per cm, The sides of the letter are 20 cm and the cross piece in the middle is 10 cm long. The apex angle is 60 . The resistance between the ends of the legs is close to: (1) 50.0Ω (2) 10Ω (3) 36.7Ω (4) 26.7Ω

Q17.A dc source of emf E1 = 100 V and internal resistance r = 0.5Ω, a storage battery of emf E2 = 90 V and an external resistance R are connected as shown in figure. For what value of R no current will pass through the JEE Main 2013 (22 Apr Online) JEE Main Previous Year Paper battery? (1) 5.5Ω (2) 3.5Ω (3) 4.5Ω (4) 2.5Ω

Q18.Which of the four resistances P, Q, R and S generate the greatest amount of heat when a current flows from A to B ? (1) Q (2) S (3) P (4) R

Q18.A shunt of resistance 1 Ω is connected across a galvanometer of 120 Ω resistance. A current of 5.5 ampere gives full scale deflection in the galvanometer. The current that will give full scale deflection in the absence of the shunt is nearly : (1) 5.5 ampere (2) 0.5 ampere (3) 0.004 ampere (4) 0.045 ampere

Q18.Two short bar magnets of length 1 cm each have magnetic moments 1 .20 A m2 and 1 .00 A m2 respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the south. They have a common magnetic equator and are separated by a distance of 20 .0 cm. The value of the resultant horizontal magnetic induction at the mid-point O of the line joining their centres is close to ( Horizontal component of earth's magnetic induction is 3 .6 ×10−5 Wb m−2 ) (1) 3 .50 ×10−4 Wb m−2 (2) 5 .80 ×10−4 Wb m−2 (3) 3 .6 ×10−5 Wb m−2 (4) 2 .56 ×10−4 Wb m−2