Practice Questions

Q14.Two sitar strings, A and B playing the note ' Dha' are slightly out of tune and produce beats of frequency 5 Hz . The tension of the string B is slightly increased and the beat frequency is found to decrease by 3 Hz. If the frequency of A is 425 Hz. The original frequency of B is (1) 428 Hz (2) 430 Hz (3) 422 Hz (4) 420 Hz

Q14.A charge Q is placed at a distance a/2 above the centre of a square surface of side length a. The electric flux through the square surface due to the charge would be? (1) Q (2) Q 6ϵ0 2ϵ0 (3) Q (4) Q 3ϵ0 ϵ0 JEE Main 2018 (15 Apr) JEE Main Previous Year Paper

Q14.A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 × 103 kg m−3 and its Young's modulus is 9.27 × 1010 Pa. What will be the fundamental frequency of the longitudinal vibrations? (1) 7. 5 kHz (2) 5 kHz (3) 2. 5 kHz (4) 10 kHz

Q15.Two identical conducting spheres A and B carry an equal charges. They are separated by a distance much larger than their diameters, and the force between them is F . A third identical conducting sphere, C , is uncharged. Sphere C is first touched to A , then to B, and then removed. As a result, the force between A and B would be equal to: (1) 3F (2) F 4 2 (3) 3F (4) F 8

Q15.The equivalent capacitance between A and B in the circuit is given below. (1) 3. 6 μF (2) 2. 4 μF (3) 4. 9 μF (4) 5. 4 μF

Q15.Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities +σ, −σ and +σ respectively. The potential of shell B is: (1) + + ε0 σ [ b2−c2c a] (2) ε0σ [ a2−b2a c] (3) + + ε0 σ [ a2−b2b c] (4) ε0σ [ b2−c2b a]

Q15.The equivalent capacitance between A and B in the circuit given below is: (1) 4.9μF (2) 3.6μF (3) 5.4μF (4) 2.4μF

Q16.In a meter bridge as shown in the figure, it is given that resistance Y = 12.5 Ω and that the balance is obtained at a distance 39. 5 cm from end A (by jockey J ). After interchanging the resistances X and Y a new balance point is found at a distance l2 from end A. What are the values of X (in Ω) and l2 ? (1) 19. 15 Ω and 39. 5 cm (2) 8. 16 Ω and 60. 5 cm (3) 8. 16 Ω and 39. 5 cm (4) 19. 15 Ω and 60. 5 cm

Q16.A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge density of the rod is ρ, how long will the charges take to travel a distance d ? (1) 2ρdA (2) 2ρdA IT I (3) ρdA (4) ρdA I IT

Q16.In the given circuit all resistances are of value R ohm each. The equivalent resistance between A and B is: (1) 2R (2) 5R2 (3) 5R (4) 3R 3 JEE Main 2018 (15 Apr Shift 1 Online) JEE Main Previous Year Paper

Q16.In the following circuit the switch S is closed at t = 0. The charge on the capacitor C1 as a function of time will be given by (Ceq = C1+C1C2C2 ) (1) C1E [1 −exp(−tRC1 )] (2) CeqE exp[− RCeqt ] (3) CeqE [1 −exp(− RCeqt )] (4) C2E [1 −exp(− RC2t )]

Q16.A parallel plate capacitor of capacitance 90 pF is connected to a battery of EMF 20 V. If a dielectric material of dielectric constant K = 53 is inserted between the plates, the magnitude of the induced charge will be: (1) 0. 9 nC (2) 1. 2 nC (3) 0. 3 nC (4) 2. 4 nC

Q17.Two batteries with e.m.f. 12 V and 13 V are connected in parallel across a load resistor of 10 Ω. The internal resistance of the two batteries are 1 Ω and 2 Ω respectively. The voltage across the load lies between, (1) 11. 7 V and 11. 8 V (2) 11. 6 V and 11. 7 V (3) 11. 5 V and 11. 6 V (4) 11. 4 V and 11. 5 V

Q17.A heating element has a resistance of 100 Ω at room temperature. When it is connected to a supply of 220 V, a steady current of 2 A passes in it and temperature is 500 oC more than the room temperature. The temperature coefficient of resistance of the heating element is (1) 5 × 10−4 oC−1 (2) 2 × 10−4 oC−1 (3) 1 × 10−4 oC−1 (4) 0.5 × 10−4 oC−1

Q17.In the given circuit all resistance is of the value of R ohm each. The equivalent resistance between A and B is: (1) 5R (2) 3R 2 (3) 5R (4) 2R 3

Q17.In a meter bridge, as shown in the figure, it is given that resistance Y = 12.5Ω and that the balance is obtained at a distance 39.5 cm from end A (by jockey J). After interchanging the resistances X and Y , a new balance point is found at a distance l2 from end A . What are the values of X and l2 ? (1) 19.15Ω and 39.5 cm (2) 8.16Ω and 60.5 cm (3) 19.15Ω and 60.5 cm (4) 8.16Ω and 39.5 cm

Q17.A parallel plate capacitor with area 200 cm2 and separation between the plates 1.5 cm, is connected across a battery of emf V. If the force of attraction between the plates is 25 × 10−6 N , the value of V is approximately: C2 2 = 8.85 × 10−12 (ε0 N.m ) ) (1) 150 V (2) 100 V (3) 250 V (4) 300 V

Q18.The B-H curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solenoid with 1000 turns/cm.. The current that should be passed in the solenoid to demagnetize the ferromagnet completely is: (1) 2 mA (2) 1 mA (3) 40μA (4) 20μA

Q18.On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 kΩ . How much was the resistance on the left slot before interchanging the resistances? (1) 910 Ω (2) 990 Ω (3) 505 Ω (4) 550 Ω JEE Main 2018 (08 Apr) JEE Main Previous Year Paper

Q18.A capacitor C1 is charged up to a voltage V = 60 V by connecting it to battery B through switch (1), Now C1 is disconnected from battery and connected to a circuit consisting of two uncharged capacitors C2 = 3.0μF JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper and C3 = 6.0μF through a switch (2) as shown in the figure. The sum of final charges on C2 and C3 is: (1) 36μC (2) 20μC (3) 54μC (4) 40μC

Q18.A galvanometer with its coil resistance 25 Ω requires a current of 1 mA for its full deflection. In order to construct an ammeter to read up to a current of 2 A the approximate value of the shunt resistance should be: (1) 1.25 × 10−2 Ω (2) 2.5 × 10−3 Ω (3) 2.5 × 10−2 Ω (4) 1.25 × 10−3 Ω

Q19.In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by a resistance of 5 Ω ,a balance is found when the cell is connected across 40 cm of the wire. Find the internal resistance of the cell. (1) 2.5 Ω (2) 1 Ω (3) 1.5 Ω (4) 2 Ω

Q19.A Helmholtz coil has pair of loops, each with N turns and radius R. They are placed coaxially at distance R and the same current I flows through the loops in the same direction. The magnitude of magnetic field at P , midway between the centres A and C , is given by (Refer to figure): (1) 4Nμ0I (2) 8Nμ0I 53/2R 53/2R (3) 4Nμ0I (4) 8Nμ0I 51/2R 51/2R

Q19.A constant voltage is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be: (1) Increased 8 times (2) Doubled (3) Halved (4) Unchanged

Q19.A Helmholtz coil has a pair of loops, each with N turns and radius R. They are placed coaxially at distance R and the same current I flows through the loops in the same direction. The magnitude of the magnetic field at P, midway between the centres A and C, is given by [Refer to figure given below]: (1) 8Nμ0I (2) 4Nμ0I 51/2R 53/2R (3) 4Nμ0I (4) 8Nμ0I 51/2R 53/2R