Practice Questions

Q10.A Carnot freezer takes heat from water at 0oC inside it and rejects it to the room at a temperature of 27oC. The latent heat of ice is 336 × 103 Jkg−1. If 5kg of water at 0oC is converted into ice at 0oC by the freezer, then the energy consumed by the freezer is close to : (1) 1 .51 ×105 J (2) 1 .68 ×106 J (3) 1 .71 ×107 J (4) 1 .67 ×105 J

Q10.The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is (1) 2 (2) 3 5 2 (3) 3 (4) 2 5 3 Q11. 200 g water is heated from 40 oC to 60 oC . Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water = 4184 J kg−1 K−1 ): (1) 167.4 kJ (2) 8.4 kJ (3) 4.2 kJ (4) 16.7 kJ

Q10.A particle performs simple harmonic motion with amplitude A. Its speed is tripled at the instant that it is at a distance 2A from equilibrium position. The new amplitude of the motion is: 3 (1) A√3 (2) 7A3 (3) A 3 √41 (4) 3A

Q11.A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now: (1) 2f (2) f (3) f (4) 3f 2 4

Q11.Which of the following shows the correct relationship between the pressure ′P′ and density ρ of an ideal gas at constant temperature ? (1) (2) (3) (4) JEE Main 2016 (10 Apr Online) JEE Main Previous Year Paper

Q12.A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is (Take, g = 10 m s−2 ) (1) 2√2 s (2) √2 s (3) 2π√2 s (4) 2 s

Q12.In an engine the piston undergoes vertical simple harmonic motion with amplitude 7cm. A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to : (1) 0.7 Hz (2) 1.9 Hz (3) 1.2 Hz (4) 0.1 Hz

Q12.Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and T , respectively. At time t = 0 one particle has displacement A while the other one has displacement −A2 and they are moving towards each other. If they cross each other at time t, then t is: (1) 5T (2) T 6 3 (3) T (4) T 4 6

Q13.The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density ρ = Ar , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, JEE Main 2016 (03 Apr) JEE Main Previous Year Paper is: (1) 2Q (2) 2Q π(a2−b2) πa2 (3) Q (4) Q 2πa2 2π(b2−a2)

Q13.Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. one of them is blowing a whistle of frequency 540 Hz. Calculate the frequency heard by driver of second engine before they pass each other. speed of sound is 330 m/sec: (1) 450 Hz (2) 540 Hz (3) 270 Hz (4) 648 Hz

Q13.A toy-car, blowing its horn, is moving with a steady speed of 5 m s−1 , away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beats per second. If the velocity of sound in air is 340 m s−1 the frequency of the horn of the toy car is close to (1) 680 Hz (2) 510 Hz (3) 340 Hz (4) 170 Hz

Q14.A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the 4 μF and 9 μF capacitors), at a point distant 30 m from it, would equal: (1) 420 N/C (2) 480 N/C (3) 240 N/C (4) 360 N/C

Q14.Within a spherical charge distribution of charge density ρ(r), N equipotential surfaces of potential V0, V0 + ΔV , V0 + 2 Δ V , … V0 + N Δ V (ΔV > 0), are drawn and have increasing radii r0, r1, r2, … rN, respectively. If the difference in the radii of the surfaces is constant for all values of V0 and Δ V then : (1) ρ(r) = constant (2) ρ (r) ∝ 1 r2 (3) ρ (r) ∝ 1r (4) ρ (r) ∝ r

Q14.The potential (in volts) of a charge distribution is given by V(z) = 30 −5z2 for |z| ≤1 m V(z) = 35 −10 |z| for |z| ≥1 m . V(z) does not depend on x and y. If this potential is generated by a constant charge per unit volume ρ0 (in units of ϵ0 ) which is spread over a certain region, then choose the correct statement. (1) ρ0 = 20 ϵ0 in the entire region (2) ρ0 = 10 ϵ0 for |z| ≤1 m and ρ0 = 0 else where (3) ρ0 = 20 ϵ0 for |z| ≤1 m and ρ0 = 0 else where (4) ρ0 = 40 ϵ0 in the entire region JEE Main 2016 (09 Apr Online) JEE Main Previous Year Paper

Q15.Three capacitors each of 4 μF are to be connected in such a way that the effective capacitance is 6 μF . This can be done by connecting them (1) all in series (2) all in parallel (3) two in parallel and one in series (4) two in series and one in parallel

Q15.Figure shows a network of capacitors where the number indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be 1 μF is : (1) 32 μF (2) 31 μF 23 23 (3) 33 μF (4) 34 μF 23 23

Q15.A galvanometer having a coil resistance of 100 Ω gives a full scale deflection, when a current of 1 mA is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of 10 A, is: (1) 0.1 Ω (2) 3 Ω (3) 0.01 Ω (4) 2 Ω JEE Main 2016 (03 Apr) JEE Main Previous Year Paper

Q16.Hysteresis loops for two magnetic materials A and B are given below: These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use: (1) A for transformers and B (2) B for electromagnets and transformers. for electric generators. (3) A for electric generators and transformers. (4) A for electromagnets and B for electric generators.

Q16. In the circuit shown, the resistance r is a variable resistance. If for r = fR , the heat generation in r is maximum then the value of f is (1) 1 (2) 1 2 (3) 1 (4) 3 4 4

Q16.A galvanometer has a 50 division scale. Battery has no internal resistance. It is found that there is deflection of 40 divisions when R.B. = 2400 Ω . Deflection becomes 20 divisions when resistance taken from resistance box is 4900 Ω. Then we can conclude : Note: This question is awarded as the bonus. Now the question is corrected. (1) Current sensitivity of galvanometer is (2) Resistance of galvanometer is 200 Ω. 20 μA/division (3) Resistance required on R.B. for a deflection of 10 (4) Full scale deflection current is 2 mA. divisions is 9800 Ω.

Q17.The resistance of an electrical toaster has a temperature dependence given by R(T) = R0[1 + α(T −T0)] in its range of operation. At T0 = 300 K, R = 100 Ω and at T = 500 K, R = 120 Ω . The toaster is connected JEE Main 2016 (10 Apr Online) JEE Main Previous Year Paper to a voltage source at 200 V and its temperature is raised at a constant rate from 300 to 500 K in 30 s. The total work done in raising the temperature is : Note: This question was awarded as the bonus since all options were incorrect in the exam. (1) 60000 ln( 65 ) J (2) 200 ln 32 J (3) 300 J (4) 400 ln( 1.31.5 ) J

Q17.To know the resistance G of a galvanometer by half deflection method, a battery of emf VE and resistance R is used to deflect the galvanometer by angle θ . If a shunt of resistance S is needed to get half deflection the G, R and S are related by the equation: (1) S(R + G) = RG (2) 2S(R + G) = RG (3) 2G = S (4) 2S = G

Q17.Two identical wires A and B, each of length l, carry the same current I . Wire A is bent into a circle of radius R and wire B is bent to form a square of side a . If BA and BB are the values of magnetic field at the centres of the circle and square respectively, then the ratio BA is BB (1) π2 (2) π2 16 8√2 (3) π2 (4) π2 8 16√2

Q18.An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to: (1) 0.044 H (2) 0.065 H (3) 80 H (4) 0.08 H

Q18.A 50 Ω resistance is connected to a battery of 5 V . A galvanometer of resistance 100 Ω is to be used as an ammeter to measure current through the resistance, for this a resistance rS is connected to the galvanometer. Which of the following connections should be employed if the measured current is with in 1% of the current without the ammeter in the circuit? (1) rS = 0.5Ω in series with galvanometer (2) rS = 1 Ω in series with galvanometer (3) rS = 1 Ω in parallel with galvanometer (4) rS = 0.5 Ω in parallel with the galvanometer