Practice Questions

Q9. A charge q is placed at one corner of a cube as shown in figure. The flux of electrostatic field E through the shaded area is: (1) q (2) q 8ε0 24ε0 (3) q (4) q 48ε0 4ε0

Q9. A refrigerator consumes an average 35 W power to operate between temperature −10°C to 25°C. If there is no loss of energy then how much average heat per second does it transfer? (1) 350 J s−1 (2) 298 J s−1 (3) 263 J s−1 (4) 35 J s−1

Q9. Consider a mixture of gas molecule of types A, B and C having masses mA < mB < mC. The ratio of their root mean square speeds at normal temperature and pressure is: (1) vA = vB = vC = 0 (2) 1 > 1 > 1 vA vB vC (3) vA = vB ≠vC (4) 1 < 1 < 1 vA vB vC

Q9. For an ideal gas the instantaneous change in pressure P with volume V is given by the equation dP = −aP. If dV P = P0 at V = 0 is the given boundary condition, then the maximum temperature one mole of gas can attain is: (Here R is the gas constant) (1) aP0 (2) infinity eR (3) 0°C (4) aeRP0

Q9. Match List I with List II . List I List II (a) Isothermal (i) Pressure constant (b) Isochoric (ii) Temperature constant (c) Adiabatic (iii) Volume constant (d) Isobaric (iv) Heat content is constant Choose the correct answer from the options given below: (1) ( a ) →( ii ) , ( b ) →( iii ) , ( c ) →( iv ) , ( d ) →( i ) (2) ( a ) →( iii ) , ( b ) →( ii ) , ( c ) →( i ) , ( d ) →( iv ) (3) ( a ) →( i ) , ( b ) →( iii ) , ( c ) →( ii ) , ( d ) →( iv ) (4) ( a ) →( ii ) , ( b ) →( iv ) , ( c ) →( iii ) , ( d ) →( i ) Q10.𝑛 mole of a perfect gas undergoes a cyclic process 𝐴𝐵𝐶𝐴 (see figure) consisting of the following processes. 𝐴→𝐵: Isothermal expansion at temperature 𝑇 so that the volume is doubled from 𝑉1 to 𝑉2 = 2𝑉1 and pressure changes from 𝑃1 to 𝑃2 𝐵→𝐶: Isobaric compression at pressure 𝑃2 to initial volume 𝑉1 . 𝐶→𝐴: Isochoric change leading to change of pressure from 𝑃2 to 𝑃1 Total work done in the complete cycle 𝐴𝐵𝐶𝐴 is: JEE Main 2021 (24 Feb Shift 1) JEE Main Previous Year Paper 1 (1) 𝑛𝑅𝑇ln2 - (2) 𝑛𝑅𝑇ln2 2 (3) 𝑛𝑅𝑇ln2 + 1 (4) 0 2

Q9. A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J , the rise in heat energy per unit volume will be: (1) 2TrJ (2) 3TrJ (3) 2TJ ( 1r −1R ) (4) 3TJ ( 1r −1R )

Q9. A mixture of hydrogen and oxygen has volume 500 cm3, temperature 300 K, pressure 400 𝑘Pa and mass 0 . 76 g . The ratio of masses of oxygen to hydrogen will be: (1) 16 : 3 (2) 3 : 8 (3) 8 : 3 (4) 3 : 16

Q9. A block of mass 1 kg attached to a spring is made to oscillate with an initial amplitude of 12 cm . After 2 minutes the amplitude decreases to 6 cm . Determine the value of the damping constant for this motion. (take ln 2 = 0. 693 ) (1) 1. 16 × 10−2 kg s−1 (2) 3. 3 × 102 kg s−1 (3) 1. 16 × 102 kg s−1 (4) 5. 7 × 10−3 kg s−1

Q9. Find out the surface charge density at the intersection of point x = 3 m plane and x-axis, in the region of uniform line charge of 8 nC m−1 lying along the z-axis in free space. (1) 0. 424 nC m−2 (2) 47. 88 nC m−2 (3) 0. 07 nC m−2 (4) 4. 0 nC m−2

Q9. If the R.M.S. speed of oxygen molecules at 0°C is 160 m s−1 . Find the R.M.S. speed of hydrogen molecules at 0°C . (1) 40 m s−1 (2) 80 m s−1 (3) 640 m s−1 (4) 332 m s−1

Q9. Four identical long solenoids A, B, C and D are connected to each other as shown in the figure. If the magnetic field at the center of A is 3 T the field at the center of C would be : (Assume that the magnetic field is confined with in the volume of respective solenoid). (1) 12 T (2) 6 T (3) 9 T (4) 1 T

Q9. The internal energy (U), pressure (P) and volume (V ) of an ideal gas are related as U = 3PV + 4. The gas is (1) either monoatomic or diatomic (2) polyatomic only (3) monoatomic only (4) diatomic only

Q9. For a gas 𝐶P - 𝐶V = 𝑅 in a state 𝑃 and 𝐶P - 𝐶V = 1 . 10𝑅 in a state 𝑄, 𝑇P and 𝑇Q are the temperatures in two different states 𝑃 and 𝑄, respectively. Then (1) 𝑇P = 𝑇Q (2) 𝑇P < 𝑇Q (3) 𝑇P = 0 . 9𝑇Q (4) 𝑇P > 𝑇Q

Q9. Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g , the time period of pendulum will be : 2 (1) √3T (2) T √3 (3) (4) T T √32 √23

Q9. The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy 2 × 10−9 J per molecule is: (1) 0. 75 × 1011 (2) 3 × 1011 (3) 1. 5 × 1011 (4) 6 × 1011

Q9. The material filled between the plates of a parallel plate capacitor has resistivity 200 Ω m . The value of capacitance of the capacitor is 2 pF. If a potential difference of 40 V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is: (given the value of relative permittivity of material is 50 ) (1) 0.9 mA (2) 9.0 mA (3) 9.0 μA (4) 0.9 μA

Q9. If the time period of a two meter long simple pendulum is 2 s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is: (1) 2π2 m s−2 (2) 16 m s−2 (3) π2 m s−2 (4) 9. 8 m s−2

Q9. A polyatomic ideal gas has 24 vibrational modes. What is the value of γ? (1) 1. 03 (2) 1. 30 (3) 1. 37 (4) 10. 3

Q9. Due to cold weather, a 1 m water pipe of cross-sectional area 1 cm2 is filled with ice at -10 °C . Resistive heating is used to melt the ice. Current of 0 . 5 A is passed through 4 kΩ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required? (Given latent heat of fusion for water/ice = 3 . 33 × 105 J kg-1, specific heat of ice = 2 × 103 J kg-1 °C-1 and density of ice = 103 kg m-3 ) (1) 3 . 53 s (2) 0 . 353 s (3) 35 . 3 s (4) 70 . 6 s

Q9. An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is S1 and that of the other part is S2 . Given that S1 > S2 . If the piston is removed then the total entropy of the system will be: (1) S1 × S2 (2) S1 −S2 (3) S1 (4) S1 + S2 S2

Q9. Two spherical soap bubbles of radii r1 and r2 in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to: (1) r1r2 (2) √r1r2 r1+r2 + r22 2 (3) √r21 (4) r1+r2

Q9. Which of the following equations represents a travelling wave? (1) y = A sin(15x −2t) (2) y =Aex cos(ωt −θ) (3) y = Ae−x2(vt + θ) (4) y = A sin x cos ωt

Q9. An electric dipole is placed on x−axis in proximity to a line charge of linear charge density 3. 0 × 10−6 C m−1. Line charge is placed on z− axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm from the origin respectively. If total force of 4 N is exerted on the dipole, find out the amount of positive or negative charge of the dipole. (1) 815. 1 nC (2) 8. 8 μC (3) 0. 485 mC (4) 4. 44 μC

Q9. The length of a metal wire is ℓ1, when the tension in it is T1 and is ℓ2 when the tension is T2. The natural length of the wire is: JEE Main 2021 (20 Jul Shift 2) JEE Main Previous Year Paper (1) √ℓ1ℓ2 (2) ℓ1 TT2−ℓ22−T1T 1 (3) ℓ1 T 2+ℓ2 T 1 (4) ℓ1+ℓ2 T 2+T1 2

Q10.In a ferromagnetic material, below the curie temperature, a domain is defined as: (1) a macroscopic region with saturation magnetization. (2) a macroscopic region with consecutive magnetic dipoles oriented in opposite direction. (3) a macroscopic region with zero magnetization. (4) a macroscopic region with randomly oriented magnetic dipoles. JEE Main 2021 (25 Feb Shift 2) JEE Main Previous Year Paper