Practice Questions

Q8. A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The amount of heat energy supplied to the engine from the source in each cycle is: (1) 3200 J (2) 1800 J (3) 1600 J (4) 2400 J

Q8. A glass tumbler having inner depth of 17 . 5 cm is kept on a table. A student starts pouring water 𝜇= 4 into it 3 while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled ? (1) 10 cm (2) 11 . 7 cm (3) 7 . 5 cm (4) 8 . 75 cm JEE Main 2021 (01 Sep Shift 2) JEE Main Previous Year Paper

Q8. In the experiment of Ohm's law, a potential difference of 5. 0 V is applied across the end of a conductor of length 10. 0 cm and diameter of 5. 00 mm. The measured current in the conductor is 2. 00 A. The maximum permissible percentage error in the resistivity of the conductor is :- (1) 3. 9 (2) 8. 4 (3) 7. 5 (4) 3. 0

Q8. A mass of 50 kg is placed at the center of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the center is V kg m−1 . The value of V is: (1) +2G (2) −20G (3) −4G (4) −60G

Q8. The entropy of any system is given by, + S = α2β ln[ μJβ2kR 3] where α and β are the constants. μ, J, k and R are number of moles, mechanical equivalent of heat, Boltzmann's constant and gas constant, respectively. [Take S = dQT ] Choose the incorrect option from the following: (1) α and J have the same dimensions. (2) S, β, k and μR have the same dimensions. (3) S and α have different dimensions. (4) α and k have the same dimensions.

Q8. If one mole of the polyatomic gas is having two vibrational modes and β is the ratio of molar specific heats for polyatomic gas (β = CPCv ) then the value of β is : (1) 1. 02 (2) 1. 2 (3) 1. 25 (4) 1. 35

Q8. In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process A →B and C →D are T1 and T2( T 1 > T2) respectively. JEE Main 2021 (27 Jul Shift 1) JEE Main Previous Year Paper Choose the correct option out of the following for work done if processes BC and DA are adiabatic. (1) WAB = WDC (2) WAD = WBC (3) WBC + WDA > 0 (4) WAB < WCD

Q8. A balloon carries a total load of 185 kg at normal pressure and temperature of 27°C. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is −7°C. Assuming the volume constant? (1) 214. 15 kg (2) 123. 54 kg (3) 219. 07 kg (4) 181. 46 kg JEE Main 2021 (27 Aug Shift 1) JEE Main Previous Year Paper

Q8. Consider a binary star system of star A and star B with masses mA and mB revolving in a circular orbit of radii rA and rB, respectively. If TA and TB are the time period of star A and star B, respectively, then: (1) TA rA 23 (2) TA = TB = TB ( rB ) (3) TA > TB (if mA > mB ) (4) TA > TB (if rA > rB )

Q8. Y = A sin(ωt + ϕ0) is the time-displacement equation of a SHM. At t = 0 the displacement of the particle is Y = A2 and it is moving along negative x-direction. Then the initial phase angle ϕ0 will be: (1) 2π (2) π 3 6 (3) 5π (4) π 6 3 →

Q8. The length of metallic wire is l1 when tension in it is T1 . It is l2 when the tension is T2 . The original length of the wire will be : (1) T2l1+T1l2 (2) l1+l2 T1+T2 2 (3) T2l1−T1l2 (4) T1l1−T2l2 T2−T1 T2−T1

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. 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. 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. 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. 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. 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. One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27°C to 37°C . If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? [R = 8. 314 J mol−1k−1] (1) work done by the gas is close to 332 J (2) work done on the gas is close to 582 J (3) work done by the gas is close to 582 J (4) work done on the gas is close to 332 J

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. 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 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. 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

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. 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. 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