Practice Questions

Q9. Which statements are correct about degrees of freedom? A. A molecule with n degrees of freedom has n2 different ways of storing energy. B. Each degree of freedom is associated with 1 RT average energy per mole. 2 C. A monoatomic gas molecule has 1 rotational degree of freedom where as diatomic molecule has 2 rotational degrees of freedom D. CH4 has a total to 6 degrees of freedom. Choose the correct answer from the option given below: (1) B and C only (2) B and D only (3) A and B only (4) C and D only

Q9. The root mean square speed of smoke particles of mass 5 × 10-17 kg in their Brownian motion in air at NTP is approximately. [Given 𝑘= 1 . 38 × 10-23J K-1] (1) 60 mm s-1 (2) 12 mm s-1 (3) 15 mm s-1 (4) 36 mm s-1

Q9. A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC . The internal energy of the gas at A is 1560 J. The work done by the gas during the part CA is (1) 20 J (2) 30 J (3) −30 J (4) −60 J

Q9. Two cells of the same EMF 𝐸 but different internal resistances 𝑟1 and 𝑟2 are connected in series with an external resistance 𝑅 as shown in the figure. The terminal potential difference across, the second cell is found to be zero. The external resistance 𝑅 must then be: (1) 𝑟1𝑟2 (2) 𝑟1 - 𝑟2 (3) 𝑟2 - 𝑟1 (4) 𝑟1 + 𝑟2

Q9. Time period of a simple pendulum in a stationary lift is T . If the lift accelerates with g vertically upwards then 6 the time period will be (Where g = acceleration due to gravity) (1) (2) T T √65 √56 (3) (4) T T √67 √76

Q9. In figure (A), mass 2𝑚 is fixed on mass 𝑚 which is attached to two springs of spring constant 𝑘. In figure (B), mass 𝑚 is attached to two spring of spring constant 𝑘 and 2𝑘. If mass 𝑚 in (A) and (B) are displaced by distance 𝑥 horizontally and then released, then time period 𝑇1 and 𝑇2 corresponding to (A) and (B) respectively follow the relation. 𝑇1 3 𝑇1 3 (1) (2) = √2 𝑇2 = √ 2 𝑇2 2 √2 (3) 𝑇1 (4) 𝑇1 = = √ 3 3 𝑇2 𝑇2

Q9. A uniform electric field E = ( 8me )V m−1 is created between two parallel plates of length 1 m as shown in figure, (where m = mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of 2 m s−1 . The angle of the deviation (θ) of the path of the electron as it comes out of the field will be _____ . (1) tan−1(4) (2) tan−1(2) (3) tan−1( 13 ) (4) tan−1(3)

Q9. Two metallic wires of identical dimensions are connected is series. If σ1 and σ2 are the conductivities of the these wires respectively, the effective conductivity of the combination is : (1) σ1σ2 (2) 2σ1σ2 σ1+σ2 σ1+σ2 (3) σ1+σ2 (4) σ1+σ2 2σ1σ2 σ1σ2

Q9. A vessel contains 16 g of hydrogen and 128 g of oxygen at standard temperature and pressure. The volume of the vessel in cm3 is : (1) 72 × 105 (2) 32 × 105 (3) 27 × 104 (4) 54 × 104

Q10.Two capacitors having capacitance C1 and C2 respectively are connected as shown in figure. Initially, capacitor C1 is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor C1 is now connected to uncharged capacitor C2 by closing the switch S . The amount of charge on the capacitor C2 , after equilibrium, is JEE Main 2022 (26 Jun Shift 1) JEE Main Previous Year Paper (1) C1C2 V (2) (C1+C2) V (C1+C2) C1C2 (3) (C1 + C2)V (4) (C1 −C2)V

Q10.Statement-I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive. Statement-II : An electric dipole is placed in a uniform electric field. The net electric force on the dipole will not be zero. (1) Both statement-I and statement-II are true. (2) Both statement-I and statement-II are false. (3) Statement-I is true but statement-II is false. (4) Statement-I is false but statement-II is true.

Q10.The equations of two waves are given by : y1 = 5 sin 2π(x −vt) cm y2 = 3 sin 2π(x −vt + 1. 5) cm These waves are simultaneously passing through a string. The amplitude of the resulting wave is : (1) 2 cm (2) 4 cm (3) 5. 8 cm (4) 8 cm

Q10.A cylinder of fixed capacity of 44. 8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20. 0°C will be (Given gas constant R = 8. 3 J K−1 mol−1 ) (1) 249 J (2) 415 J (3) 498 J (4) 830 J

Q10.A slab of dielectric constant K has the same crosssectional area as the plates of a parallel plate capacitor and thickness 3 d, where d is the separation of the plates. The capacitance of the capacitor when the slab is inserted 4 JEE Main 2022 (28 Jul Shift 2) JEE Main Previous Year Paper between the plates will be : (Given C0 = capacitance of capacitor with air as medium between plates.) (1) 4KC0 (2) 3KC0 3+K 3+K (3) 3+K (4) K 4KC0 4+K

Q10.The charge on capacitor of capacitance 15μF in the figure given below is (1) 60 μC (2) 130 μC (3) 260 μC (4) 585 μC

Q10.What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen? (1) The velocity of atomic oxygen remains same (2) The velocity of atomic oxygen doubles (3) The velocity of atomic oxygen becomes half (4) The velocity of atomic oxygen becomes four times

Q10.Two uniformly charged spherical conductors 𝐴 and 𝐵 of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere 𝐴 and 𝐵 will be (1) 1: 2 (2) 2: 1 (3) 1: 1 (4) 1: 4

Q10.The total charge on the system of capacitance C1 = 1μF, C2 = 2μF, C3 = 4μF and C4 = 3μF connected in parallel is (Assume a battery of 20 V is connected to the combination) (1) 200μC (2) 200C (3) 10μC (4) 10C

Q10.According to kinetic theory of gases, A. The motion of the gas molecules freezes at 0°C. B. The mean free path of gas molecules decreases if the density of molecules is increased. C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant. D. Average kinetic energy per molecule per degree of freedom is 3 2 kBT (for monoatomic gases). Choose the most appropriate answer from the options given below (1) A and C only (2) B and C only (3) A and B only (4) C and D only

Q10.If 𝑛 represents the actual number of deflections in a converted galvanometer of resistance 𝐺 and shunt resistance 𝑆. Then the total current 𝐼 when its figure of merit is 𝐾 will be (1) 𝐾𝑆 (2) 𝐺+ 𝑆 𝑆+ 𝐺 𝑛𝐾𝑆 𝑛𝐾𝑆 𝑛𝐾𝐺+ 𝑆 (3) (4) 𝐺+ 𝑆 𝑆

Q10.Two capacitors, each having capacitance 40𝜇F are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant 𝐾 such that the equivalence capacitance of the system became 24𝜇F. The value of 𝐾 will be : (1) 1 . 5 (2) 2 . 5 (3) 1 . 2 (4) 3

Q10.Two light beams of intensities in the ratio of 9 : 4 are allowed to interfere. The ratio of the intensity of maxima and minima will be : (1) 9 : 4 (2) 16 : 81 (3) 25 : 169 (4) 25 : 1

Q10.The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination α, is given by : (1) 2π√ (g cosL α) (2) 2π√ (g sinL α) (3) 2π√Lg (4) 2π√ (g tanL α)

Q10.The motion of a simple pendulum executing S.H.M. is represented by the following equation y = A sin(πt + ϕ), where time is measured in second. The length of pendulum is (1) 97. 23 cm (2) 25. 3 cm (3) 99. 4 cm (4) 406. 1 cm

Q11.An aluminium wire is stretched to make its length, 0. 4% larger. The percentage change in resistance is (1) 0. 4% (2) 0. 2% (3) 0. 8% (4) 0. 6%