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. For a perfect gas, two pressures P1 and P2 are shown in figure. The graph shows (1) P1 > P2 (2) P1 < P2 (3) P1 = P2 (4) Insufficient data to draw any conclusion

Q9. When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be (1) Circular (2) Ellipitical (3) Sinusoidal (4) Straight line

Q9. A wire of length L is hanging from a fixed support. The length changes to L1 and L2 when masses 1 kg and 2 kg are suspended respectively from its free end. Then the value of L is equal to (1) √L1 L2 (2) L1+L22 (3) 2L1 −L2 (4) 3L1 −L2

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. A transverse wave is represented by 𝑦= 2sin𝜔𝑡- 𝑘𝑥cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be (1) 4𝜋 (2) 2𝜋 (3) 𝜋 (4) 2

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. In the wave equation 𝑦= 0 . 5sin 𝜆400𝑡- 𝑥𝑚 the velocity of the wave will be : (1) 200 m s-1 (2) 200√2 m s-1 (3) 400 m s-1 (4) 400√2 m s-1

Q9. Two massless springs with spring constants 2k and 9k, carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective JEE Main 2022 (24 Jun Shift 2) JEE Main Previous Year Paper amplitudes will be : (1) 3 : 2 (2) 1 : 2 (3) 3 : 1 (4) 2 : 3

Q9. Let η1 is the efficiency of an engine at T1 = 447°C and T2 = 147°C while η2 is the efficiency at T1 = 947°C and T2 = 47°C. The ratio η2η1 will be (1) 0. 41 (2) 0. 56 (3) 0. 73 (4) 0. 70

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. 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. Sixty four conducting drops each of radius 0. 02 m and each carrying a charge of 5 μC are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be (1) 1 : 4 (2) 4 : 1 (3) 1 : 8 (4) 8 : 1

Q9. A Carnot engine whose heat sinks at 27°C, has an efficiency of 25%. By how many degrees should the temperature of the source be changed to increase the efficiency by 100% of the original efficiency ? (1) Increases by 18°C (2) Increases by 200°C (3) Increases by 120°C (4) Increases by 73°C

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

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.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.A long straight wire with a circular cross-section having radius 𝑅, is carrying a steady current 𝐼. The current 𝐼 is uniformly distributed across this cross-section. Then the variation of magnetic field due to current 𝐼 with distance 𝑟𝑟< 𝑅 from its centre will be (1) 𝐵∝𝑟 (2) 𝐵∝1 𝑟 1 (3) 𝐵∝𝑟2 (4) 𝐵∝ 𝑟2

Q10.The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is (1) 12 s (2) 8 s (3) 36 s (4) 6 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.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.Two identical metallic spheres 𝐴 and 𝐵 when placed at certain distance in air repel each other with a force of 𝐹 . Another identical uncharged sphere 𝐶 is first placed in contact with 𝐴 and then in contact with 𝐵 and finally placed at midpoint between spheres 𝐴and 𝐵. The force experienced by sphere 𝐶 will be : 3𝐹 3𝐹 (1) (2) 2 4 (3) 𝐹 (4) 2𝐹

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

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 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