Practice Questions

Q6. The P −V diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work done during an adiabatic process CD is (use γ = 1. 4) : JEE Main 2021 (18 Mar Shift 1) JEE Main Previous Year Paper (1) –500 J (2) –400 J (3) 400 J (4) 200 J

Q7. In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant k, the frequency of oscillation of given body is: (1) 1 2k (2) 1 k sin α 2π √ Mg sin α 2π √ Mg (3) 1 k (4) 1 2π √ 2M 2π √2kM

Q7. Calculate the value of the mean free path (λ) for oxygen molecules at temperature 27°C and pressure 1. 01 × 105 Pa . Assume the molecular diameter 0. 3 nm and the gas is ideal. (k = 1. 38 × 10−23 J K−1) (1) 58 nm (2) 32 nm (3) 86 nm (4) 102 nm

Q8. The amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500 g , Decay constant = 20 g s−1 then how much time is required for the amplitude of the system to drop to half of its initial value? (ln 2 = 0. 693) (1) 34. 65 s (2) 17. 32 s (3) 0. 034 s (4) 15. 1 s

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

Q10.Two electrons each are fixed at a distance 2d. A third charge proton placed at the midpoint is displaced slightly by a distance x(x ≪d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency: ( m = mass of charged particle) (1) πε0md3 12 (2) 2πε0md3 12 ( 2q2 ) ( q2 ) 2 (3) 1 1 ( 2πε0md3q2 ) 2 (4) ( πε0md32q2 )

Q11.In the given figure, there is a circuit of potentiometer of length 𝐴𝐵= 10 m. The resistance per unit length is 0 . 1 Ω per cm. Across 𝐴𝐵, a battery of emf 𝐸 and internal resistance 𝑟 is connected. The maximum value of emf measured by this potentiometer is: JEE Main 2021 (25 Jul Shift 1) JEE Main Previous Year Paper (1) 5 V (2) 2 . 25 V (3) 6 V (4) 2 . 75 V

Q12.The figure shows a circuit that contains four identical resistors with resistance R = 2. 0 Ω, two identical inductors with inductance L = 2. 0 mH and an ideal battery with E.M.F. E = 9 V. The current i just after the switch S is closed will be: JEE Main 2021 (24 Feb Shift 2) JEE Main Previous Year Paper (1) 9 A (2) 3. 37 A (3) 2. 25 A (4) 3. 0 A

Q12.A capacitor is connected to a 20 V battery through a resistance of 10Ω . It is found that the potential difference across the capacitor rises to 2 V in 1 μs . The capacitance of the capacitor is ________μF . Given In 10 = 0 . 105 9 (1) 0 . 95 (2) 9 . 52 (3) 1 . 85 (4) 0 . 105 JEE Main 2021 (01 Sep Shift 2) JEE Main Previous Year Paper

Q13.An X-ray tube is operated at 1. 24 million volt. The shortest wavelength of the produced photon will be: (1) 10−3 nm (2) 10−2 nm (3) 10−4 nm (4) 10−1 nm

Q16.The de Broglie wavelength of a proton and α -particle are equal. The ratio of their velocities is (1) 4 : 1 (2) 4 : 3 (3) 1 : 4 (4) 4 : 2

Q16.The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V . What should nearly be the ratio of their wavelengths ? ( mp = 1. 00727 u, me = 0. 00055 u) (1) 1860 : 1 (2) (1860)2 : 1 (3) 41. 4 : 1 (4) 43 : 1

Q17.The half-life of Au198 is 2. 7 days. The activity of 1. 50 mg of Au198 , if its atomic weight is 198 g mol−1 is, (NA = 6 × 1023 mol−1) (1) 240 Ci (2) 357 Ci (3) 535 Ci (4) 252 Ci JEE Main 2021 (16 Mar Shift 2) JEE Main Previous Year Paper

Q18.Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 min . (1) 60 min (2) 20 min (3) 40 min (4) 13 min

Q18.The half-life of 198Au is 3 days. If atomic weight of 198Au is 198 g mol-1, then the activity of 2 mg of 198Au is [in disintegration second-1]: (1) 2 . 67 × 1012 (2) 6 . 06 × 1018 (3) 32 . 36 × 1012 (4) 16 . 18 × 1012

Q20.In amplitude modulation, the message signal 𝑉m ( 𝑡) = 10sin2𝜋× 105𝑡 volts and carrier signal 𝑉C𝑡= 20sin2𝜋× 107𝑡 volts. The modulated signal now contains the message signal with lower side band and upper side band frequency, therefore the bandwidth of modulated signal is 𝛼 kHz. The value of 𝛼 is: (1) 200 kHz (2) 500 kHz (3) 100 kHz (4) 0

Q20.Two identical antennas mounted on identical towers are separated from each other by a distance of 45 km. What should nearly be the minimum height of receiving antenna to receive the signals in line of sight ? (Assume radius of earth is 6400 km) (1) 19. 77 m (2) 39. 55 m (3) 79. 1 m (4) 158. 2 m

Q21.In the reported figure of earth, the value of acceleration due to gravity is same at point A and C but it is smaller than that of its value at point B (surface of the earth). The value of OA : AB will be x : 5 . The value of x is Q22. 1 mole of rigid diatomic gas performs a work of Q5 when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is xR 8 . The value of x is [ R universal gas constant]

Q21.The average translational kinetic energy of 𝑁2 gas molecules at _________∘C becomes equal to the K . E . of an electron accelerated from rest through a potential difference of 0 . 1 volt . (Given 𝑘𝐵= 1 . 38 × 10-23 J K-1 (Fill the nearest integer).

Q21.The acceleration due to gravity is found up to an accuracy of 4% on a planet. The energy supplied to a simple pendulum of known mass m to undertake oscillations of time period T is being estimated. If time period is measured to an accuracy of 3% , the accuracy to which E is known as ________ %

Q21.The resistance R = VI , where V = (50 ± 2) V and I = (20 ± 0. 2) A . The percentage error in R is x % . The value of x to the nearest integer is ________.

Q21.If the velocity of a body related to displacement x is given by v = √5000 + 24x m s−1, then the acceleration of the body is _________ m s−2.

Q21.Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8R as shown in the figure. A satellite of mass m is projected from the surface of the planet of mass M directly towards the centre of the second planet. The minimum speed v required for the satellite to GM reach the surface of the second planet is , then the value of a is R √a7 [Given : The two planets are fixed in their position]

Q21.A body of mass m is launched up on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of friction between the body and plane is √x if the time of ascent is half of the time of descent. The 5 value of x is

Q21.In a spring gun having spring constant 100 N m−1 a small ball B of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0. 05 m. There should be a box placed at a distance d on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of 2 m above the ground. The value of d is m. (g = 10 m s−2)