Practice Questions

Q42.A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that θ(t) = 5t2 −8t, where θ(t) is the angular position of the rotating disc as a function of time t. How much power is delivered by the applied torque, when t = 2 s ? (1) 72MR2 (2) 8MR2 (3) 108MR2 (4) 60MR2

Q43.The maximum percentage error in the measurment of density of a wire is [Given, mass of wire = (0.60 ± 0.003)g radius of wire = (0.50 ± 0.01)cm length of wire = (10.00 ± 0.05)cm] (1) 8 (2) 5 (3) 4 (4) 7 for another diatomic molecules, but for rigid molecules and γ2 =

Q43.Which of the following circuits has the same outpur as that of the given circuit? (1) (2) (3) (4)

Q43.The energy of a system is given as E(t) = α3e−βt , where t is the time and β = 0.3 s−1 . The errors in the measurement of α and t are 1.2% and 1.6% , respectively. At t = 5 s, maximum percentage error in the energy is : (1) 6% (2) 8.4% (3) 11.6% (4) 4%

Q43.A parallel plate capacitor of capacitance 1μ F is charged to a potential difference of 20 V . The distance between plates is 1μ m . The energy density between plates of capacitor is. (1) 2 × 10−4 J/m3 (2) 1.8 × 105 J/m3 (3) 1.8 × 103 J/m3 (4) 2 × 102 J/m3

Q43.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion-(A) : If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer. Reason-(R) : The speed of light reduces in an optically denser medium than air while its frequency does not change. In the light of the above statements, choose the most appropriate answer from the options given below : (1) Both (A) and (R) are true but (R) is not the (2) Both (A) and (R) are true and (R) is the correct correct explanation of (A) explanation of (A) (3) (A) is true but (R) is false (4) (A) is false but (R) is true

Q44.Match List - I with List - II. List - I List - II (A) Permeability of free space (I) [M L2 T−2] (B) Magnetic field (II) [M T−2 A−1] (C) Magnetic moment (III) [M L T−2 A−2] (D) Torsional constant (IV) [L2 A] Choose the correct answer from the options given below : (1) (A)-(IV), (B)-(III), (C)-(I), (D)-(II) (2) (A)-(III), (B)-(II), (C)-(IV), (D)-(I) (3) (A)-(I), (B)-(IV), (C)-(II), (D)-(III) (4) (A)-(II), (B)-(I), (C)-(III), (D)-(IV)

Q44.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases. Reason (R): Free expansion of an ideal gas is an irreversible and an adiabatic process. In the light of the above statements, choose the correct answer from the options given below : (1) Both (A) and (R) are true but (R) is NOT the (2) (A) is false but (R) is true correct explanation of (A) (3) (A) is true but (R) is false (4) Both (A) and (R) are true and (R) is the correct explanation of (A)

Q44.Identify the valid statements relevant to the given circuit at the instant when the key is closed. A. There will be no current through resistor R. B. There will be maximum current in the connecting wires. C. Potential difference between the capacitor plates A and B is minimum. D. Charge on the capacitor plates is minimum. Choose the correct answer from the options given below: (1) A, C Only (2) A, B, D Only (3) C, D Only (4) B, C, D Only

Q44.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain. Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa. In the light of the above statements, choose the most appropriate answer from the options given below : (1) Both (A) and (R) are true and (R) is the correct (2) (A) is true but (R) is false explanation of (A) (3) (A) is false but (R) is true (4) Both (A) and (R) are true but (R) is not the correct explanation of (A)

Q44.An object of mass ' m ' is projected from origin in a vertical xy plane at an angle 45∘ with the x axis with an initial velocity v0 . The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [ g is acceleration due to gravity] (1) mv3 o along negative z -axis (2) mv3 o along positive z -axis 2√2g 4√2g (3) mv3o along negative z -axis (4) mv3o along positive z -axis 4√2g 2√2g

Q44.For a diatomic gas, if γ1 = ( CpCv ) ( CpCv ) also having vibrational modes. Then, which one of the following options is correct ? (Cp and Cv are specific heats of the gas at constant pressure and volume) 2025 (22 Jan Shift 2) JEE Main Previous Year Paper (1) γ2 = γ1 (2) 2γ2 = γ1 (3) γ2 < γ1 (4) γ2 > γ1 →

Q44.A parallel-plate capacitor of capacitance 40μ F is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant K = 2. Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are (1) 4 mC and 0.2 J (2) 8 mC and 2.0 J (3) 2 mC and 0.4 J (4) 2 mC and 0.2 J 2025 (22 Jan Shift 1) JEE Main Previous Year Paper

Q45.A proton of mass ' mp ' has same energy as that of a photon of wavelength ' λ '. If the proton is moving at non- relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is. (1) 1 (2) 1 c √Emp c √2Emp (3) 1 (4) 1 E 2c √Emp c √ 2 mp

Q45.A solid sphere of mass ' m ' and radius ' r ' is allowed to roll without slipping from the highest point of an inclined plane of length ' L ' and makes an angle 30∘ with the horizontal. The speed of the particle at the bottom of the plane is v1 . If the angle of inclination is increased to 45∘ while keeping L constant. Then the new speed of the sphere at the bottom of the plane is v2 . The ratio v21 : v22 is (1) 1 : √2 (2) 1 : √3 (3) 1 : 3 (4) 1 : 2 2025 (23 Jan Shift 1) JEE Main Previous Year Paper

Q45.Which of the following resistivity ( ρ ) v/s temperature (T) curves is most suitable to be used in wire bound standard resistors? (1) (2) (3) (4)

Q45.An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density σo . Choose the correct option from the following. (1) Potential energy and torque both are maximum. (2) Torque on dipole is zero and net force is directed away from the sheet. (3) Torque on dipole is zero and net force acts (4) Potential energy of dipole is minimum and torque towards the sheet. is zero.

Q45.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path. Reason (R): The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below : (1) (A) is true but (R) is false (2) Both (A) and (R) are true but (R) is NOT the correct explanation of (A) (3) Both (A) and (R) are true and (R) is the correct (4) (A) is false but (R) is true explanation of (A)

Q45. In the circuit shown here, assuming threshold voltage of diode is negligibly small, then voltage VAB is correctly represented by : (1) VAB would be zero at all times (2) (3) (4)

Q45.A body of mass ' m ' connected to a massless and unstretchable string goes in verticle circle of radius ' R 'under gravity g. The other end of the string is fixed at the center of circle. If velocity at top of circular path is n√gR, where, n ⩾1, then ratio of kinetic energy of the body at bottom to that at top of the circle is (1) n2 (2) n2+4 n2+4 n2 (3) n+4 (4) n n n+4

Q46.In a hydraulic lift, the surface area of the input piston is 6 cm2 and that of the output piston is 1500 cm2 . If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is _______ kJ. 2025 (29 Jan Shift 1) JEE Main Previous Year Paper

Q46.The ratio of the power of a light source S1 to that the light source S2 is 2. S1 is emitting 2 × 1015 photons per second at 600 nm . If the wavelength of the source S2 is 300 nm , then the number of photons per second emitted by S2 is … … ×1014 . 2025 (24 Jan Shift 2) JEE Main Previous Year Paper

Q46.A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of 2 × 105 ms−1 . When the electric field is switched off, the proton moves along a circular path of radius 2 cm . The magnitude of electric field is x × 104 N/C. The value of x is _______ Take the mass of the proton = 1.6 × 10−27 kg.

Q46.A current of 5A exists in a square loop of side 1 m . Then the magnitude of the magnetic field B at the centre √2 of the square loop will be p × 10−6 T. where, value of p is _____ . [ Take μ0 = 4π × 10−7TmA−1].

Q46.The magnetic field inside a 200 turns solenoid of radius 10 cm is 2.9 × 10−4Tesla. If the solenoid carries a current of 0.29 A , then the length of the solenoid is ________ πcm .