Practice Questions

Q27.A ray of light is incident at an angle of incidence 60° on the glass slab of refractive index √3. After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is 4√3 cm . The thickness of the glass slab is _____ cm .

Q28.A convex lens of focal length 20 cm is placed in front of convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is _____ cm.

Q29.The X −Y plane be taken as the boundary between two transparent media M1 and M2 . M1 in Z ≥0 has a refractive index of √2 and M2 with Z < 0 has a refractive index of √3. A ray of light travelling in M1 along → the direction given by the vector A = 4√3i −3√3j −5ˆk, is incident on the plane of separation. The value of difference between the angle of incident in M1 and the angle of refraction in M2 will be _____ degree.

Q29.A Zener of breakdown voltage VZ = 8 V and maximum Zener current, IZM = 10 mA is subjected to an input voltage Vi = 10 V with series resistance R = 100 Ω . In the given circuit RL represents the variable load resistance. The ratio of maximum and minimum value of RL is _____ .

Q29.An AC source is connected to an inductance of 100 mH , a capacitance of 100 μF and a resistance of 120 Ω as shown in figure. The time in which the resistance having a thermal capacity 2 J ∘C−1 will get heated by 16°C is _____ s.

Q29.An object ' O' is placed at a distance of 100 cm in front of a concave mirror of radius of curvature 200 cm as shown in the figure. The object starts moving towards the mirror at a speed 2 cm s−1 . The position of the image from the mirror after 10 s will be at _____ cm.

Q29.In a hydrogen spectrum λ be the wavelength of first transition line of Lyman series. The wavelength difference will be " aλ" between the wavelength of 3rd transition line of Paschen series and that of 2nd transition line of Balmer Series where a = _____.

Q30.The current in a coil of self inductance 𝐿= 2 . 0 H is increasing according to the law 𝑖= 2sin𝑡2. Find the amount of energy spent (in J) during the period when the current changes from 0 to 2 A.

Q30.A modulating signal 2sin6 . 28 × 106𝑡 is added to the carrier signal 4sin12 . 56 × 109𝑡 for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass filter. The bandwidth of the output signal of band pass filter will be _____ MHz.

Q2. A particle is projected with velocity v0 along x-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. ma = −αx2. The distance at which the particle stops: (1) 2v0 13 (2) 3mv20 1 ( 3α ) ( 2α ) 3 (3) 3v20 12 (4) 2v20 12 ( 2α ) ( 3α )

Q3. A particle of mass m moves in a circular orbit under the central potential field, U(r) = −Cr , where C is a positive constant. The correct radius - velocity graph of the particle's motion is : JEE Main 2021 (18 Mar Shift 2) JEE Main Previous Year Paper (1) (2) (3) (4)

Q3. A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to 10081 of the height through which it falls. Find the average speed of the ball. (Take g = 10 m s−2 ) (1) 3. 0 m s−1 (2) 3. 5 m s−1 (3) 2. 0 m s−1 (4) 2. 50 m s−1

Q3. The normal reaction N for a vehicle of 800 kg mass, negotiating a turn on a 30° banked road at maximum possible speed without skidding is ____ ×103 kg m s−2 . (1) 10. 2 (2) 7. 2 (3) 12. 4 (4) 6. 96

Q4. A triangular plate is shown. A force F = 4ˆi −3ˆj is applied at point P. The torque at point P with respect to point O and Q are: (1) −15 −20√3, 15 −20√3 (2) 15 + 20√3, 15 −20√3 (3) 15 −20√3, 15 + 20√3 (4) −15 + 20√3, 15 + 20√3

Q4. A huge circular arc of length 4. 4 ly subtends an angle 4s at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second? Given : 1 ly = 9. 46 × 1015 m 1 AU = 1. 5 × 1011 m (1) 3. 5 × 106 s (2) 4. 5 × 1010 s (3) 4. 1 × 108 s (4) 7. 2 × 108

Q4. A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force F1. Now a spherical cavity of radius ( R2 ) is made in the sphere (as shown in figure) and the force becomes F2 . The value of F1 : F2 is: (1) 41 : 50 (2) 50 : 41 (3) 25 : 36 (4) 36 : 25 JEE Main 2021 (25 Feb Shift 1) JEE Main Previous Year Paper

Q4. A body of mass M moving at speed V0 collides elastically with a mass m at rest. After the collision, the two masses move at angles θ1 and θ2 with respect to the initial direction of motion of the body of mass M.. The largest possible value of the ratio M m , for which the angles θ1 and θ2 will be equal, is : (1) 3 (2) 4 (3) 2 (4) 1

Q4. A block of mass 𝑚 slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is: Given 𝑚= 8 kg, 𝑀= 16 kg Assume all the surfaces shown in the figure to be frictionless. 3 4 (1) g (2) g 5 3 6 2 (3) g (4) 5 3g

Q5. An automobile of mass m accelerates starting from the origin and initially at rest, while the engine supplies constant power P . The position is given as a function of time by: JEE Main 2021 (27 Jul Shift 2) JEE Main Previous Year Paper 1 1 2 (1) 3 (2) t 2 t 3 ( 89Pm ) 2 ( 98Pm ) 2 1 1 3 (3) 3 (4) t 2 t 2 ( 9m8P ) 2 ( 98Pm ) 2

Q5. Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be: JEE Main 2021 (24 Feb Shift 1) JEE Main Previous Year Paper + 2√2 (1) √𝐺1 + 2√2 (2) √ 𝐺21 𝐺 2√2𝐺 (3) (4) √1 + √ 22√2 - 1 2

Q5. An inclined plane making an angle of 30° with the horizontal is placed in a uniform horizontal electric field 200 NC as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a height of 1 m. If the coefficient of friction is 0. 2, find the time taken by the body to reach the bottom. [g = 9. 8 m s−2; sin 30°= 12 ; cos 30°= √32 ] (1) 0. 92 s (2) 1. 3 s (3) 0. 46 s (4) 2. 3 s

Q6. A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height h is S. (1) h 23 (2) h 23 + + g Re ) Re ) √Re2 g [(1 [(1 −1] √2Re −1] (3) 1 h 23 (4) 1 h 23 + + Rc ) Re ) 3 √Re2 g [(1 3 √2Rcg [(1 −1] −1] JEE Main 2021 (22 Jul Shift 1) JEE Main Previous Year Paper

Q9. The material filled between the plates of a parallel plate capacitor has resistivity 200 Ω m . The value of capacitance of the capacitor is 2 pF. If a potential difference of 40 V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is: (given the value of relative permittivity of material is 50 ) (1) 0.9 mA (2) 9.0 mA (3) 9.0 μA (4) 0.9 μA

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

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