Practice Questions

Q90.Let the line x−3 7 = −1 = z−3−4 intersect the plane containing the lines x−41 = y+1−2 = 1z and 4ax −y + 5z −7a = 0 = 2x −5y −z −3, a ∈R at the point P(α, β, γ). Then the value of α + β + γ equals ______. JEE Main 2022 (27 Jul Shift 1) JEE Main Previous Year Paper

Q90.The plane passing through the line 𝐿: 𝑙 𝑥- 𝑦+ 31 - 𝑙 𝑧= 1, 𝑥+ 2𝑦- 𝑧= 2 and perpendicular to the plane 3𝑥+ 2𝑦+ 𝑧= 6 is 3𝑥- 8𝑦+ 7𝑧= 4. If 𝜃 is the acute angle between the line 𝐿 and the 𝑦-axis, then 415 cos2𝜃 is equal to ______. JEE Main 2022 (26 Jul Shift 2) JEE Main Previous Year Paper

Q90.Let S = {E, E2 … E8} be a sample space of raddom experiment such that P(En) = 36n for every n = 1, 2 … . 8. Then the number of elements in the set {A ⊂S : P(A) ≥45 } is _____. JEE Main 2022 (27 Jun Shift 2) JEE Main Previous Year Paper

Q90.The line of shortest distance between the lines = = and = = makes an angle of 0 1 1 2 2 1 with the plane 𝑃: 𝑎𝑥- 𝑦- 𝑧= 0, 𝑎> 0. If the image of the point 1, 1, - 5 in the plane 𝑃 is 𝛼, 𝛽, 𝛾, sin-1√ 272 then 𝛼+ 𝛽- 𝛾 is equal to _____ . JEE Main 2022 (25 Jul Shift 1) JEE Main Previous Year Paper

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. 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

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

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 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 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 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

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

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 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. 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. 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

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. For an ideal gas the instantaneous change in pressure P with volume V is given by the equation dP = −aP. If dV P = P0 at V = 0 is the given boundary condition, then the maximum temperature one mole of gas can attain is: (Here R is the gas constant) (1) aP0 (2) infinity eR (3) 0°C (4) aeRP0

Q9. An electric dipole is placed on x−axis in proximity to a line charge of linear charge density 3. 0 × 10−6 C m−1. Line charge is placed on z− axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm from the origin respectively. If total force of 4 N is exerted on the dipole, find out the amount of positive or negative charge of the dipole. (1) 815. 1 nC (2) 8. 8 μC (3) 0. 485 mC (4) 4. 44 μC

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 )

Q10.Two Carnot engines A and B operate in series such that engine A absorbs heat at T1 and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at T3 . When workdone in both the cases is equal, to value of T is : (1) 2 3 T1 + 23 T3 (2) 31 T1 + 32 T3 (3) 32 T1 + 31 T3 (4) 32 T1 + 31 T3

Q10.A parallel plate capacitor with plate area '𝐴' and distance of separation '𝑑' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as: 𝜀𝑥= 𝜀0 + 𝑘𝑥, for 0 < 𝑥≤ 𝑑2 ≤𝑥≤𝑑 𝜀𝑥= 𝜀0 + 𝑘𝑑- 𝑥, for 𝑑2 𝑘𝑑 (1) 2 / 𝑘𝐴 𝑘𝐴 (2) 𝜀0 + 2𝑙𝑛2𝜀0 + 𝑘𝑑 2 2𝜀0 (3) 0 (4) 𝑘𝐴 ln 2𝜀0 2 2𝜀0 - 𝑘𝑑