Practice Questions

Q90.Let the plane P contain the line 2x + y −z −3 = 0 = 5x −3y + 4z + 9 and be parallel to the line x+2 2 = 3−y−4 = z−75 . Then the distance of the point A(8, −1, −19) from the plane P measured parallel to the line −3 x = y−54 = −122−z is equal to _________. JEE Main 2023 (15 Apr Shift 1) JEE Main Previous Year Paper

Q90.A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is q . If p : q = m : n, where m and n are co-prime, then m + n is equal to JEE Main 2023 (30 Jan Shift 2) JEE Main Previous Year Paper

Q90.Let the foot of perpendicular from the point 𝐴4, 3, 1 on the plane 𝑃: 𝑥- 𝑦+ 2𝑧+ 3 = 0 be 𝑁. If 𝐵( 5, 𝛼, 𝛽) , 𝛼, 𝛽∈ℤ is a point on plane 𝑃 such that the area of the triangle 𝐴𝐵𝑁 is 3√2, then 𝛼2 + 𝛽2 + 𝛼𝛽 is equal to _____________ JEE Main 2023 (10 Apr Shift 2) JEE Main Previous Year Paper

Q90.Let the image of the point 𝑃( 1, 2, 3 ) in the plane 2𝑥– 𝑦+ 𝑧= 9 be 𝑄. If the coordinates of the point 𝑅 are ( 6, 10, 7 ) , then the square of the area of the triangle 𝑃𝑄𝑅 is _______ . JEE Main 2023 (06 Apr Shift 1) JEE Main Previous Year Paper

Q90.The shortest distance between the lines = = and = = is equal to ______ 3 2 2 3 2 0 JEE Main 2023 (24 Jan Shift 1) JEE Main Previous Year Paper

Q2. The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is (1) 2. 0 (2) 1. 0 (3) 0. 5 (4) 1. 5

Q7. The efficiency of a Carnot's engine, working between steam point and ice point, will be (1) 26. 81% (2) 37. 81% (3) 47. 81% (4) 57. 81%

Q7. A steel wire of length 3. 2 m(YS = 2. 0 × 1011 N m−2) and a copper wire of length 4. 4 m (YC = 1. 1 × 1011 N m−2) , both of radius 1. 4 mm are connected end to end. When stretched by a load, the net elongation is found to be 1. 4 mm. The load applied, in Newton, will be: (Given π = 227 ) (1) 360 (2) 180 (3) 1080 (4) 154

Q11.An aluminium wire is stretched to make its length, 0. 4% larger. The percentage change in resistance is (1) 0. 4% (2) 0. 2% (3) 0. 8% (4) 0. 6%

Q12.A compass needle of oscillation magnetometer oscillates 20 times per minute at a place P of dip 30° . The number of oscillations per minute become 10 at another place Q of 60° dip. The ratio of the total magnetic field at the two places (BQ : BP) is: (1) √3 : 4 (2) 4 : √3 (3) √3 : 2 (4) 2 : √3 JEE Main 2022 (27 Jul Shift 2) JEE Main Previous Year Paper

Q13.A cyclotron is used to accelerate protons. If the operating magnetic field is 1. 0 T and the radius of the cyclotron 'dees' is 60 cm, the kinetic energy of the accelerated protons in MeV will be : [use mp = 1. 6 × 10−27 kg, e = 1. 6 × 10−19 C] (1) 12 (2) 18 (3) 16 (4) 32

Q14.A series LCR circuit has L = 0. 01 H, R = 10 Ω and C = 1 μF and it is connected to ac voltage of amplitude (Vm) 50 V . At frequency 60% lower than resonant frequency, the amplitude of current will be approximately (1) 466 mA (2) 312 mA (3) 238 mA (4) 196 mA

Q14.The magnetic flux through a coil perpendicular to its plane is varying according to the relation ϕ = (5t3 + 4t2 + 2t −5) Weber. If the resistance of the coil is 5 ohm , then the induced current through the coil at t = 2 s will be, (1) 15. 6 A (2) 16. 6 A (3) 17. 6 A (4) 18. 6 A

Q16.Two coherent sources of light interfere. The intensity ratio of two sources is 1 : 4. For this interference pattern if the value of Imax+Imin is equal to 2α+1 , then α will be Imax−Imin β+3 β (1) 1. 5 (2) 2 (3) 0. 5 (4) 1

Q18.The activity of a radioactive material is 6. 4 × 10−4 curie. Its half life is 5 days. The activity will become 5 × 10−6 curie after (1) 7 days (2) 15 days (3) 25 days (4) 35 days JEE Main 2022 (27 Jul Shift 2) JEE Main Previous Year Paper

Q18.How many alpha and beta particles are emitted when Uranium 92U238 decays to lead 82 Pb206 ? (1) 3 alpha particles and 5 beta particles (2) 6 alpha particles and 4 beta particles (3) 4 alpha particles and 5 beta particles (4) 8 alpha particles and 6 beta particles

Q19.For a constant collector-emitter voltage of 8 V , the collector current of a transistor reached to the value of 6 mA from 4 mA , whereas base current changed from 20 μA to 25 μA value. If transistor is in active state, small signal current gain (current amplification factor) will be (1) 240 (2) 400 (3) 0. 0025 (4) 200

Q20.A square wave of the modulating signal is shown in the figure. The carrier wave is given by C(t) = 5 sin(8πt) Volt. The modulation index is (1) 0. 2 (2) 0. 1 (3) 0. 3 (4) 0. 4

Q21.A ball of mass m is thrown vertically upward. Another ball of mass 2 m is thrown an angle θ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is 1 . The value of x is _____ . x

Q21.A car covers AB distance with first one-third at velocity v1 m s−1 , second one-third at v2 m s−1 and last one- third at v3 m s−1 . If v3 = 3v1, v2 = 2v1 and v1 = 11 m s−1 , then the average velocity of the car is _____ m s−1 .

Q21.A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity 𝑥√𝐹 rad s-1. If 𝐹 be the force exerted by the liquid at the other end then the value of 𝑥 will be _____ .

Q21.The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I1 . The x same rod is bent into a ring and its moment of inertia about a diameter is I2 . If I2I1 is xπ23 , then the value of will be ______.

Q21.In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0. 5 s is measured from time of 100 oscillation with a watch of 1 s resolution. If measured value of length is 10 cm known to 1 mm accuracy. The accuracy in the determination of g is found to be x%. The value of x is

Q21.A hanging mass M is connected to a four times bigger mass by using a string pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is x 5 Mg for x =_____. Neglect mass of the string and friction of the block (bigger mass) with ice slab. (Given g = acceleration due to gravity)

Q21.An object is projected in the air with initial velocity u at an angle θ. The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be _____ degree.