Practice Questions

Q90.If d1 is the shortest distance between the lines x + 1 = 2 y = −12 z, x = y + 2 = 6 z −6 and d2 is the shortest distance between the lines x−1 2 = y+8−7 = z−45 , x−12 = y−21 = z−6−3 , then the value of 32√3d2 d1 is : JEE Main 2024 (30 Jan Shift 1) JEE Main Previous Year Paper

Q90.Let →a = ^i −3^j + 7^k, b = 2^i −^j + ^k and→cbe a vector such that (→a+ 2b) ×→c= 3(→c×→a) . If →a ⋅→c = 130 , then →b ⋅→c is equal to _______ JEE Main 2024 (05 Apr Shift 1) JEE Main Previous Year Paper

Q90.In a tournament, a team plays 10 matches with probabilities of winning and losing each match as 1 and 2 3 3 respectively. Let x be the number of matches that the team wins, and y be the number of matches that team loses. If the probability P(|x −y| ≤ 2) is p , then 39p equals ______ JEE Main 2024 (04 Apr Shift 2) JEE Main Previous Year Paper

Q90.A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required and let a = P(X = 3), b = P(X ≥3) and c = P(X ≥6 ∣X > 3). Then b+ca is equal to JEE Main 2024 (27 Jan Shift 1) JEE Main Previous Year Paper

Q90.Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables X and Y respectively denote the number of blue and yellow balls. If ¯X and ¯Y are the means of X and Y respectively, then 7¯X + 4¯Y is equal to________ JEE Main 2024 (08 Apr Shift 1) JEE Main Previous Year Paper

Q90.The square of the distance of the image of the point (6, 1, 5) in the line x−13 = 2y = z−24 , from the origin is _________ JEE Main 2024 (09 Apr Shift 2) JEE Main Previous Year Paper

Q90.Let O be the origin, and M and N be the points on the lines x−5 4 = y−41 = z−53 and x+812 = y+25 = z+119 −−→ → respectively such that MN is the shortest distance between the given lines. Then OM ⋅ON is equal to _________. JEE Main 2024 (29 Jan Shift 2) JEE Main Previous Year Paper

Q90.Let →𝑎= ^𝑖+ ^𝑗+ ^𝑘, →𝑏= − ^𝑖−8 ^𝑗+ 2 ^𝑘 and →𝑐= 4 ^𝑖+ 𝑐2 ^𝑗+ 𝑐3 ^𝑘 be three vectors such that →𝑏× →𝑎= →𝑐× →𝑎. If the angle between the vector →𝑐 and the vector 3 ^𝑖+ 4 ^𝑗+ ^𝑘 is 𝜃, then the greatest integer less than or equal to tan2𝜃 is: JEE Main 2024 (01 Feb Shift 2) JEE Main Previous Year Paper

Q1. If P = 3ˆi + √3ˆj + 2ˆk and Q = 4ˆi + √3ˆj + 2. 5ˆk then, the unit vector in the direction of P × Q is x is x 1 (√3ˆi +ˆj −2√3ˆk). The value of

Q1. In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5. 25 mm and apparent thickness of the glass slab at 5. 00 mm . Travelling microscope has 20 divisions in one cm on main scale and 50 divisions on Vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is x × 10−3 , where x is ______ 10

Q2. For a train engine moving with speed of 20 ms–1 , the driver must apply brakes at a distance of 500 m before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed √x ms−1 . The value of x is ______. (Assuming same retardation is produced by brakes)

Q2. A tennis ball is dropped on to the floor from a height of 9. 8 m. It rebounds to a height 5. 0 m. Ball comes in contact with the floor for 0. 2 s . The average acceleration during contact is ______ m s−2 . [Given g = 10 m s−2 ]

Q3. As per given figure, a weightless pulley 𝑃 is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if 𝑔= 10 m s-2) (1) 4√3 + 1 N (2) 4√3 + 1 N (3) 4√3 - 1 N (4) 4√3 - 1 N

Q4. Two bodies are projected from ground with same speeds 40 m s−1 at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of 60° , with horizontal then sum of the maximum heights, attained by the two projectiles, is _____ m. (Given g = 10 m s−2 )

Q4. A block is fastened to a horizontal spring. The block is pulled to a distance x = 10 cm from its equilibrium position (at x = 0 ) on a frictionless surface from rest. The energy of the block at x = 5 cm is 0. 25 J . The spring constant of the spring is ______ N m−1 .

Q4. A stone tied to 180 cm long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is 1936 x m s−2 . The value of x ______. [Take π = 227 ]

Q5. A body of mass 5 kg is moving with a momentum of 10 kg m s−1 . Now a force of 2 N acts on the body in the direction of its motion for 5 s. The increase in the Kinetic energy of the body is _____ J.

Q5. A force F = (5 + 3y2) acts on a particle in the y-direction, where F is newton and y is in meter. The work done by the force during a displacement from y = 2 m to y = 5 m is ______ J .

Q5. A particle of mass 100 g is projected at time t = 0 with a speed 20 m s–1 at an angle 45° to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time t = 2 s is found to be √K kg m2 s−1 . The value of K is ______. (Take g = 10 m s−2 )

Q5. The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth 𝑅𝑒= 6400 km) (1) 9 . 8 N (2) 4 . 9 N (3) 19 . 6 N (4) 8 N

Q5. To maintain a speed of 80 km h−1 by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be _____ kJ. [The coefficient of friction between tyre of bus and road is 0. 04 ]

Q5. A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2 . The ratio of their 1 nuclear sizes will be ( x3 ) 3 . The value of ‘ x’ is:

Q5. An object of mass m initially at rest on a smooth horizontal plane starts moving under the action of force F = 2 N . In the process of its linear motion, the angle θ (as shown in figure) between the direction of force and horizontal varies as θ = kx , where k is a constant and x is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be E = nk sin θ . The value of n is ______.

Q5. A block of mass 5 kg starting from rest pulled up on a smooth incline plane making an angle of 30° with horizontal with an effective acceleration of 1 m s−2 . The power delivered by the puling force at t = 10 s from the start is _____ W. [Use g = 10 m s−2 ] (Calculate the nearest integer value)

Q5. A body is dropped on ground from a height h1 and after hitting the ground, it rebounds to a height h2 . If the ratio of velocities of the body just before and after hitting ground is 4 , then percentage loss in kinetic energy of the body is x . The value of x is _____. 4