Practice Questions

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

Q90.Let P(α, β, γ) be the image of the point Q(1, 6, 4) in the line x1 = y−12 = z−23 . Then 2α + to_______ JEE Main 2024 (08 Apr Shift 2) JEE Main Previous Year Paper

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

Q1. Two resistance are given as 𝑅1 = ( 10 ± 0 . 5 ) Ω and 𝑅2 = ( 15 ± 0 . 5 ) Ω . The percentage error in the measurement of equivalent resistance when they are connected in parallel is (1) 6 . 33 (2) 2 . 33 (3) 5 . 33 (4) 4 . 33

Q1. Two trains A and B of length l and 4l are travelling into a tunnel of length L in parallel tracks from opposite directions with velocities 108 km h−1 and 72 km h−1, respectively. If train A take 35 s less time than train B to cross the tunnel then, length L of tunnel is: (Given L = 60 l) (1) 1200 m (2) 900 m (3) 1800 m (4) 2700 m

Q1. Three forces F1 = 10 N, F2 = 8 N, F3 = 6 N are acting on a particle of mass 5 kg. The forces F2 and F3 are applied perpendicularly so that particle remains at rest. If the force F1 is removed, then the acceleration of the particle is (1) 7 m s–2 (2) 0. 5 m s–2 (3) 4. 8 m s–2 (4) 2 m s–2

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. A body is moving with constant speed, in a circle of radius 10 m. The body completes one revolution in 4 s. At the end of 3rd second, the displacement of body (in m) from its starting point is: (1) 30 (2) 15 π (3) 5 π (4) 10√2

Q1. If the velocity of light c, universal gravitational constant G and planck's constant h are chosen as fundamental quantities. The dimensions of mass in the new system is: 2 c 2 G1] (2) h1c1G−1 (1) [h 1 1 2 c 2 G 2 ] (4) [h 2 c 2 G−12 ] (3) [h−1 1 1 1 1

Q1. A cylindrical wire of mass (0. 4 ± 0. 01) g has length (8 ± 0. 04) cm and radius (6 ± 0. 03) mm . The maximum error in its density will be (1) 3. 5% (2) 5% (3) 1% (4) 4%

Q1. In the equation 𝑋+ 𝑎 𝑏] = 𝑅𝑇, 𝑋 is pressure, 𝑌 is volume, 𝑅 is universal gas constant and 𝑇 is 𝑌2[𝑌- temperature. The physical quantity equivalent to the ratio 𝑎 is: 𝑏 (1) Pressure gradient (2) Energy (3) Impulse (4) Coefficient of viscosity

Q1. Match List I with List II List I List II A. Torque I. M L−2 T−2 B. Stress II. M L2 T−2 C. Pressure gradient III. M L−1 T−1 Coefficient of D. IV. M L−1 T−2 viscosity Choose the correct answer from the options given below : (1) A-II, B-I, C-IV, D-III (2) A-IV, B-II, C-III, D-I (3) A-II, B-IV, C-I, D-III (4) A-III, B-IV, C-I, D-II

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. The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is (1) 192 m (2) 136 m (3) 272 m (4) 68 m

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 ]

Q2. The speed of a wave produced in water is given by ν = λagbρc . Where λ, g and ρ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a, b and c respectively, are (1) 1, −1, 0 (2) 12 , 0, 12 (3) 1, 1, 0 (4) 21 , 12 , 0

Q2. If force (F), velocity (V ) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be : (1) F V 4 T −6 (2) F V −4 T −2 (3) F 2 V −2 T 6 (4) F V −2 T 2

Q2. Match Column-I with Column-II : Column-I (x-t graphs) Column-II (v-t graphs) A I B II C III D IV Choose the correct answer from the options given below: (1) A- II B-IV, C-III, D-I (2) A- I. B-II, C-III, D-IV (3) A- II B-III, C-IV, D-I (4) A- I, B-III. C-IV, D-II

Q2. A disc is rolling without slipping on a surface. The radius of the disc is R. At t = 0, the top most point on the disc is A as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is (1) 2R (2) R√(π2 + 4) (3) R√(π2 + 1) (4) 2R√(1 + 4π2)

Q2. An object moves with speed 𝑣1, 𝑣2 and 𝑣3 along a line segment 𝐴𝐵, 𝐵𝐶 and 𝐶𝐷 respectively as shown in figure. Where 𝐴𝐵 = 𝐵𝐶 and 𝐴𝐷 = 3 𝐴𝐵, then average speed of the object will be : (1) 𝑣1 + 𝑣2 + 𝑣3 (2) 𝑣1𝑣2𝑣3 3 3𝑣1𝑣2 + 𝑣2𝑣3 + 𝑣3𝑣1 3𝑣1𝑣2𝑣3 𝑣1 + 𝑣2 + 𝑣3 (3) (4) 𝑣1𝑣2 + 𝑣2𝑣3 + 𝑣3𝑣1 3𝑣1𝑣2𝑣3

Q2. Form the 𝑣 - 𝑡 graph shown, the ratio of distance to displacement in 25 s of motion is: 1 (1) 1 (2) 2 (3) 5 (4) 3 3 5

Q2. The frequency (ν) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s) of the liquid as: ν = raρbsc . The values of a, b and c respectively are (1) (−32 , −12 , 12 ) (2) (−32 , 12 , 12 ) (3) ( 23 , 12 , −12 ) (4) ( 32 , −12 , 12 )

Q2. The initial speed of a projectile fired from ground is 𝑢. At the highest point during its motion, the speed of √3 projectile is 𝑢. The time of flight of the projectile is: 2 (1) 𝑢 (2) 𝑢 2𝑔 𝑔 2𝑢 √3𝑢 (3) (4) 𝑔 𝑔

Q2. As shown in the figure, a particle is moving with constant speed π m s−1 . Considering its motion from A to B, the magnitude of the average velocity is: (1) √3 m s−1 (2) π m s−1 (3) 1. 5√3 m s−1 (4) 2√3 m s−1

Q2. A particle is moving with constant speed in a circular path. When the particle turns by an angle 90°, the ratio of instantaneous velocity to its average velocity is 𝜋: 𝑥√2 . The value of 𝑥 will be (1) 2 (2) 5 (3) 1 (4) 7