Practice Questions

Q20.There are 100 divisions on the circular scale of a screw gauge of pitch 1 mm . With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found that 4 linear scale divisions are clearly visible while 60 divisions on circular scale coincide with the reference line. The diameter of the wire is : (1) 3.35 mm (2) 4.65 mm (3) 4.55 mm (4) 4.60 mm

Q20.One main scale division of a vernier caliper is equal to m units. If nth division of main scale coincides with (n + 1)th division of vernier scale, the least count of the vernier caliper is : (1) n (2) 1 (n+1) (n+1) (3) m (4) m (n+1) n(n+1) 5 for |→a| = n|→b| The integer

Q20.The truth table for this given circuit is: JEE Main 2024 (29 Jan Shift 2) JEE Main Previous Year Paper (1) (2) (3) (4)

Q20.The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to 1 mm . The main scale reading is 2 cm and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 g, the density of the sphere is: (1) 2.0 g/cm3 (2) 1.7 g/cm3 (3) 2.2 g/cm3 (4) 2.5 g/cm3 JEE Main 2024 (08 Apr Shift 1) JEE Main Previous Year Paper −−−

Q20.In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its 4th division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is 0.04 mm then how many main scale divisions are there in 1 cm ? (1) 10 (2) 5 (3) 20 (4) 40

Q21.A body moves on a frictionless plane starting from rest. If Sn is distance moved between t = n −1 and t = n and Sn−1 is distance moved between t = n −2 and t = n −1, then the ratio Sn−1 is (1 −2x ) for n = 10 . The Sn value of x is ______.

Q21.A body starts falling freely from height 𝐻 hits an inclined plane in its path at height ℎ. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of 𝐻 for which ℎ the body will take the maximum time to reach the ground is _____.

Q21.A particle initially at rest starts moving from reference point 𝑥= 0 along 𝑥-axis, with velocity 𝑣 that varies as 𝑣= 4√𝑥 m s-1. The acceleration of the particle is _____ m s-2.

Q21.A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of 100 m from the foot of the tower. A body of mass 2M thrown at a velocity 2v from the top of the tower of height 4H will touch the ground at a distance of _____ m . JEE Main 2024 (08 Apr Shift 2) JEE Main Previous Year Paper

Q21.Three vectors OP,→ OQ→ and OR→ each of magnitude A are acting as shown in figure. The resultant of the three vectors is A√x. The value of x is ________ .

Q21.A particle starts from origin at t = 0 with a velocity 5ˆi m s−1 and moves in x −y plane under action of a force which produces a constant acceleration of + m s−2 . If the x-coordinate of the particle at that instant is (3ˆi 2ˆj) 84 m, then the speed of the particle at this time is √α m s−1 . The value of α is _______.

Q21.The maximum height reached by a projectile is 64 m. If the initial velocity is halved, the new maximum height of the projectile is _____ m . JEE Main 2024 (05 Apr Shift 2) JEE Main Previous Year Paper

Q21.Two identical spheres each of mass 2 kg and radius 50 cm are fixed at the ends of a light rod so that the separation between the centers is 150 cm. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is 𝑥 kg m2, where the value of 𝑥 is 20

Q21.The displacement and the increase in the velocity of a moving particle in the time interval of t to (t + 1) s are 125 m and 50 m s−1 , respectively. The distance travelled by the particle in (t + 2)th s is ___________ m .

Q21.Two forces ¯F1 and ¯F2 are acting on a body. One force has magnitude thrice that of the other force and the 1 ) resultant of the two forces is equal to the force of larger magnitude. The angle between →F1 and →F2 is cos−1 ( n . The value of |n| is _____.

Q21.A ball rolls off the top of a stairway with horizontal velocity u. The steps are 0. 1 m high and 0. 1 m wide. The minimum velocity u with which that ball just hits the step 5 of the stairway will be √x m s−1 , where x = _______ [use g = 10 m s−2 ].

Q21.A particle is moving in one dimension (along 𝑥 axis) under the action of a variable force. It's initial position was 16 m right of origin. The variation of its position 𝑥 with time 𝑡 is given as 𝑥= – 3𝑡3 + 18𝑡2 + 16𝑡, where 𝑥 is in m and 𝑡 is in s . The velocity of the particle when its acceleration becomes zero is _________ m s-1 . JEE Main 2024 (01 Feb Shift 1) JEE Main Previous Year Paper

Q21.A body falling under gravity covers two points A and B separated by 80 m in 2 s. The distance of upper point A from the starting point is _____m. Use g = 10 m s-2

Q21.A particle moves in a straight line so that its displacement x at any time t is given by x2 = 1 + t2 . Its acceleration at any time t is x−n where n = ___________

Q21.A particle is moving in a circle of radius 50 cm in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at t = 0 is 4 m s−1 , the time taken to complete the first revolution will be 1 [1 −e−2π] s, where α =______. α

Q21.For three vectors →A = (−x^i −6^j −2^k), →B = (−^i + 4^j + 3^k) and →C = (−8^i −^j + 3^k), if →A ⋅(→B × →C) = 0, then value of x is _________

Q21.A bus moving along a straight highway with speed of 72 km/h is brought to halt within 4s after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is _____m.

Q21.The resultant of two vectors →A and →B is perpendicular to →A and its magnitude is half that of →B. The angle between vectors →A and →B is ______ ∘.

Q21.If →a and →b makes an angle cos−1 ( 9 ) with each other, then |→a + →b| = √2|→a −→b| value of n is ____

Q21.A vector has magnitude same as that of 𝐴= 3 ^j + 4 ^j and is parallel to 𝐵= 4 ^i + 3 ^j. The 𝑥 and 𝑦 components of this vector in first quadrant are 𝑥 and 3 respectively where x = ____.