STATEMENT-1 : No external force acts on system of two spheres which undergo a perfectly elastic head on collision. The minimum kinetic energy of this system is zero if the net momentum of this system is zero
STATEMENT-2 : In any two body system undergoing perfectly elastic head on collision, at the instant of maximum deformation, the complete kinetic energy of the system is converted to deformation potential energy of the system.

The equation of the tangent to the parabola y =  (x – 3)² parallel to the chord joining the points (3, 0) and (4, 1) is -

Length of the latus rectum of the parabola whose focus at (2, 3) and directrix is the line x – 4y + 3 = 0 is

• The length of the latus rectum of the parabola is always equivalent to four times the focal length of the parabola.
  

Let A be a 2 × 2 matrix
Statement- 1: adj (adj A) = A
Statement -2 : | adj A | = | A |

A uniform rope of linear mass density and length is coiled on a smooth horizontal surface. One end is pulled up with constant velocity v. Then the average power applied by the external agent in pulling the entire rope just off the ground is:

Two particles of mass m, constrained to move along the circumference of a smooth circular hoop of equal mass m, are initially located at opposite ends of a diameter and given equal velocities shown in the figure. The entire arrangement is located in gravity free space. Their velocity just before collision is

A ball of mass 1 kg strikes a heavy platform, elastically, moving upwards with a velocity of 5m/s. The speed of the ball just before the collision is 10m/s downwards. Then the impulse imparted by the platform on the ball is

Three balls A, B and C are placed on a smooth horizontal surface. Ball B collides with ball C with an initial velocity v as shown in the figure. Total number of collisions between the balls will be (All collisions are elastic)

Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix. Denote by tr (A), the sum of diagonal entries of A, Assume that A² = I
Statement- 1:If A ≠ I and A ≠ – I, then det A = – 1
Statement -2 :If A ≠ I and A  ≠–I, then tr (A)  ≠ 0

Statement I : If A =  , then A^–1 = 
Statement II : The inverse of a diagonal matrix is a diagonal matrix..

The figure shows the positions and velocities of two particles. If the particles move under the mutual attraction of each other, then the position of centre of mass at t =1 s is

The velocity of centre of mass of the system as shown in the figure

Three man A, B & C of mass 40 kg, 50 kg & 60 kg are standing on a plank of mass 90 kg, which is kept on a smooth horizontal plane. If A & C exchange their positions then mass B will shift

Considering a system having two masses m1 and m2 in which first mass is pushed towards centre of mass by a distance a, the distance required to be moved for second mass to keep centre of mass at same position is

A uniform wire of length is bent into the shape of 'V' as shown. The distance of its centre of mass from the vertex A is

Centre of mass of two uniform rods of same length but made up of different materials & kept as shown, if the meeting point is the origin of co–ordinates