STATEMENT-1 : One end of ideal massless spring is connected to fixed vertical wall and other end to a block of mass m initially at rest on smooth horizontal surface. The spring is initially in natural length. Now a horizontal force F acts on block as shown. Then the maximum extension in spring is equal to maximum compression in spring.

STATEMENT-2 : To compress and to expand an ideal unstretched spring by equal amount, same work is to be done on spring

Statement I : Trace of matrix  A =  is equal to a₁₁ + a₂₂ + a₃₃
Statement II : Trace of a matrix is equal to sum of its diagonal elements.

The trace has several properties that are used to prove important results in matrix algebra and its applications.
 Let A and B be two K X K matrices. Then,

Statement I : The inverse of the matrix A    does not exist.
Statement II : |A|   .

the focus of parabola (y – k)² = 4 (x – h) always lies between the line x + y = 1 and x + y = 3 then  -

If the parabola y² = 4ax passes through (3, 2), then length of latus rectum of the parabola is

The value of 'λ' such that vertex of parabola y = x² + 2λx + 13 is 4 unit above x axis & lies in first quadrant is

PSQ is a focal chord of a parabola whose focus is S & vertex A . PA and QA are produced to meet the directrix in R and T respectively then 

In the figure shown initially spring is in unstretched state & blocks are at rest. Now 100 N force is applied on block A & B as shown in the figure. After some time velocity of 'A' becomes 2 m/s & that of 'B' is 4 m/s & block A displaced by amount 10 cm and spring is stretched by amount 30 cm. Then work done by spring (in joule) force on A will be

In the figure, the ball A is released from rest when the spring is at its natural length. For the block B, of mass M to leave contact with the ground at some stage, the minimum mass of A must be:

In the track shown in figure section AB is a quadrant of a circle of 1 metre radius. A block is released at A and slides without friction until it reaches B. After B it moves on a rough horizontal floor and comes to rest at distance 3 metres from B. What is the coefficient of friction between floor and body ?

A particle of mass m moving along a straight line experiences force F which varies with the distance x travelled as shown in the figure. If the velocity of the particle at x0 is , then velocity at 4 is:-

Power versus time graph for a given force is given below. Work done by the force up to time t(£ t0 )

A particle A of mass is moving in the positive direction of x. Its initial position is x = 0 & initial velocity is 1 m/s. The velocity at x = 10 is in m/s (use the graph given)

Block ‘A‘ is hanging from a vertical spring and is at rest. Block ‘B‘ strikes the block ‘A’ with velocity ‘v‘ and sticks to it. Then the value of ‘ v ‘ for which the spring just attains natural length is

Statement 1:Sound waves cannot propagate through vacuum but light waves can
Statement 2:Sound waves cannot be polarised but light waves can be polarized

Straight line x + my + n = 0 touches parabola y² = 4ax if n = am^k then k =