Statement I : The determinant of matrix  
Statement II : The determinant of a skew symmetric matrix of odd order is zero.

A spring lies along an x axis attached to a wall at one end and a block at the other end. The block rests on a frictionless surface at x = 0. A force of constant magnitude F is applied to the block that begins to compress the spring, until the block comes to a maximum displacement During the first half of the motion, applied force transfers more energy to the

A spring lies along an x axis attached to a wall at one end and a block at the other end. The block rests on a frictionless surface at x = 0. A force of constant magnitude F is applied to the block that begins to compress the spring, until the block comes to a maximum displacement During the displacement, which of the curves shown in the graph best represents the work done on the spring block system by the applied force.

A spring lies along an x axis attached to a wall at one end and a block at the other end. The block rests on a frictionless surface at x = 0. A force of constant magnitude F is applied to the block that begins to compress the spring, until the block comes to a maximum displacement . During the displacement, which of the curves shown in the graph best represents the kinetic energy of the block?

A block of mass m slides down a wedge of mass m as shown. The whole system is at rest, when the height of the block is h = 10 m. Above the ground. The wedge surface is smooth and gradually flattens. There is no friction between wedge and ground. If there is no friction anywhere, the speed of the wedge, as the block leaves the wedge is :

A block of mass m slides down a wedge of mass m as shown. The whole system is at rest, when the height of the block is h = 10 m. Above the ground. The wedge surface is smooth and gradually flattens. There is no friction between wedge and ground. If there would have been friction between wedge and block, which of the following quantities would still remain conserved?

A block of mass m slides down a wedge of mass m as shown. The whole system is at rest, when the height of the block is h = 10 m. Above the ground. The wedge surface is smooth and gradually flattens. There is no friction between wedge and ground. As the block slides down, which of the following quantities associated with the system remains conserved?

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: