Two blocks A and B of masses m and 2m respectively are connected by a spring of spring constant k. The masses are moving to the right with a uniform velocity $v subscript 0 end subscript$ each, the heavier mass leading the lighter one. The spring is of natural length during this motion. Block B collides head on with a third block C of mass 2m. at rest, the collision being completely inelastic. The velocity of block B just after collision is-

Statement I : The order of the matrix A is 4 × 5 and that of B is 3 × 4. Then the matrix AB is not possible.
Statement II : AB is defined if number of columns of A = number of rows of B

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. If both A and B are square matrices of the same order, then both AB and BA are defined. If AB and BA are both defined, it is not necessary that AB = BA.

Statement I : The order of the matrix A is 4 × 5 and that of B is 3 × 4. Then the matrix AB is not possible.
Statement II : AB is defined if number of columns of A = number of rows of B

maths-

Statement I : The determinant of matrix $open square brackets table attributes columnalign center center center columnspacing 1em end attributes row 0 cell p minus q end cell cell p minus r end cell row cell q minus p end cell 0 cell q minus r end cell row cell r minus p end cell cell r minus q end cell 0 end table close square brackets equals 0$
Statement II : The determinant of a skew symmetric matrix of odd order is zero.

maths-General

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 $X subscript m a x end subscript$ 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 $X subscript m a x end subscript$ 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 $X subscript m a x end subscript$ . 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 = $open square brackets table attributes columnalign left left left columnspacing 1em end attributes row cell a subscript 11 a subscript 12 a subscript 13 end cell row cell a subscript 21 a subscript 22 a subscript 23 end cell row cell a subscript 31 a subscript 32 a subscript 33 end cell end table close square brackets$ 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 : Trace of matrix A = $open square brackets table attributes columnalign left left left columnspacing 1em end attributes row cell a subscript 11 a subscript 12 a subscript 13 end cell row cell a subscript 21 a subscript 22 a subscript 23 end cell row cell a subscript 31 a subscript 32 a subscript 33 end cell end table close square brackets$ 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 $equals open square brackets table attributes columnalign center center center columnspacing 1em end attributes row 1 4 cell negative 1 end cell row 2 3 0 row 0 1 2 end table close square brackets$ does not exist.
Statement II : |A| . $not equal to 0 open square brackets because vertical line A vertical line equals open vertical bar table attributes columnalign center center center columnspacing 1em end attributes row 1 4 cell negative 1 end cell row 2 3 0 row 0 1 2 end table close vertical bar equals open vertical bar table attributes columnalign center center center columnspacing 1em end attributes row 1 4 cell negative 1 end cell row 0 cell negative 5 end cell 2 row 0 1 2 end table close vertical bar equals negative 10 minus 2 equals negative 12 not equal to 0 close square brackets$

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