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

Statement I : The inverse of the matrix   does not exist.
Statement II : The matrix   is singular. [ = 0, since R₂ = 2R₁]

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 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 maximum compression of the spring after collision is –

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 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 centre of mass of system of block A, B & C is-

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 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-

Two blocks A and B are joined together with a compressed spring. When the system is released, the two blocks appear to be moving with unequal speeds in the opposite directions as shown in figure. Select incorrect statement(s)

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 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