Commerce (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

______ matrix is both symmetric and skew-symmetric matrix.

Sum of two skew-symmetric matrices is always ______ matrix.

If A is a symmetric matrix, then A³ is a ______  matrix.

If A is a skew-symmetric matrix, then A² is a ______.

If A is skew-symmetric, then kA is a ______. (k is any scalar)

If A and B are symmetric matrices, then AB – BA is a ______.

If A and B are symmetric matrices, then BA – 2AB is a ______.

If A is symmetric matrix, then B′AB is ______.

If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.

If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.

If A and B are any two matrices of the same order, then (AB)′ = A′B′.

AA′ is always a symmetric matrix for any matrix A.

If A is skew-symmetric matrix, then A² is a symmetric matrix.

The function f(x) = cot x is discontinuous on the set ______.

Trigonometric and inverse-trigonometric functions are differentiable in their respective domain.

f(x) = x^x has a stationary point at ______.

If P is of order 2 x 3 and Q is of order 3 x 2, then PQ is of order ____________.

If A and B are symmetric matrices of the same order, then ____________.

Solve the differential equation `"dy"/"dx" + y/x` = x².

`("e"^(-2sqrt(x))/sqrt(x) - y/sqrt(x))("d"x)/("d"y) = 1(x ≠ 0)` when written in the form `"dy"/"dx" + "P"y` = Q, then P = ______.