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

If A and B are matrices of same order, then (AB′ – BA′) is a ______.

______ 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.

`2^(cos^(2_x)`

`8^x/x^8`

`log (x + sqrt(x^2 + "a"))`

`log [log(logx^5)]`

If x^m . yⁿ = (x + y)^m+n, prove that `"dy"/"dx" = y/x`

If y = `log ((1 - x^2)/(1 + x^2))`, then `"dy"/"dx"` is equal to ______.