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

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 ______.

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 ____________.

Find the general solution of the differential equation `"dy"/"dx" = y/x`.

A solution of the differential equation `("dy"/"dx")^2 - x "dy"/"dx" + y` = 0 is ______.

`lim_("x" -> 0)(1 - "cos x")/"x"^2` is equal to ____________.

`lim_("x" -> -2) sqrt ("x"^2 + 5 - 3)/("x" + 2)` is equal to ____________.

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

If A = `[(3, "x" - 1),(2"x" + 3, "x" + 2)]` is a symmetric matrix, then x = ____________.

If A is any square matrix, then which of the following is skew-symmetric?