Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions

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 ____________.

`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?

If A `= [(6,8,5),(4,2,3),(9,7,1)]` is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is ____________.

If `"f" ("x") = sqrt (1 + "cos"^2 ("x"^2)), "then the value of f'" (sqrtpi/2)` is ____________.

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

If y `= "e"^(3"x" + 7), "then the value" |("dy")/("dx")|_("x" = 0)` is ____________.