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

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 ____________.

The diagonal elements of a skew symmetric matrix are ____________.

If A = [a_ij] is a skew-symmetric matrix of order n, then ______.

Find `int (dx)/sqrt(4x - x^2)`

Find: `int (dx)/(x^2 - 6x + 13)`

If `[(2, 0),(5, 4)]` = P + Q, where P is symmetric, and Q is a skew-symmetric matrix, then Q is equal to ______.

Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is ______.

The derivative of x^2x w.r.t. x is ______.

The value of |A|, if A = `[(0, 2x - 1, sqrt(x)),(1 - 2x, 0, 2sqrt(x)),(-sqrt(x), -2sqrt(x), 0)]`, where x ∈ R⁺, is ______.