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

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 ______.

Two schools P and Q want to award their selected students on the values of discipline, politeness and punctuality. The school P wants to award Rs x each, Rs y each and Rs z each for the three respective values to its 3, 2 and 1 students with a total award money of Rs 1,000. School Q wants to spend Rs 1,500 to award its 4, 1 and 3 students on the respective values (by giving the same award money for the three values as before). If the total amount of awards for one prize on each value is Rs 600, using matrices, find the award money for each value.
Apart from the above three values, suggest one more value for awards.