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

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 ____________.

The points (1, 2, 3), (–2, 3, 4) and (7, 0, 1) are collinear.

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

Find the equation of the plane through the points (2, 1, 0), (3, –2, –2) and (3, 1, 7).

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 ____________.

Find the general solution of the following differential equation:

`x (dy)/(dx) = y - xsin(y/x)`

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

The general solution of the differential equation y dx – x dy = 0 is ______.

Solve the differential equation: y dx + (x – y²)dy = 0

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 ______.

Two vectors `veca = a_1 hati + a_2 hatj + a_3 hatk` and `vecb = b_1 hati + b_2 hatj + b_3 hatk` are collinear if ______.

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 ______.

If `veca = 4hati + 6hatj` and `vecb = 3hatj + 4hatk`, then the vector form of the component of `veca` along `vecb` is ______.

The general solution of the differential equation ydx – xdy = 0; (Given x, y > 0), is of the form

(Where 'c' is an arbitrary positive constant of integration)