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

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 ____________.

Given that A is a square matrix of order 3 and |A| = −4, then |adj A| is equal to:

Given that A = [a_ij] is a square matrix of order 3 × 3 and |A| = −7, then the value of `sum_("i" = 1)^3 "a"_("i"2)"A"_("i"2)`, where A_ij denotes the cofactor of element a_ij is:

If matrices A and B are inverse of each other then ____________.

If A `= [(5, "x"),("y", 0)]` and A = A' then ____________.

If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximating error in calculating its volume.

Find the approximate value of f(3.02), where f(x) = 3x² + 5x + 3

Find the general solution of the following differential equation:

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

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

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

Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`

Find: `int e^x.sin2xdx`

Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`

Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.

Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.

Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.

Find `int e^x ((1 - sinx)/(1 - cosx))dx`.