Commerce (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

Evaluate the definite integral:

`int_0^pi (sin^2  x/2 - cos^2  x/2) dx`

Evaluate the definite integral:

`int_0^2 (6x +3)/(x^2 + 4)` dx

Evaluate the definite integral:

`int_0^1 (xe^x + sin  (pix)/4)`

`int_1^(sqrt3)dx/(1+x^2) ` equals:

`int_0^(2/3) dx/(4+9x^2)` equals:

Evaluate : \[\int\frac{x \cos^{- 1} x}{\sqrt{1 - x^2}}dx\] .

Find `("d"^2"y")/"dx"^2`, if y = `"x"^-7`

`sin xy + x/y` = x² – y

sec(x + y) = xy

tan^–1(x² + y²) = a

(x² + y²)² = xy

If ax² + 2hxy + by² + 2gx + 2fy + c = 0, then show that `"dy"/"dx" * "dx"/"dy"` = 1 

If x sin (a + y) + sin a cos (a + y) = 0, prove that `"dy"/"dx" = (sin^2("a" + y))/sin"a"`

If y = tan^–1x, find `("d"^2y)/("dx"^2)` in terms of y alone.

The derivative of cos^–1(2x² – 1) w.r.t. cos^–1x is ______.

If y = 5 cos x – 3 sin x, then `("d"^2"y")/("dx"^2)` is equal to:

Derivative of cot x° with respect to x is ____________.

If y = `sqrt(ax + b)`, prove that `y((d^2y)/dx^2) + (dy/dx)^2` = 0.

If x = A cos 4t + B sin 4t, then `(d^2x)/(dt^2)` is equal to ______.

If y = tan x + sec x then prove that `(d^2y)/(dx^2) = cosx/(1 - sinx)^2`.