Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

Prove that (A^–1)′ = (A′)^–1, where A is an invertible matrix.

Show that if the determinant ∆ = `|(3, -2, sin3theta),(-7, 8, cos2theta),(-11, 14, 2)|` = 0, then sinθ = 0 or `1/2`.

If `|(2x, 5),(8, x)| = |(6, -2),(7, 3)|`, then value of x is ______.

Show that the local maximum value of `x + 1/x` is less than local minimum value.

Find the maximum and minimum values of f(x) = secx + log cos²x, 0 < x < 2π

Find the area of greatest rectangle that can be inscribed in an ellipse `x^2/"a"^2 + y^2/"b"^2` = 1

Find the difference between the greatest and least values of the function f(x) = sin2x – x, on `[- pi/2, pi/2]`

An isosceles triangle of vertical angle 2θ is inscribed in a circle of radius a. Show that the area of triangle is maximum when θ = `pi/6`

The values of a for which y = x² + ax + 25 touches the axis of x are ______.

If f(x) = `1/(4x^2 + 2x + 1)`, then its maximum value is ______.

Minimum value of f if f(x) = sinx in `[(-pi)/2, pi/2]` is ______.

The maximum value of sinx + cosx is ______.

At what point, the slope of the curve y = – x³ + 3x² + 9x – 27 is maximum? Also find the maximum slope.

Prove that f(x) = sinx + `sqrt(3)` cosx has maximum value at x = `pi/6`

At x = `(5pi)/6`, f(x) = 2 sin3x + 3 cos3x is ______.

The least value of the function f(x) = `"a"x + "b"/x` (where a > 0, b > 0, x > 0) is ______.

Evaluate `int tan^8 x sec^4 x"d"x`

Find `int "dx"/(2sin^2x + 5cos^2x)`

Find `int x^2tan^-1x"d"x`

`int "e"^x (cosx - sinx)"d"x` is equal to ______.