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

The sum of the products of elements of any row with the co-factors of corresponding elements is equal to ______.

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 ______.

The value of cos²15° - cos²30° + cos²45° - cos²60° + cos²75° is ______.

The maximum value of sinx + cosx is ____________.

The minimum value of sinx - cosx is ____________.

If `"sec" theta = "x" + 1/(4 "x"), "x" in "R, x" ne 0,`then the value of  `"sec" theta + "tan" theta` is ____________.

If the graph of a differentiable function y = f (x) meets the lines y = – 1 and y = 1, then the graph ____________.

The function f : A → B defined by f(x) = 4x + 7, x ∈ R is ____________.