English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

`(1 + tan^2 "A")/(1 + cot^2 "A")` is equal to ______.

If cos A + cos² A = 1, then sin² A + sin⁴ A is equal to ______.

If cos (81 + θ)° = sin`("k"/3 - theta)^circ` where θ is an acute angle, then the value of k is ______.

3 sin² 20° – 2 tan² 45° + 3 sin² 70° is equal to ______.

If sin 2A = `1/2` tan² 45° where A is an acute angle, then the value of A is ______.

`(sin theta)/(1 + cos theta)` is ______.

If x sin (90° – θ) cot (90° – θ) = cos (90° – θ), then x is equal to ______.

The value of cos 0°. cos 1°. cos 2°. cos 3°… cos 89° cos 90° is ______.

If A and (2A – 45°) are acute angles such that sin A = cos (2A – 45°), then tan A is equal to ______.

If sin θ + sin² θ = 1, then cos² θ + cos⁴ θ = ______.

5 tan² A – 5 sec² A + 1 is equal to ______.

In the figure given below, ABCD is a square of side 14 cm with E, F, G and H as the mid points of sides AB, BC, CD and DA respectively. The area of the shaded portion is ______.

The polynomial equation x(x + 1) + 8 = (x + 2) (x – 2) is:

Which of the following are the roots of the quadratic equation, x² – 9x + 20 = 0 by factorisation?

If the surface areas of two spheres are in ratio 16 : 9, then their volumes will be in the ratio ______.

If the volumes of a cube is 1728 cm³, the length of its edge is equal to ______.

The radius of spherical balloon increases from 8 cm to 12 cm. The ratio of the surface areas of balloon in two cases is ______.

Two cubes each of volume 8 cm³ are joined end to end, then the surface area of the resulting cuboid is ______.

The total surface area of a solid hemisphere of radius r is ________.

Eight solid sphere of same size are made by melting a solid metallic cylinder of base diameter 6 cm and height 32 cm. The diameter of each sphere is ______.