English Medium इयत्ता १० - CBSE Question Bank Solutions

Five years ago, a woman’s age was the square of her son’s age. Ten years hence, her age will be twice that of her son’s age. Find:

1. the age of the son five years ago.
2. the present age of the woman.

The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates of point of trisection are ______.

The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio ______.

sin (45° + θ) – cos (45° – θ) is equal to ______.

If `sqrt2 sin (60° – α) = 1` then α is ______.

The value of sin² 30° – cos² 30° is ______.

If cos (40° + A) = sin 30°, then value of A is ______.

If cosec θ - cot θ = `1/3`, the value of (cosec θ + cot θ) is ______.

`(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 ______.