English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

Find an acute angle θ when `(cos θ - sin θ)/(cos θ + sin θ) = (1 - sqrt(3))/(1 + sqrt(3))`

If θ is an acute angle of a right angled triangle, then which of the following equation is not true?

If θ is an acute angle and sin θ = cos θ, find the value of tan² θ + cot² θ – 2.

Evaluate 2 sec² θ + 3 cosec² θ – 2 sin θ cos θ if θ = 45°.

If sin θ – cos θ = 0, then find the value of sin⁴ θ + cos⁴ θ.

(3 sin² 30° – 4 cos² 60°) is equal to ______.

In a right triangle PQR, right angled at Q. If tan P = `sqrt(3)`, then evaluate 2 sin P cos P.

In ΔBC, right angled at C, if tan A = `8/7`, then the value of cot B is ______.

Evaluate: 5 cosec² 45° – 3 sin² 90° + 5 cos 0°.

If A(4, 3), B(-1, y) and C(3, 4) are the vertices of a right triangle ABC, right-angled at A, then find the value of y.

If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b). Prove that bx = ay.

The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) and R(–3, 6), find the coordinates of P.

If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.

If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB.

If the point P(2, 2) is equidistant from the points A(–2, k) and B(–2k, –3), find k. Also, find the length of AP.

Find the distance between two points

(i) P(–6, 7) and Q(–1, –5)

(ii) R(a + b, a – b) and S(a – b, –a – b)

(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`

If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.

Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.

Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.

Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.