English Medium कक्षा १० - CBSE Question Bank Solutions

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

If α and β are roots of the quadratic equation x² – 7x + 10 = 0, find the quadratic equation whose roots are α² and β².

The distance of the point (–4, 3) from y-axis is ______.

The coordinates of the point where the line 2y = 4x + 5 crosses x-axis is ______.

If 'p' is a root of the quadratic equation x² – (p + q) x + k = 0, then the value of 'k' is ______.

The roots of the equation x² + 3x – 10 = 0 are ______.

The distance of the point (–1, 7) from x-axis is ______.

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.

The distance of the point (3, 5) from x-axis (in units) is ______.

Assertion (A): The point (0, 4) lies on y-axis.

Reason (R): The x-coordinate of a point on y-axis is zero.

Find the roots of the quadratic equation x² – x – 2 = 0.

The boilers are used in thermal power plants to store water and then used to produce steam. One such boiler consists of a cylindrical part in middle and two hemispherical parts at its both ends.

Length of the cylindrical part is 7 m and radius of cylindrical part is `7/2` m.

Find the total surface area and the volume of the boiler. Also, find the ratio of the volume of cylindrical part to the volume of one hemispherical part.

(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°.

Distance of the point (6, 5) from the y-axis is ______.

Statement A (Assertion): Total Surface area of the top is the sum of the curved surface area of the hemisphere and the curved surface area of the cone.

Statement R( Reason): Top is obtained by joining the plane surfaces of the hemisphere and cone together.