English Medium Class 10 - CBSE Important Questions

How many multiples of 4 lie between 10 and 205?

In an A.P., if S_n = 3n² + 5n and a_k = 164, find the value of k.

If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.

The ratio of the 11^th term to the 18^th term of an AP is 2 : 3. Find the ratio of the 5^th term to the 21^st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.

Write the next two terms of the A.P.: `sqrt(27), sqrt(48), sqrt(75)`......

Find the sum of first 16 terms of the A.P. whose n^th term is given by an = 5n – 3.

Find the sum of first 25 terms of the A.P. whose nth term is given by a_n = 5 + 6n. Also, find the ratio of 20^th term to 45^th term.

If the vertices of ΔABC  be A(1, -3) B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p

Find the point on the y-axis which is equidistant from the points (5, −2) and (−3, 2).

The point R divides the line segment AB, where A(−4, 0) and B(0, 6) such that AR=34AB.">AR = `3/4`AB. Find the coordinates of R.

In what ratio does the point P(−4, y) divides the line segment joining the points A(−6, 10) and B(3, −8)? Hence find the value of y.

The distance of the point P(–6, 8) from the origin is ______.

The distance of the point (–6, 8) from x-axis is ______.

If cot θ = `7/8` evaluate `((1+sin θ )(1-sin θ))/((1+cos θ)(1-cos θ))`.

Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.

Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`

Find A if tan 2A = cot (A-24°).

Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°.

Prove that: 2(sin⁶ θ + cos⁶ θ) – 3 (sin⁴ θ + cos⁴ θ) + 1 = 0.

A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.