English Medium Class 10 - CBSE Important Questions

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.

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 ______.

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.

There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole.

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

If 1 + sin²θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.

`(cos^2 θ)/(sin^2 θ) - 1/(sin^2 θ)`, in simplified form, is ______.

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

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