English Medium Class 10 - CBSE Important Questions for Mathematics

Find the value of 'k' so that the quadratic equation 3x² – 5x – 2k = 0 has real and equal roots.

Determine the A.P. whose 3^rd term is 16 and the 7^th term exceeds the 5^th term by 12.

The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

If the ratio of sum of the first m and n terms of an AP is m² : n², show that the ratio of its  m^th and n^th terms is (2m − 1) : (2n − 1) ?

The next term of the A.P. \[\sqrt{7}, \sqrt{28}, \sqrt{63}\] is ______.

The Sum of first five multiples of 3 is ______.

If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.

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.

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°).