English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

Find the sum of first n terms of an AP whose nth term is (5 – 6n). Hence, find the sum of its first 20 terms.

The sum of the first n terms of an AP is (3n² + 6n). Find the nth term and the 15th term of this AP.

The sum of the first n terms of an AP is given by S_n = (3n² – 4n). Find its

1. nth term,
2. first term and
3. common difference.

The sum of the first n terms of an AP is `((5n^2)/2 + (3n)/2)`. Find the nth term and the 20th term of this AP.

The sum of the first n terms of an AP is `((3n^2)/2 + (5n)/2)`. Find its nth term and the 25th term.

How many terms of the A.P. 21, 18, 15, ... must be added to get the sum 0?

How many terms of the AP 63, 60, 57, 54, ... must be taken so that their sum is 693? Explain the double answer.

How many terms of the AP `20, 19 1/3 , 18 2/3, ...` must be taken so that their sum is 300? Explain the double answer.

Find the sum of all natural numbers between 200 and 400 which are divisible by 7.

Find the sum of all multiples of 9 lying between 300 and 700.

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) ?

Find the positive value(s) of k for which quadratic equations x² + kx + 64 = 0 and x² – 8x + k = 0 both will have real roots ?

Find the 25^th term of the AP \[- 5, \frac{- 5}{2}, 0, \frac{5}{2}, . . .\]

The fourth term of an A.P. is 11. The sum of the fifth and seventh terms of the A.P. is 34. Find its common difference.

Solve for x :

x² + 5x − (a² + a − 6) = 0

If x = −2 is a root of the equation 3x² + 7x + p = 1, find the values of p. Now find the value of k so that the roots of the equation x² + k(4x + k − 1) + p = 0 are equal.

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

If 1 is a root of the quadratic equation 3x² + ax – 2 = 0 and the quadratic equation a(x² + 6x) – b = 0 has equal roots, find the value of b ?

The nth term of an A.P. is given by (–4n + 15). Find the sum of first 20 terms of this A.P.

Draw a triangle PQR in which QR = 6 cm, PQ = 5 cm and times the corresponding sides of ΔPQR?