English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

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

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

How many terms of the AP 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 AP is given by (−4n + 15). Find the sum of first 20 terms of this AP?

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

Find the value(s) of k so that the quadratic equation 3x² − 2kx + 12 = 0 has equal roots ?

The Sum of first five multiples of 3 is ______.

If the common differences of an A.P. is 3, then a₂₀ − a₁₅ is