English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

Solve (a – b) x + (a + b) y = `a^2 – 2ab – b^2 (a + b) (x + y) = a^2 + b^2`

The sum of three numbers in A.P. is –3, and their product is 8. Find the numbers

Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120

Divide 32 into four parts which are in A.P. such that the product of extremes is to the product of means is 7 : 15.

Find the sum of first 20 terms of the following A.P. : 1, 4, 7, 10, ........

Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22

Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3

How many terms of the series 54, 51, 48, …. be taken so that their sum is 513 ? Explain the double answer

If the m^th term of an A.P. is 1/n and the n^th term is 1/m, show that the sum of mn terms is (mn + 1)

If the term of m terms of an A.P. is the same as the sum of its n terms, show that the sum of its (m + n) terms is zero

The sum of n, 2n, 3n terms of an A.P. are S₁ , S₂ , S₃ respectively. Prove that S₃ = 3(S₂ – S₁ )

The sum of n terms of three arithmetical progression are S₁ , S₂ and S₃ . The first term of each is unity and the common differences are 1, 2 and 3 respectively. Prove that S₁ + S₃ = 2S₂

The sum of the first p, q, r terms of an A.P. are a, b, c respectively. Show that `\frac { a }{ p } (q – r) + \frac { b }{ q } (r – p) + \frac { c }{ r } (p – q) = 0`

The ratio of the sum use of n terms of two A.P.’s is (7n + 1) : (4n + 27). Find the ratio of their m^th terms

The ratio of the sums of m and n terms of an A.P. is m² : n². Show that the ratio of the m^th and n^th terms is (2m – 1) : (2n – 1)

Without solving, examine the nature of roots of the equation 2x² + 2x + 3 = 0

Without solving, examine the nature of roots of the equation 2x² – 7x + 3 = 0

Without solving, examine the nature of roots of the equation x² – 5x – 2 = 0

Without solving, examine the nature of roots of the equation 4x² – 4x + 1 = 0

For what value of m, are the roots of the equation (3m + 1)x² + (11 + m) x + 9 = 0 equal?