English Medium कक्षा १० - CBSE Question Bank Solutions

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?

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

x² – 2x – 8

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

4s² – 4s + 1

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.

6x² – 3 – 7x

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.

4u² + 8u

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

t² – 15

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

3x² – x – 4