Arts (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

Find the middle terms in the expansions of `(x/3 + 9y)^10`

The coefficients of the (r – 1)^th, r^th and (r + 1)^th terms in the expansion of (x + 1)ⁿ are in the ratio 1:3:5. Find n and r.

Prove that the coefficient of xⁿ in the expansion of (1 + x)²ⁿ is twice the coefficient of xⁿ in the expansion of (1 + x)^2n–1 .

Find a positive value of m for which the coefficient of x² in the expansion

(1 + x)^m is 6

Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of `(root4 2 + 1/ root4 3)^n " is " sqrt6 : 1`

Find the sum of odd integers from 1 to 2001.

In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20^th term is –112.

How many terms of the A.P.  -6 , `-11/2` , -5... are needed to give the sum –25?

In an A.P., if p^th term is 1/q and qth term is 1/p,  prove that the sum of first pq terms is 1/2 (pq + 1) where `p != q`

If the sum of n terms of an A.P. is (pn + qn²), where p and q are constants, find the common difference.

The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18^th terms

If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.

Sum of the first p, q and r terms of an A.P. are a, b and c, respectively.

Prove that `a/p (q - r) + b/q (r- p) + c/r (p - q) = 0`

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