Science (English Medium) Class 11 - CBSE Question Bank Solutions

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)

if `(a^n + b^n)/(a^(n-1) + b^(n-1))` is the A.M. between a and b, then find the value of n.

Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7^th and (m – 1)^th numbers is 5:9. Find the value of m.

A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs 5 every month, what amount he will pay in the 30^th installment?

The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.