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

If a₁, a₂, ..., an are in A.P. with common difference d (where d ≠ 0); then the sum of the series sin d (cosec a1 cosec a₂ + cosec a₂ cosec a₃ + ...+ cosec a_n–1 cosec a_n) is equal to cot a₁ – cot a_n 

If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad

In an A.P. the p^th term is q and the (p + q)^th term is 0. Then the q^th term is ______.

The first term of an A.P.is a, and the sum of the first p terms is zero, show that the sum of its next q terms is `(-a(p + q)q)/(p - 1)`

A man saved Rs 66000 in 20 years. In each succeeding year after the first year he saved Rs 200 more than what he saved in the previous year. How much did he save in the first year?

A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. Find his salary for the tenth month

A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. What is his total earnings during the first year?

Find the r^th term of an A.P. sum of whose first n terms is 2n + 3n² 

If the sum of p terms of an A.P. is q and the sum of q terms is p, show that the sum of p + q terms is – (p + q). Also, find the sum of first p – q terms (p > q).

If the sum of n terms of an A.P. is given by S_n = 3n + 2n², then the common difference of the A.P. is ______.

If 9 times the 9^th term of an A.P. is equal to 13 times the 13^th term, then the 22^nd term of the A.P. is ______.

If in an A.P., S_n = qn² and S_m = qm², where S_r denotes the sum of r terms of the A.P., then Sq equals ______.

Let S_n denote the sum of the first n terms of an A.P. If S_2n = 3S_n then S_3n: S_n is equal to ______.

The sum of terms equidistant from the beginning and end in an A.P. is equal to ______.

Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.

If the sum of n terms of a sequence is quadratic expression then it always represents an A.P

Find the distance of the point whose position vector is `(2hati + hatj - hatk)` from the plane `vecr * (hati - 2hatj + 4hatk)` = 9

Find the distance of the point (– 2, 4, – 5) from the line `(x + 3)/3 = (y - 4)/5 = (z + 8)/6`

Find the distance of the point (–1, –5, – 10) from the point of intersection of the line `vecr = 2hati - hatj + 2hatk + lambda(3hati + 4hatj + 2hatk)` and the plane `vecr * (hati - hatj + hatk)` = 5.

The distance of a point P(a, b, c) from x-axis is ______.