Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + 4 × 5 + …

Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

How many terms of G.P. 3, 3², 3³, … are needed to give the sum 120?

Find the sum of all numbers between 200 and 400 which are divisible by 7.

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.

The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q² = ps.

Find the derivative of x at x = 1.

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.

Name the octants in which the following points lie:

(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (–4, 2, 5), (–3, –1, 6), (2, –4, –7)

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

Find the sum to n terms of the series 5² + 6² + 7² + ... + 20²

If the first and the nth term of a G.P. are a ad b, respectively, and if P is the product of n terms, prove that P² = (ab)ⁿ.

How many terms of G.P. 3, 3², 3³, … are needed to give the sum 120?