Evaluate 

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.

Find the sum to n terms of the series 3 × 1² + 5 × 2² + 7 × 3² + …

Find the sum to n terms of the sequence, 8, 88, 888, 8888…

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.

Solve 24x < 100, when
   (i)   x is a natural number.         (ii)   x is an integer.

Let the sum of n, 2n, 3n terms of an A.P. be S₁, S₂ and S₃, respectively, show that S₃ = 3 (S₂– S₁)

Using Binomial Theorem, indicate which number is larger (1.1)¹⁰⁰⁰⁰ or 1000.

How many 5–digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?

Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

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

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