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

Prove that 

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.

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.

A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?

If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are .

The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.

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?

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

Find the derivative of 99x at x = l00.

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

Find the derivative of x at x = 1.

For what values of x, the numbers are in G.P?