Prove the following by using the princip | Class 11 Mathematics Chapter Principle of Mathemetical Induction, Principle of Mathemetical Induction NCERT Solutions

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 first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.

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 30th installment?

Find the sum to n terms of the series whose nth terms is given by n² + 2n

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.

Given a G.P. with a = 729 and 7th term 64, determine S₇.

Find the equation of the circle with centre (–2, 3) and radius 4

Insert two numbers between 3 and 81 so that the resulting sequence is G.P.

If the sum of n terms of an A.P. is 3n² + 5n and its mth term is 164, find the value of m.

Find a G.P. for which sum of the first two terms is –4 and the fifth term is 4 times the third term.

Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4th by 18.