Rohan's mother gave him ₹ 3xy² and his father gave him ₹ 5(xy²+2). Out of this total money he spent ₹ (10–3xy²) on his birthday party. How much money is left with him?

In a rectangular plot, 5 square flower beds of side (x + 2) metres each have been laid (see figure given below). Find the total cost of fencing the flower beds at the cost of ₹ 50 per 100 metres:

A wire is (7x – 3) metres long. A length of (3x – 4) metres is cut for use. Now, answer the following questions:

(a) How much wire is left?

(b) If this left out wire is used for making an equilateral triangle. What is the length of each side of the triangle so formed?

(i) A triangle is made up of 2 red sticks and 1 blue sticks . The length of a red stick is given by r and that of a blue stick is given by b. Using this information, write an expression for the total length of sticks in the pattern given below:

(ii) In the given figure, the length of a green side is given by g and that of the red side is given by p.

Write an expression for the following pattern. Also write an expression if 100 such shapes are joined together.

The sum of first n natural numbers is given by Find

(i) The sum of first 5 natural numbers.

(ii) The sum of first 11 natural numbers.

(iii) The sum of natural numbers from 11 to 30.