1. If

be the sum of n terms of three arithmetic series, the first term of each being 1 and the common differences being 1, 2, and 3 respectively, prove that

.

2. Find the value of

if

.

3. Find 5 numbers in Geometric Progression such that their product is 32 and the product of the last two numbers is 108.

4. Using Venn Diagram, veriy

.

5. Given f(x) = 5x+2, g(x) = 2x-3, h(x) = 3x+1, verify
fo(goh) = (fog)oh.

6. Roger borrowed $6000 at 6% simple interest per anum and immediately lent it to Neil at 6% compound interest. How much did Roger gain after 3 years?

7. Martin invested $500 every month for 2 years in a bank and collected $12500 at the end of two years. What is the rate of simple interest paid by the bank on the recurring deposit?

8. Through a pipe of diameter 14 centimeters, water flows uniformly at the rate of 3 kilometers per hour. How much water would flow through it in 10 minutes?

9. A hollow spherical shell has an inner radius of 8 centimeters. If the volume of the material used is

cubic centimeters, what is the thickness of the shell?

10. A sector containing an angle of 90° is cut from a circle of radius 20 centimeters and folded into a cone. Find the curved surface area of the cone.