1. The first term of an Arithmetic Progression is 1 and the last term is 58.5. If their sum is 714, find the number of terms.

2. Find the geometric progression whose fifth term is

and the seventh term is

. Also find which term is

.

3. The seventh term of an Arithmetic Progression is -15 and the sixteenth term is 30. Find the sum of the first 19 terms.

4. Sohail invests $25 in a bank at the beginning of each month for 36 months. If he gets $1066.50 at the end of 36 months, what is the rate of interest?

5. Mohammad invested an amount of $12,000 in a Fixed Deposit with a bank for 3 years paying interest @ 12% per annum. If the bank compounded interest half yearly, what is the maturity value of the deposit?

6. A solid metal sphere of radius 3.4 centimeters is dropped into a cylindrical can containing water. The base diameter of the cylindrical can is 8.2 centimeters. Find the rise in level of water to the nearest millimeter.

7. A cone of height 8 centimeters and base radius 6 centimeters is opened out to form a sector. Find the perimeter of the sector.

8. A cone and a cylinder have bases of equal area. The height of the cone is 9 times that of the cylinder. If the cylinder can hold 150 cubic centimeters of water, what is thecapacity of the cone?

9. If  a = x²-2x+1, b = x²-3x+2, c = 6x-6, d = 3x-6, then find

and

.

10. Find the quotient and the remainder when

is divided by (2x+1).

11. If a, b, c are real, show that the following equation has real roots:

.

12. Find the value of k if the sum of the roots of the following equation is three times their product:

.