1. For what value of n would the n^th term of the series 3, 10, 17, ... and that of 63, 65, 67, ... be the same?

2. Find the three numbers a, b, and c between 2 and 18 such that their sum is 25. The numbers 2, a, and b are in Arithmetic Progression and  b, c, and 18 are in Geometric Progression.

3. In an Arithmetic Progression, the sum of the first 10 terms is 175 and the sum of the next 10 terms is 475. Find the Arithmetic Progression.

4. If

are in Arithmetic Progression, show that

are also in Arithmetic Progression.

5. A survey of 500 farmers in a state showed the following:
125 grew only wheat;
110 grew only corn;
90 grew only ragi;
200 grew wheat;
60 grew wheat and corn;
50 grew wheat and ragi; and
180 grew corn.
Find the number of farmers who
(i) grew atleast one of the three.
(ii) grew all the three.
(iii) did not grow any of the three.
(iv) grew exactly two of the three.

6. If f(x) = 3+x, g(x) = x², h(x) = 1/x, show that the composition of functions is associative.

7. A person remits a sum of $500 per month in a Recurring Deposit account of a bank. He gets a sum of $21,663 at the end of 3 years. What is the rate of interest given by the bank?

8. Find the Principal if the difference between Simple Interest and Compound Interest is $61 at 5% per annum for 3 years.

9. A solid cylinder has a total surface area of 231 cm². Its curved Surface Area is

of the total surface area. Find the volume of the cylinder.

10. a sector of a circle of radius 12 centimeters has an angle 120°. It is rolled and the two radii are joined together to form a cone. What is the volume of the cone?

11. A cup has the shape of a hemisphere surmounted by a cylinder. The diameter of the hemisphere is 6 centimeters. What is its volume?

12. Find the value of k for which the equation
(k-12)x² + 2(k-12)x + 2 = 0 has equal roots.

13. Factorize:

.

14. Simplify:-

.

15. Find A - B if

.