Part - 1

**Miscellaneous Exercise **

**Question 1.** Find *a*, *b* and *n* in the expansion of (a+b)^n if the first three terms of the expansion are 729, 7290 and 30375, respectively.

**Question 3.** Find the coefficient of x^5 in the product (1+2x)^6(1-x)^7 using binomial theorem.

**Question 4.** If *a *and *b* are distinct integers, prove that (a-b) is a factor of a^n-b^n, whenever *n* is a positive integer.

Part - 2

**Miscellaneous Exercise **

**Question 8.** Find *n*, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of \left ( \sqrt[4]{2}+\ \frac{1}{\sqrt[4]{3}} \right )^n is \sqrt{6} : 1.

**Question 9.** Expand using Binomial Theorem \left ( 1 + \frac{x}{2}- \frac{2}{x} \right )^4 , x \ne 0.

**Question 10.** Find the expansion of (3x^2-2ax+3a^2)^3 using binomial theorem.