It does not matter how slowly you go as long as you do not stop. – Confucius

# Lecture - 5 Chapter 8 Binomial Theorem

NCERT 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.

**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.