# Lecture 5 Chapter 8 Binomial Theorem Class 11

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 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.