## Lecture 4 Middle Terms Binomial Theorem Class 11

Never give up. Great things take time. Be patient.

# Lecture - 4 Chapter 8 Binomial Theorem

Method to find Middle term in a Binomial Expansion

 NCERT Exercise 8.2

Find the middle terms in the expansions of

Question 7. $$\left ( 3 – \frac{x^3}{6} \right )^7$$

Question 8. $$\left ( \frac{x}{3} + 9y \right )^{10}$$

Question 10. The coefficients of the $$(r-1)^{th}, r^{th} \text{ and } (r+1)^{th}$$ terms in the expansion of $$(x+1)^n$$ are in the ratio 1 : 3 : 5. Find n and r.

Question 11. Prove that the coefficient of $$x^n$$ in the expansion of $$(1+x)^{2n}$$ is twice the coefficient of $$x^n$$ in the expansion of $$(1+x)^{2n-1}$$.

 NCERT Miscellaneous Exercise

Question 2. Find a if the coefficients of $$x^2 \text{ and } x^3$$ in the expansion of $$(3+ax)^9$$ are equal.

Question 5. Evaluate $$(\sqrt{3}+\sqrt{2})^6-(\sqrt{3}-\sqrt{2})^6$$.

Question 6. Find the value of $$\left ( a^2 + \sqrt{a^2-1} \right )^4 + \left ( a^2 – \sqrt{a^2-1} \right )^4$$

Question 7. Find an approximation of $$(0.99)^5$$ using the first three terms of its expansion.