# 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.