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# 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.