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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.
