Exercise 8.1 Chapter 8 Binomial Theorem Lecture 2

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NCERT Exercise 8.1

Question 4. $\left ( \frac{x}{3}+\frac{1}{x} \right )^5$

Question 5. $\left ( x + \frac{1}{x} \right )^6$

Using binomial theorem, evaluate each of the following:

Question 6. $(96)^3$

Question 7. $(102)^5$

Question 8. $(101)^4$

Question 9. $(99)^5$

Question 10. Using Binomial Theorem, indicate which number is larger $(1.1)^{10000}$ or 1000.

Question 11. Find $(a+b)^4 -(a-b)^4$ . Hence, evaluate $(\sqrt{3}+\sqrt{2})^4-(\sqrt{3}-\sqrt{2})^4$ .

Question 12. Find $(x+1)^6+(x-1)^6$ . Hence or otherwise evaluate $(\sqrt{2}+1)^6-(\sqrt{2}-1)^6$ .

Question 13. Show that $9^{n+1}-8n-9$ is divisible by 64, whenever n is a positive integer.

Question 14. Prove that $\sum_{r=0}^{n} 3^r {^nC_r} = 4^r$ .