# Exercise 8.1 Chapter 8 Binomial Theorem Lecture 2

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# Lecture - 2 Chapter 8 Binomial Theorem

 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 $$\sum_{r=0}^{n} 3^r {^nC_r} = 4^r$$.