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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.