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