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