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