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1. If a and b are distinct integers, prove that \(a-b\) is a factor of \(a^n-b^n\), whenever n is a positive integer.

Binomial Theorem

Miscellaneous Exercise

Ncert Solutions Class 11 Chapter 7 Binomial Theorem Miscellaneous Exercise Question 1
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Class 11

Binomial Theorem

Miscellaneous Exercise

1. If a and b are distinct integers, prove that \(a-b\) is a factor of \(a^n-b^n\), whenever n is a positive integer.

2. Evaluate \((\sqrt{3}+\sqrt{2})^6-(\sqrt{3}-\sqrt{2})^6\).

3. Find the value of \((a^2+\sqrt{a^2-1})^4+(a^2-\sqrt{a^2-1})^4\).

4. Find an approximation of \((0.99)^5\) using the first three terms of its expansion.

5. Expand using Binomial Theorem \((1+\frac{x}{2}-\frac{2}{x})^4\), x≠0.

6. Find the expansion of \((3x^2-2ax+3a^2 )^3\) using binomial theorem.