Question

Assertion :The greatest coefficient in the expansion of ${(1+x)}^{2n+2}$ is $\frac{(2n+2)!}{{((n+1)!)}^2}$ Reason: The greatest coefficient in the expansion of ${(1+x)}^{2n}$ is the middle term.

• A. Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion,
• B. Both Assertion and Reason are correct but Reason is not the correct explahe nation for Assertion
• C. Assertion is true but Reason is false,
• D. Assertion is false but Reason is true.

Answer 1

The correct option is A Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion,

The greatest coefficient in $(1+x{)}^n$ type expansion, is the middle term.
Hence the greatest coefficient in $(1+x{)}^{2n+2}$ will be $(n+2)th$ term.
$={}^{2n+2}{C}_{n+1}$
$=\frac{(2n+2)!}{(n+1)!.(n+1)!}$