Question

Assertion :If the greatest term in the expansion ${(1+x)}^{2n}$ has also the greatest coefficient, then $\frac{n}{n+1}<x<\frac{n+1}{n}$ Reason: $T_n<T_{n+1}>T_{n+2}$

• A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion,
• B. Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of 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 & Reason is correct explanation of Assertion,

For numerically greatest term,
$T_n<T_{n+1}>T_{n+2}$
Hence
${}^{2n}{C}_{n-1}{x}^{n-1}<{}^{2n}{C}_n{x}^n$
$\frac{n}{n+1}<x$
And
$T_{n+1}>T_{n+2}$
${}^{2n}{C}_n{x}^n>{}^{2n}{C}_{n+1}{x}^{n+1}$
$x>\frac{n}{n+1}$
$x<\frac{n+1}{n}$
Hence $xϵ(\frac{n}{n+1},\frac{n+1}{n})$