Question

Find the middle term(s) in the expansion of $(a+b{)}^{20}$

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is A

In the expansion of $(a+b{)}^n$,if n is even , there wiil be only one middle term, which is $(\frac{n+2}{2}{)}^{th}$ term.

In this case n = 20.The middle term will be $(\frac{20+2}{2}{)}^{th}$ term or ${11}^{th}$ term.

The middle is ${11}^{th}$ term

$T_{11}=T_{10+1}={}^{20}{C}_{10}{a}^{20-10}{b}^{10}$

= ${}^{20}{C}_{10}{a}^{10}{b}^{10}$