Question

Consider the expansion of $(x+y{)}^{20}$. ${12}^{th}$ term from the end = $p^{th}$ term from the beginning. Find the value of p

• A. 12
• B. 11
• C. 10
• D. 9

Answer 1

The correct option is C

10

In the expansion of $(a+b{)}^n$, there will be (n+1) terms in total.
$1^{st}$ term from the end = $(n+1{)}^{th}$ term from the beginning
$2^{nd}$ term from the end = $(n+1-1{)}^{th}$ term from the beginning
Similarly, $q^{th}$ term from the end =$(n+1-(q-1){)}^{th}$ term from the beginning
$\Rightarrow {12}^{th}$ term from the end =$(n+1-(12-1){)}^{th}$ term from the beginning
Here, n=20
$\Rightarrow (20+1-(12-1){)}^{th}$ term = ${10}^{th}$ term