Question

In the $5$th term of $(x+y{)}^n$, the exponent of y is $4$, then the exponent of y in the $8$th term is

• A. $1$
• B. $7$
• C. $5$
• D. $9$

Answer 1

The correct option is B $7$

Given,

$(x+y{)}^n$

General term

$T_{r+1}={}^n{C}_r{x}^{n-r}{y}^r$

$T_{r+1}={}^n{C}_r(x{)}^{n-r}{y}^r$

Given, in the $5^{th}$ term the exponent of $y$ is $4$

$T_5=T_{4+1}={}^n{C}_4(x{)}^{n-4}{y}^4$

$T_8=T_{7+1}={}^n{C}_7(x{)}^{n-7}{y}^7$

Hence exponent of $y$ in the $8^{th}$ term is $7$

Hence, correct option is B.