Question

Find the coefficient of $x^5{y}^7$ in $(x-7y{)}^{12}$.

• A. ${}^{12}{C}_5{.7}^7$
• B. ${-}^{12}{C}_5{.7}^7$
• C. $0$
• D. ${}^{12}{C}_5{.7}^5$

Answer 1

Answer: (B)

${-}^{12}{C}_5{.7}^7$

$x^5{y}^7$ in $(x-7y{)}^{12}$

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

${}^{12}{C}_7\left(x{)}^{12-7}\right(-7{)}^7\left(y^7\right)$

We know that

${}^n{C}_r{=}^n{C}_{n-r}$

${}^{12}{C}_7{=}^{12}{C}_5$

${\Rightarrow }^{12}{C}_5,x^5(-7{)}^7{y}^7$

${}^{12}{C}_5(-7{)}^7{x}^5{y}^7$

Coefficient of $x^5{y}^7$ is ${}^{12}{C}_5(-7{)}^5$

$\left(x\right)=x^3-3x^2+5x-39\left(x\right)=x^2-2$