Question

The co-efficient of $x^{53}$ in the expansion $(x-3{)}^{100}$ is?

• A. $-$ ${}^{100}{C}_{53}$
• B. ${}^{100}{C}_{53}$
  
• C. ${}^{65}{C}_{53}$
• D. None of these

Answer 1

The correct option is D None of these

$\text{co efficient of}{x}^{53}\text{in}(x-3{)}^{100}$

$T_{r+1}=100\text{Cr}{x}^4(-3{)}^{100-r}$

$T_{54}=100C_{53}{x}^{53}(-3{)}^{47}$

$coefficientis(-3{)}^{47}{}^{100}{C}_{53}$