Question

The coefficient of $x^{33}$ in the expansion of $\sum _{r=0}^{50}{}^{50}{C}_r(x-4{)}^{50-r}{3}^r$

• A. ${}^{50}{C}_{33}$
• B. ${-}^{50}{C}_{32}$
• C. ${-}^{50}{C}_{17}$
• D. $Noneofthese$

Answer 1

The correct option is C ${-}^{50}{C}_{17}$

$x^{33}=?$

$\sum +{r=0}^{50}{}^{50}{C}_{\lambda }(x-4{)}^{50-\lambda }{3}^r$

${=}^{50}{C}_0(x-4{)}^{50}{3}^o+{}^{50}{C}_1(x-4{)}^{49}{3}^2+{}^{50}{C}_2(x-4{)}^{48}{3}^3+{}^{50}{C}_{50}(x-4{)}^o{3}^{50}$

coefficient of $x^{33}$

$50-r=33$

$r=50-33$

$r=17$

Hence ${}^{50}{C}_{17}$