7.Binomial Theorem
normal

Number of rational terms in the expansion of ${\left( {{3^{\frac{1}{8}}} + {5^{\frac{1}{3}}}} \right)^{400}}$ is

A

$17$

B

$20$

C

$102$

D

$150$

Solution

${{\rm{T}}_{({\rm{r}} + 1)}}{ = ^{400}}{{\rm{C}}_{\rm{r}}}{3^{\left( {50 – \frac{{\rm{r}}}{8}} \right)}}\,{5^{\frac{r}{3}}}$

$r=0,24, \ldots ., 24 \times 16$

Total terms $=17$

Standard 11
Mathematics

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