- Home
- Standard 11
- Mathematics
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