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7.Binomial Theorem
hard
The total number or irrational terms in the binomial expansion of $\left( {{7^{1/5}} - {3^{1/10}}} \right)^{60}$ is
A
$55$
B
$49$
C
$48$
D
$54$
(JEE MAIN-2019)
Solution
General term $\mathrm{T}_{\mathrm{r}+1}=^{60} \mathrm{C}_{\mathrm{r}}, 7^{\frac{\mathrm{e}-\mathrm{r}}{5}} 3^{\frac{\mathrm{r}}{10}}$
for rational term, $\mathrm{r}=0,10,20,30,40,50,60$
$\Rightarrow$ number of rational terms $=7$
$\therefore $ number of irrational terms $=54$
Standard 11
Mathematics
