The number of rational terms in the binomial expansion of ${\left( {{4^{{1 \over 4}}} + {5^{{1 \over 6}}}} \right)^{120}}$ is _______________.
Answer (integer)
21
Solution
${\left( {{4^{{1 \over 4}}} + {5^{{1 \over 6}}}} \right)^{120}}$<br><br>${T_{r + 1}} = {}^{120}{C_r}{({2^{1/2}})^{120 - r}}{(5)^{r/6}}$<br><br>for rational terms r = 6$\lambda$ <br><br>0 $\le$ r $\le$ 120<br><br>So total no of terms are 21.
About this question
Subject: Mathematics · Chapter: Binomial Theorem · Topic: Binomial Expansion
This question is part of PrepWiser's free JEE Main question bank. 193 more solved questions on Binomial Theorem are available — start with the harder ones if your accuracy is >70%.