JEE MAIN - Mathematics (2021 - 20th July Morning Shift - No. 18)
The number of rational terms in the binomial expansion of $${\left( {{4^{{1 \over 4}}} + {5^{{1 \over 6}}}} \right)^{120}}$$ is _______________.
Answer
21
Explanation
$${\left( {{4^{{1 \over 4}}} + {5^{{1 \over 6}}}} \right)^{120}}$$
$${T_{r + 1}} = {}^{120}{C_r}{({2^{1/2}})^{120 - r}}{(5)^{r/6}}$$
for rational terms r = 6$$\lambda$$
0 $$\le$$ r $$\le$$ 120
So total no of terms are 21.
$${T_{r + 1}} = {}^{120}{C_r}{({2^{1/2}})^{120 - r}}{(5)^{r/6}}$$
for rational terms r = 6$$\lambda$$
0 $$\le$$ r $$\le$$ 120
So total no of terms are 21.
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