JEE PYQ: Binomial Theorem Question 1
Question 1 - 2021 (16 Mar Shift 1)
If $n$ is the number of irrational terms in the expansion of $\left(3^{1/4} + 5^{1/8}\right)^{60}$, then $(n-1)$ is divisible by:
(1) 26 (2) 30 (3) 8 (4) 7
Show Answer
Answer: (1)
Solution
General term $T_{r+1} = {}^{60}C_r \cdot 3^{(60-r)/4} \cdot 5^{r/8}$. For rational terms, $r$ must be divisible by 8. That gives 8 rational terms out of 61 total. So $n = 53$, $n-1 = 52 = 2 \times 26$.
BETA
