JEE Main 2025 — Binomial Theorem Question with Solution
JEE Main 2025 (8 Apr Shift 2)
Question
The number of integral terms in the expansion of is
Choose an option
Show full solutionCorrect option: D
Correct answer
D128
Step-by-step explanation
$\begin{aligned}
& \mathrm{T}_{\mathrm{r}}={ }^{1016} \mathrm{C}_{\mathrm{r}}(5)^{\frac{1016-\mathrm{r}}{2}} 7^{\frac{\mathrm{r}}{8}} \\
& \Rightarrow \mathrm{r}=0,8,16,24, \ldots ., 1016 \\
& 1016=0+(\mathrm{n}-1) 8 \\
& \Rightarrow \mathrm{n}-1=\frac{1016}{8}=127
\end{aligned}$
So, .
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This is a previous-year question from JEE Main 2025, covering the Binomial Theorem chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.