Binomial Theorem
Middle Term
JEE Main 2020
Grade 11

Question:

The middle term in the expansion of $(1 + x)^{10}$ is:
(1) $\binom{10}{5} x^5$
(2) $\binom{10}{4} x^5$
(3) $\binom{10}{6} x^5$
(4) $\binom{10}{5} x^4$

Step-by-Step Solution

Key Concept: Since the expansion of $(1+x)^{10}$ has 11 terms (an odd number), there is a single middle term — identify its position as $\left(\frac{10}{2} + 1\right)^{\text{th}}$ and write down $T_{r+1} = \binom{10}{r} x^r$ for that value of $r$.
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Correct Answer: (1)

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