MP Board · Class 11 · Mathematics · Binomial TheoremIf $n$ is odd, the middle terms in the expansion of $(x + y)^{n}$ are:
Step-by-Step Solution
When $n$ is odd, the total number of terms is $n + 1$ (which is even). Consequently, there are two middle terms, given by $T_{\frac{n+1}{2}}$ and $T_{\frac{n+3}{2}}$.
Detailed Options Breakdown
Option : $T_{\frac{n}{2}}$ and $T_{\frac{n}{2}+1}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 1: $T_{\frac{n+1}{2}}$ and $T_{\frac{n+3}{2}}$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: $T_{\frac{n-1}{2}}$ and $T_{\frac{n+1}{2}}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 3: $T_{n}$ and $T_{n+1}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
💡 Study Guide: This question tests core syllabus concepts from Binomial Theorem. For formulas, key summaries, and mock exam reference guides, read the full Binomial Theorem Revision Notes.