NCERT · Class 11 · Mathematics · Binomial TheoremIf $n$ is even, the middle term in the expansion of $(x + y)^{n}$ is:
Step-by-Step Solution
When $n$ is an even integer, the total number of terms in $(x + y)^{n}$ is $n + 1$ (which is odd). Therefore, there is only one middle term, which is given by $T_{\frac{n}{2} + 1} = {}^{n}C_{\frac{n}{2}} x^{\frac{n}{2}} y^{\frac{n}{2}}$.
Detailed Options Breakdown
Option : $T_{\frac{n}{2}}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 1: $T_{\frac{n}{2} + 1}$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: $T_{\frac{n+1}{2}}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 3: $T_{\frac{n+2}{2}}$
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.