NCERT · Class 11 · Mathematics · Binomial TheoremWhat is the coefficient of $x^{0}$ (constant term) in the expansion of $(x + \frac{1}{x})^{2n}$?
Step-by-Step Solution
The general term is $T_{r+1} = {}^{2n}C_{r} x^{2n-r} (\frac{1}{x})^{r} = {}^{2n}C_{r} x^{2n-2r}$. For the coefficient of $x^{0}$, set $2n - 2r = 0 \implies r = n$. Thus, the coefficient is ${}^{2n}C_{n}$.
Detailed Options Breakdown
Option : ${}^{2n}C_{n}$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: ${}^{2n}C_{n-1}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 2: ${}^{n}C_{n}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 3: ${}^{2n}C_{2n}$
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.