MP Board · Class 11 · Mathematics · Binomial TheoremWhat is the general term ($r+1$-th term) in the expansion of $(x + y)^{n}$?
Step-by-Step Solution
The general term, denoted by $T_{r+1}$, in the binomial expansion of $(x + y)^{n}$ is given by the formula $T_{r+1} = {}^{n}C_{r} x^{n-r} y^{r}$.
Detailed Options Breakdown
Option : ${}^{n}C_{r} x^{r} y^{n-r}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 1: ${}^{n}C_{r-1} x^{n-r} y^{r}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 2: ${}^{n}C_{r} x^{n-r} y^{r}$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: ${}^{n}C_{r+1} x^{n-r} y^{r}$
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.