MP Board · Class 11 · Mathematics · Binomial TheoremWhat is the value of ${}^{n}C{r} + {}^{n}C{r-1}$?
Step-by-Step Solution
Using the standard Pascal's identity for combinations, ${}^{n}C_{r} + {}^{n}C_{r-1} = {}^{n+1}C_{r}$.
Detailed Options Breakdown
Option : ${}^{n+1}C_{r}$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: ${}^{n}C_{r+1}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 2: ${}^{n+1}C_{r+1}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 3: ${}^{n}C_{r-1}$
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.