MP Board · Class 11 · Mathematics · Binomial TheoremWhat is the sum of binomial coefficients ${}^{n}C{0} + {}^{n}C{1} + {}^{n}C{2} + \dots + {}^{n}C{n}$?
Step-by-Step Solution
The sum of all binomial coefficients in the expansion of $(1 + x)^{n}$ is obtained by putting $x = 1$, which yields $(1 + 1)^{n} = 2^{n}$.
Detailed Options Breakdown
Option : $2^{n-1}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 1: $2^{n}$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: $2^{n} - 1$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 3: $n^{2}$
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.