NCERT · Class 11 · Mathematics · Binomial TheoremWhat is the expansion of $(1 - x)^{n}$ when $n$ is a positive integer?
Step-by-Step Solution
The binomial expansion of $(1 - x)^{n}$ alternates in sign: ${}^{n}C_{0} - {}^{n}C_{1}x + {}^{n}C_{2}x^{2} - \dots + (-1)^{n}{}^{n}C_{n}x^{n}$.
Detailed Options Breakdown
Option : ${}^{n}C_{0} + {}^{n}C_{1}x + \dots + {}^{n}C_{n}x^{n}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 1: ${}^{n}C_{0} - {}^{n}C_{1}x + {}^{n}C_{2}x^{2} - \dots + (-1)^{n}{}^{n}C_{n}x^{n}$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: -(${}^{n}C_{0} + {}^{n}C_{1}x + \dots + {}^{n}C_{n}x^{n}$)
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 3: ${}^{n}C_{0}x^{n} - {}^{n}C_{1}x^{n-1} + \dots$
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.