CBSE · Class 11 · Mathematics · Binomial TheoremWhat is the number of terms in the expansion of $(x + y)^{n}$?
Step-by-Step Solution
The number of terms in the expansion of $(x + y)^{n}$ is always $n + 1$, where $n$ is a positive integer. This is because the powers of $x$ decrease from $n$ to $0$ while the powers of $y$ increase from $0$ to $n$, giving a total of $(n - 0) + 1 = n + 1$ terms.
Detailed Options Breakdown
Option : $n$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 1: $n + 1$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: $n - 1$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Binomial Theorem.
Option 3: $2n$
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.