By the Binomial Theorem, the expansion of $(a+b)^n$ for positive integer $n$ is

1. NCERT §7.2 states the Binomial Theorem: $(a+b)^n = \sum_{r=0}^{n} \binom{n}{r}\,a^{n-r}\,b^r$. 2. Note: option B's formula $\sum \binom{n}{r}\,a^r\,b^{n-r}$ is also correct because $\binom{n}{r} = \binom{n}{n-r}$ (symmetric). However, A is the standard NCERT form. 3. Coefficients $\binom{n}{r}$ are called BINOMIAL COEFFICIENTS, and they appear in PASCAL'S triangle row $n$. 4. The expansion has $n+1$ terms (one for each value $r = 0, 1, \ldots, n$). 5. Options C, D are missing most of the terms — only first and last, or a wrong partial form. _Source: NCERT Class 11 Mathematics, Ch 7 "Binomial Theorem", §7.2 (Statement of the theorem), p. 1–3._