The coefficient of $x^n$, where $n$ is any positive integer, in the expansion of $(1+2x+3x^2+\ldots)^{-1/2}$ is

$1 + \frac{1}{3}x + \frac{1 \cdot 4}{3 \cdot 6}x^2 + \frac{1 \cdot 4 \cdot 7}{3 \cdot 6 \cdot 9}x^3 + \dots$ is equal to

The first four terms in the expansion of $(1 - x)^{3/2}$ are

Assertion $(A) : 1+\frac{2}{3} \cdot \frac{1}{2}+\frac{2 \cdot 5}{3 \cdot 6} \cdot \frac{1}{4}+\frac{2 \cdot 5 \cdot 8}{3 \cdot 6 \cdot 9} \cdot \frac{1}{8}+\ldots \infty = \sqrt[3]{4}$
Reason $(R) : |x| < 1, (1-x)^{-n} = 1+nx+\frac{n(n+1)}{1 \cdot 2} x^2+\frac{n(n+1)(n+2)}{1 \cdot 2 \cdot 3} x^3+\ldots$ The correct answer is

The coefficient of $x^2$ in the expansion of $(1-3x)^{\frac{1}{3}}(1+2x)^{-\frac{1}{2}}$ is

If $x$ is positive,the first negative term in the expansion of $(1 + x)^{27/5}$ is