If $A$ and $B$ are coefficients of $x^{\mathrm{n}}$ in the expansions of $(1+x)^{2 \mathrm{n}}$ and $(1+x)^{2 \mathrm{n}-1}$ respectively, then $\mathrm{A} / \mathrm{B}$ is equal to

Question

If $A$ and $B$ are coefficients of $x^{\mathrm{n}}$ in the expansions of $(1+x)^{2 \mathrm{n}}$ and $(1+x)^{2 \mathrm{n}-1}$ respectively, then $\mathrm{A} / \mathrm{B}$ is equal to, 4, 2, 9, 6

MARKS App · Accepted Answer

$\begin{array}{r}\text {Hints: } A={ }^{2 n} C_n \ B={ }^{2 n-1} C_n \end{array}$ $\frac{\mathrm{A}}{\mathrm{B}}=\frac{{ }^{2 \mathrm{n}} \mathrm{C}_{\mathrm{n}}}{{ }^{2 \mathrm{n}-1} \mathrm{C}_{\mathrm{n}}}=\frac{2 \mathrm{n}}{\mathrm{n}}=2$

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