If the coefficients of $x^{2} a n d x^{3}$ in the expansion of $(3 + k x)^{9}$ are equal, then the value of k is

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Solution

The correct option is B
$C o e f f i c i e n t o f x^{2} = c o e f f i c i e n t o f x^{3} ∴^{9} C_{2} 3^{9 - 2} k^{2} =^{9} C_{3} 3^{9 - 3} k^{3} \Rightarrow 36 = 28 k \Rightarrow k = \frac{9}{7}$

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