First slide

Binomial theorem for positive integral Index

Question

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

Moderate

A

$- \frac{9}{8}$
B

$\frac{9}{7}$
C

$\frac{7}{9}$
D

$\frac{8}{9}$

Solution

$\begin{array}{l} ^{9} C_{2} (3)^{7} k^{2} =^{9} C_{3} (3)^{8} (k)^{3} \\ \Rightarrow k = \frac{9}{7} \end{array}$

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