If the 6 th term in $\left(\frac{2 p}{3}+\frac{3 q}{2}\right)^9$ is " $a p^b q^{c \prime}$, then $a, b$ and $c$ respectively are

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Aicharya · Accepted Answer

The sixth term in the expansion $\left(\frac{2 p}{3}+\frac{3 q}{2}ight)^9$ is $ \begin{aligned} T_6 & =T_{5+1}={ }^9 C_5\left(\frac{2 p}{3}ight)^4\left(\frac{3 q}{2}ight)^5 \ & =\frac{9 	imes 8 	imes 7 	imes 6}{4 	imes 3 	imes 2} 	imes\left(\frac{2}{3}ight)^4\left(\frac{3}{2}ight)^5 p^4 q^5 \ & =189 p^4 q^5=a p^b q^c \end{aligned} $ (given) On comparing, we get $ a=189, b=4 	ext { and } c=5 $

If the 6 th term in $\left(\frac{2 p}{3}+\frac{3 q}{2}\right)^9$ is " $a p^b q^{c \prime}$, then $a, b$ and…

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