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  4. The term independent of x in the expansion of (√(x/3)+(3/2 x2))10 is-

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Q. The term independent of $x$ in the expansion of $\left(\sqrt{\frac{x}{3}}+\frac{3}{2 x^2}\right)^{10}$ is-

Binomial Theorem

Solution:

$T_{r+1}={ }^{10} C_r\left(\sqrt{\frac{x}{3}}\right)^{10-r}\left(\frac{3}{2 x^2}\right)^r$
$\frac{10-r}{2}-2 r=0$
$10-r-4 r=0$
$r=2$
hence term $={ }^{10} C_2 \times \frac{1}{3^4} \times \frac{3^2}{2^2}=\frac{5}{4}$