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(B) The general term $T_{r+1}$ in the expansion of $(a+b)^n$ is given by $^{n}C_{r} a^{n-r} b^{r}$.Here,$a = (x/3)^{1/2}$,$b = 3/(2x^2)$,and $n = 10$.

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$5/4$

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(B) The general term $T_{r+1}$ in the expansion of $(a+b)^n$ is given by $^{n}C_{r} a^{n-r} b^{r}$.Here,$a = (x/3)^{1/2}$,$b = 3/(2x^2)$,and $n = 10$.$T_{r+1} = ^{10}C_{r} (x/3)^{(10-r)/2} (3/(2x^2))^r$$T_{r+1} = ^{10}C_{r} (1/3)^{(10-r)/2} (3/2)^r x^{(10-r)/2 - 2r}$For the term to be independent of $x$,the exponent of $x$ must be $0$:$(10-r)/2 - 2r = 0$$5 - r/2 - 2r = 0$$5 = 5r/2 \Rightarrow r = 2$Substituting $r = 2$ into the expression:$T_{3} = ^{10}C_{2} (1/3)^{(10-2)/2} (3/2)^2$$T_{3} = 45 	imes (1/3)^4 	imes (9/4)$$T_{3} = 45 	imes (1/81) 	imes (9/4) = 45/36 = 5/4$.

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

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