Find the term independent of x in the expansion of (a) `(sqrt(x)/(3)+3/(2x^2))^10` (b) `(2x^2-3/(x^3))^25`

Explanation

(a) Given


`(sqrt{frac{x}{3}}+frac{3}{2 x^{2}})^{10} `


`T_{r+1}=\ ^{10} C_{r}(sqrt{frac{x}{3}})^{10-r}(frac{3}{2 x^{2}})^{r} `


`=\ ^{10} C_{r cdot} frac{3^{r-frac{10 r}{2}}}{2^{r}} x^{frac{10-x}{2}}-2 r`


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