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  • the position of the term independent of x in the expansion of (√(x/3)+3/2x^2 )^10 is---------

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

Answers (1)

Given: \left ( \sqrt{\frac{x}{3}}+\frac{3}{2x^{2}} \right )^{10}

Thus, T_{r+1}=^{10}C_{r}\left ( \sqrt{\frac{x}{3}} \right )^{10-r}\left ( \frac{3}{2x^{2}} \right )^{r}

Now, for constant term,

10 – 5r = 0

Thus, r = 2

Therefore, the third term is independent of x.

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infoexpert22

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