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The position of the term independent of ...

The position of the term independent of `x` in the expansion of `(sqrt((x)/(3)) + (3)/(2x^(2)))^(10)` is ......

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Given expansion is `(sqrt((x)/(3)) + (3)/(2x^(2)))^(10)`
Let the constant term be `T_(r + 1)`
Then, `T_(r + 1) = .^(10)C_(r) (sqrt((x)/(3)))^(10 - r) ((3)/(2x^(2)))^(r)`
`= .^(10)C_(r) . X^((10 - r)/(2)) . 3^((-10 + r)/(2)) .3^(r).2^(-r). x^(-2r)`
`= .^(10)C_(r) x^((10 - 5r)/(2)) 3^((-10 + 3r)/(2)) 2^(-r)`
For constant term, `10 - 5r = 0 rArr r = 2`
Hence, third term is independent of x
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