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  • The term independent of x in <img alt="\left[\sqrt{\frac{x}{3}}+\sqrt{\left(\frac{3}{2 x^2}\

The term independent of x in \left[\sqrt{\frac{x}{3}}+\sqrt{\left(\frac{3}{2 x^2}\right)}\right]^{10} is

Option: 1

1


Option: 2

5/12


Option: 3

{ }^{10} C_1


Option: 4

None of these 


Answers (1)

best_answer

General term in the expansion is = { }^{10} \mathrm{C}_{\mathrm{r}}\left(\frac{\mathrm{x}}{3}\right)^{\frac{\mathrm{r}}{2}}\left(\frac{3}{2 \mathrm{x}^2}\right)^{\frac{10-\mathrm{r}}{2}}={ }^{10} \mathrm{C}_{\mathrm{r}} \mathrm{x}^{\frac{3 \mathrm{r}}{2}-10} \cdot \frac{3^{5-r}}{2^{\frac{10-\mathrm{r}}{2}}}

For constant term, ⇒ \frac{3 r}{2}=10 \Rightarrow r=\frac{20}{3} which is not an integer. Therefore, there will be no constant term.

Hence (D) is the correct answer.

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Gunjita

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