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  • The term independent of x in the expansion of <img alt="\left(\sqrt{\frac{x}{3}}+\frac{3}{2 x^2}\right)^{10}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%28%5Csqrt%7B%5Cfrac%7

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

Option: 1

3/2


Option: 2

5/4


Option: 3

5/2


Option: 4

None of these


Answers (1)

best_answer

(10-r)\left(\frac{1}{2}\right)+r(-2)=0 \Rightarrow 5-\frac{r}{2}-2 r=0 \Rightarrow r=2

So the term independent of x 
={ }^{10} C_2 \times\left(\frac{1}{3}\right)^4\left(\frac{3}{2}\right)^2=\frac{10 \times 9}{2 \times 1} \times \frac{1}{3 \times 3 \times 2 \times 2}=\frac{5}{4}

Posted by

SANGALDEEP SINGH

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