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Question: The term independent of *x* in the expansion of \(\left( \sqrt{\frac{x}{3}} + \frac{3}{2x^{2}} \righ...

The term independent of x in the expansion of (x3+32x2)10\left( \sqrt{\frac{x}{3}} + \frac{3}{2x^{2}} \right)^{10} will be

A

32\frac{3}{2}

B

54\frac{5}{4}

C

52\frac{5}{2}

D

None of these

Answer

54\frac{5}{4}

Explanation

Solution

(10−r)(12)+r(−2)=0⇒r=2(10 - r)\left( \frac{1}{2} \right) + r( - 2) = 0 \Rightarrow r = 2 ∴\therefore T3=10⥂C2(13)8/2(32)2=54T_{3} =^{10} ⥂ C_{2}\left( \frac{1}{3} \right)^{8/2}\left( \frac{3}{2} \right)^{2} = \frac{5}{4}