A) 10
B) 5
C) 6
D) 4
E) 11
Correct Answer: D
Solution :
The 14th term in the expansion of \[\left( \frac{3\sqrt{x}}{7}-\frac{5}{2x\sqrt{x}} \right)\]is \[{{T}_{14}}{{=}^{13n}}{{C}_{13}}{{\left( \frac{3}{7}{{x}^{1/2}} \right)}^{13n-13}}{{(-1)}^{13}}{{\left( \frac{5}{2}{{x}^{-3/2}} \right)}^{13}}\] \[{{=}^{13n}}{{C}_{13}}{{\left( \frac{3}{7} \right)}^{13n-13}}{{(-1)}^{13}}{{\left( \frac{5}{2} \right)}^{13}}{{x}^{\frac{13n-13}{2}-\frac{39}{2}}}\] For this term to be independent of\[x,\]we put \[13n-52=0\] \[\Rightarrow \] \[n=4\]
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