A) \[4\]
B) \[3\]
C) \[12\]
D) \[6\]
Correct Answer: A
Solution :
We have \[{{T}_{2}}=14\,{{a}^{\frac{5}{2}}}\] \[\Rightarrow \,{{\,}^{n}}{{C}_{1}}{{({{a}^{\frac{1}{13}}})}^{n-1}}({{a}^{\frac{3}{2}}})=14{{a}^{\frac{5}{2}}}\] \[\Rightarrow \,\,n{{a}^{\frac{n-1}{13}+\frac{3}{2}}}=14{{a}^{\frac{5}{2}}}\Rightarrow n=14\] \[\Rightarrow \,\frac{^{n}{{C}_{3}}}{^{n}{{C}_{2}}}=\frac{^{14}{{C}_{3}}}{^{14}{{C}_{2}}}=\frac{12}{3}=4\]
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