Question

If the second term in the expansion ${[a^{\frac{1}{13}}+\frac{a}{\sqrt{a^{-1}}}]}^n$ is $14a^{5/2}$, then the value of $\frac{{}^n{C}_3}{{}^n{C}_2}$ is

• A. $4$
• B. $3$
• C. $12$
• D. $6$

Answer 1

The correct option is A $4$

The first term will have a coefficient of ${}^n{C}_1=n$
Now, this coefficient has to be equal to $14.$
Therefore $n=14$
Now
$\frac{{}^{14}{C}_3}{{}^{14}{C}_2}=\frac{14!(12!)(2!)}{11!(3!)(14!)}=\frac{12}{3}=4$