Question

If the second term of the expansion ${[a^{1/13}+\frac{a}{\sqrt{a^{-1}}}]}^{n}is14a^{5/2}$ 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 general term of the expansion ${(x+y)}^n=C_r{x}^{n-r}{y}^r$

$⟹$ the second term will be of the form $n{a}^p$,

Where $p$ is some real number depending on the powers of $a$,

comparing the term to $14a^{\frac{5}{2}}$ gives $n=14$,

We know that $\frac{C_3}{C_2}=\frac{n-2}{3}$,

$⟹4$