If the second term of the expansion `[a^(1/(13))+a/(sqrt(a^(-1)))]^n` is `14 a^(5//2)` , then the value of `(^n C_3)/(^n C_2)` is.

Options

A. 19
B. 29
C. 39
D. 81

Answer

a

Explanation

`T_(2) =""^(n)C_(1) (root(13)(a))^(n-1) ((a)/(sqrt(a^(-1))))^(1) = 14a^(5//2)` [given]
`rArr n(a) ^((n-1)/(13) )a^(1+(1)/(2) )= 14a^(5//2)`
` rArr na^((n-1)/(13) )a^(3//2) = 14a^(5//2)`
When we put n= 14 , then it satisfies the above equation
`therefore (""^(n)C_(3))/(""^(n)C_(2)) = (""^(14)C_(3))/(""^(n)C_(2)) = (14-3 +1)/(3) = 4 `