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.

If the second term in the expansion of (root(13)(a)+ (a)/(sqrt(a^(-1))))^(n) is 14a^(5//2) " then value of " (""^(n)C_(3))/(""^(n)C_(2)) is

If the expansion (2x^(5)+(1)/(3x^(4)))^(n) contains a term independent of x, then the value of n can be ___________

If the fifth term of the expansion (a^(2/3)+a^(-1))^(n) does not contain 'a'. Then n is equal to 2 b.5c.10d .none of these

Show that the middle term in the expansion (x-(1)/(x))^(2n) is (1.3.5..2n-1))/(n)(-2)^(n)

If the 4 th term in the expansion of (ax+1/x)^(n) is 5/2, then a=(1)/(2) b.n=8 c.a=(2)/(3) d.n=6

The number of terms in the expansion of (x+1/x+1)^n is (A) 2n (B) 2n+1 (C) 2n-1 (D) none of these