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 constant term in the binomial expansion of (x^2-1/x)^n ,n in N is 15, then the value of n is equal to.

If .^(n+5) P_(n +1) = ((11(n-1))/2) .^(n +3) P_(n) then the value of n are

(i) What is the second term in the expansion of (1 + x)^(n) ? (ii) Write the 3^(rd) and 4^(th) terms in the expansion of (1 + x)^(n) . (iii) If the coefficients of 2^(nd) , 3^(rd) and 4^(th) terms in the expansion of (1 + x)^(n) are in A.P, then show that n^(2) - 9n + 14 = 0 .

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

If "^(2n+1)P_(n-1):^(2n-1)P_n=3:5, then find the value of ndot

If in the expansion of (x^(3)-(2)/(sqrt(x)))^(n) a term like x^(2) exists and 'n' is a double digit number, then least value of 'n' is

Show that the middle term in the expansion of (1 + x)^(2n) is (1.3.5.........(2n - 1))/(n!)2^(n)x^(n) , where n is a positive integer.