The smallest natural number n, such that the coeffiecient of x in the expansion of `(x^2+1/x^3)^n` is `""^(n)C_(23)` is :

The smallest natural number n, such that the coefficient of x in the expansion of (x^(2) + (1)/(x^(3)))^(n) is .^(n)C_(23) , is

The smallest natural number n, such that the coefficient of x in the expansion of (x^(2) + (1)/(x^(3)))^(n) is .^(n)C_(23) , is (A) 35 (B) 23 (C) 58 (D) 38

The coeffiecient of x^(n) in the expansion of log_(n)(1+x) is

The coeffiecient of x^n in the expansion of (e^(7x) +e^x)/(e^(3x)) is

Let m be the smallest positive integer such that the coefficient of x^(2) in the expansion of (1+x)^(2)+(1+x)^(3) + "……." + (1+x)^(49) + (1+mx)^(50) is (3n+1) .^(51)C_(3) for some positive integer n, then the value of n is "_____" .

Let m be the smallest positive integer such that the coefficient of x^2 in the expansion of (1+x)^2 + (1 +x)^3 + (1 + x)^4 +........+ (1+x)^49 + (1 + mx)^50 is (3n + 1) .^51C_3 for some positive integer n. Then find the value of n.

Let m be the smallest positive integer such that the coefficient of x^2 in the expansion of (1+x)^2 + (1 +x)^3 + (1 + x)^4 +........+ (1+x)^49 + (1 + mx)^50 is (3n + 1) .^51C_3 for some positive integer n. Then the value of n is

Let m be the smallest positive integer such that the coefficient of x^2 in the expansion of (1+x)^2 + (1 +x)^3 + (1 + x)^4 +........+ (1+x)^49 + (1 + mx)^50 is (3n + 1) .^51C_3 for some positive integer n. Then the value of n is