The maximum possible value of k so that ` (15)^k ` divides` (100)!`

Let the production function of a firm be Q=5L^(1//2)K^(1//2) . Find the maximum possible output that the firm can produce with 100 units of L and 100 units of K.

If the equation x^(2)-(2k+1)x+k+2=0 has exactly one root in (0,2) such that maximum possible negative integral value of k is m and minimum possible positive integral value of k is M ,then |M - m| is

If the equation x^2 - (2k + 1)x + k + 2 = 0 has exactly one root in (0, 2) such that maximum possible negative integral value of k is m and minimum possible positive integral value of k is M, then IM – m| is

What is the number of possible values of k for which the line joining the points (k,1,3) and (1,-2,k+1) also passes through the point (15,2,-4)?

A stick of length 20 units is to be divided into n parts so that the product of the length of the parts is greater than unity. The maximum possible value of n, is

A stick of length 20 units is to be divided into n parts so that the product of the length of the parts is greater than unity. The maximum possible value of n, is