Consider the following statements regarding the function f(x) = 1/(x - 5)

Statement-I: f(x) is decreasing on the intervals x < 5 and x > 5

Statement-II: f''(x) > 0 for all x ≠ 5.

Which one of the following is correct in respect of the above statements?

Consider the following statements:

Statement-I: The function  $f(x)=\frac{x^{3}+128}{x}$ has a minimum value 48 at x = 4

Statement-II: As x increases through 4, f'(x) changes sign from positive to negative.

Which one of the following is correct in respect of the above statements?

What is the harmonic mean of the numbers C(10,3) C(10,4) C(10,5) C(10,6) and C(10,7) ?

In a sample survey of a village, the probability that a farmer is in debt is 0.60. What is the probability that three randomly selected farmers are all in debt (assume independence of events)?