What is the area of the region bounded by |x| <= 2k and |y| <= k where k is a positive real number?

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) ?