Consider the functions

I. $${e^{ - x}}$$

II. $${x^2} - \sin x$$

III. $$\sqrt {{x^3} + 1} $$

Which of the above functions is/are increasing everywhere in [0,1]?

Let G be a group of 35 elements. Then the largest possible size of a subgroup of G other than G itself is ______.

Let R be the set of all binary relations on the set {1,2,3}. Suppose a relation is chosen from R at random. The probability that the chosen relation is reflexive (round off to 3 decimal places) is _____.

Consider the following five disk access requests of the form (request id, cylinder number) that are present in the disk scheduler queue at a given time.

(P, 155), (Q, 85), (R, 110), (S, 30), (T, 115)

Assume the head is positioned at cylinder 100. The scheduler follows Shortest Seek Time First scheduling to service the requests.

Which one of the following statements is FALSE?