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

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 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 _____.

Each of a set of n processes executes the following code using two semaphores a and b initialized to 1 and 0, respectively. Assume that count is a shared variable
What does the code achieve?