Let $$k = {2^n}.$$ A circuit is built by giving the output of an ݊$$n$$-bit binary counter as input to an $$n$$-to-$${2^n}$$ bit decoder. This circuit is equivalent to a

The security system at an IT office is composed of 10 computers of which exactly four are working. To check whether the system is functional, the officials inspect four of the computers picked at random (without replacement). The system is deemed functional if at least three of the four computers inspected are working. Let the probability that the system is deemed functinal be denoted by p. Then 100p = __________________.

The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2, 3 or 5 is _______________

Which one of the following Boolean expressions is NOT A tautology?