In a regular graph of $15$ vertices,the sum of the degrees of the vertices is $60$. Then,the degree of each vertex is:

Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers,with $\text{HCF}(x, y) = 16$ and $\text{LCM}(x, y) = 48000$. The number of elements in $S$ is

If $A, B,$ and $C$ are three sets such that $A \cup B = A \cup C$ and $A \cap B = A \cap C$,then

$A$ two-digit number $\overline{ab}$ is called almost prime if one obtains a two-digit prime number by changing at most one of its digits $a$ or $b$. (For example,$18$ is an almost prime number because $13$ is a prime number). The number of almost prime two-digit numbers is:

Let $S = \{ x \in \mathbb{R} : x \ge 0 \text{ and } 2|\sqrt{x} - 3| + \sqrt{x}(\sqrt{x} - 6) + 6 = 0 \}$. Then $S$:

If $P(x) = x^5 + ax^4 + bx^3 + cx^2 + dx + e$ is a polynomial such that $P(0) = 1, P(1) = 2, P(2) = 5, P(3) = 10$ and $P(4) = 17$,then $P(5) =$