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

Let $S = \{1, 2, 3, 4\}$. The total number of unordered pairs of disjoint subsets of $S$ is equal to

If a set $A$ has $5$ elements,then the number of ways of selecting two subsets $P$ and $Q$ from $A$ such that $P$ and $Q$ are mutually disjoint,is

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 $A = \{ x \in R : [x + 3] + [x + 4] \leq 3 \}$ and $B = \{ x \in R : 3^x \left( \sum_{n=1}^{\infty} \frac{3}{10^n} \right)^{x-3} < 3^{-3x} \}$,where $[t]$ denotes the greatest integer function. 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: