Let $A = \{a_1, a_2, a_3, \dots, a_n\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of $A$ are formed independently. The number of ways in which these subsets can be formed such that $(P - Q)$ contains exactly $2$ elements is:

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the event $A$ but not $C$.

In a city,$25\%$ of families have a telephone and $15\%$ have a car,while $65\%$ of families have neither a telephone nor a car. If $2000$ families have both a car and a telephone,then consider the following statements:
$1.$ $10\%$ of families have both a car and a telephone.
$2.$ $35\%$ of families have either a car or a telephone.
$3.$ $40,000$ families live in the city.
Which of these statements are true?

Let $X$ be the set consisting of the first $2018$ terms of the arithmetic progression $1, 6, 11, \dots$ and $Y$ be the set consisting of the first $2018$ terms of the arithmetic progression $9, 16, 23, \dots$. Then,the number of elements in the set $X \cup Y$ is:

The number of elements in the set $\{ n \in \mathbb{N} : 10 \leq n \leq 100 \text{ and } 3^n - 3 \text{ is a multiple of } 7 \}$ is $........$.

The number of elements in the set $\{n \in \{1, 2, 3, \ldots, 100\} \mid (11)^{n} > (10)^{n} + (9)^{n}\}$ is $.....$