$A$ number is chosen from the first $100$ natural numbers. The probability that the number is even or divisible by $5$ is:

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?

$A$ and $B$ are two subsets of set $S = \{1, 2, 3, 4\}$ such that $A \cup B = S$. Then,the number of ordered pairs $(A, B)$ is:

If a set $A$ is such that $A \cup \{1, 2\} = \{1, 2, 3, 5, 9\}$,then the set $A$ could be:

$A$ number is chosen at random from the set $\{1, 2, 3, \ldots, 2000\}$. Let $p$ be the probability that the chosen number is a multiple of $3$ or a multiple of $7$. Then the value of $500p$ is . . . . . .

Let $A = \{1, 2, 3, 4, 5, 6, 7\}$. Define $B = \{T \subseteq A : \text{either } 1 \notin T \text{ or } 2 \in T\}$ and $C = \{T \subseteq A : \text{the sum of all the elements of } T \text{ is a prime number}\}$. Then the number of elements in the set $B \cup C$ is $\dots\dots$