$A$ number $n$ is chosen at random from $S=\{1, 2, 3, \ldots, 50\}$. Let $A=\{n \in S: n+\frac{50}{n} > 27\}$,$B=\{n \in S: n \text{ is a prime}\}$ and $C=\{n \in S: n \text{ is a square}\}$. Then,the correct order of their probabilities is:

Suppose $A_1, A_2, A_3, \dots, A_{30}$ are $30$ sets each having $5$ elements and $B_1, B_2, \dots, B_n$ are $n$ sets each with $3$ elements. Let $\bigcup_{i=1}^{30} A_i = \bigcup_{j=1}^n B_j = S$ and each element of $S$ belongs to exactly $10$ of the $A_i$'s and exactly $9$ of the $B_j$'s. Then $n$ is equal to:

The smallest set $A$ such that $A \cup \{1, 2\} = \{1, 2, 3, 5, 9\}$ 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?

Let $S = \{p_1, p_2, \ldots, p_{10}\}$ be the set of the first ten prime numbers. Let $A = S \cup P$,where $P$ is the set of all possible products of distinct elements of $S$. Then the number of all ordered pairs $(x, y)$,where $x \in S$ and $y \in A$,such that $x$ divides $y$,is . . . . . .

In a class of $300$ students,every student reads $5$ newspapers and every newspaper is read by $60$ students. Then the number of newspapers is