For two different persons $x$ and $y$, the predicate $M(x, y)$ denotes that $x$ knows $y$. Consider the following statement.

There is a person who does not know anyone else, but that person is known by everyone else.

Which one of the following expressions represents the above statement?

The probability density function $f(x)$ of a random variable $X$ which takes real values is

$$ f(x)=\frac{1}{3 \sqrt{2 \pi}} \exp \left(-\frac{x^2}{18}\right), x \in(-\infty,+\infty) $$

Which one of the following statements is correct about the random variable?

Let $R$ be a binary relation on the set $\{1,2, \ldots, 10\}$, where $(x, y) \in, R$ if the product of $x$ and $y$ is square of an integer. Which of the following properties is/are satisfied by $R$ ?

For a real number $a$, let $I(a)=\int\limits_{-1}^1\left(3 x^2-a x+1\right) d x$. Which of the following statements is/are true?