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?

Consider the system of linear equations given below.

$$ \begin{aligned} a x+y & =b \\ 16 x+a y & =24 \end{aligned} $$

Suppose the values of a and b are chosen such that the system of linear equations produce multiple solutions. Then the product of $a$ and $b$ is $\_\_\_\_$ . (answer in integer)