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)

Consider a complete graph $K_n$ with $n$ vertices ( $n>4$ ). Note that multiple spanning trees can be constructed over $K_n$. Each of these spanning trees is represented as a set of edges. The Jaccard coefficient between any two sets is defined as the ratio of the size of the intersection of the two sets to the size of the union of the two sets. Which one of the following options gives the lowest possible value for the Jaccard coefficient between any two spanning trees of $K_n$ ?