Mathematics Mock Test - 10

The number of $2\times 2$ matrices $A$, with each element as a real number and satisfying $A+A^T=I$ and $A^{T}A=I$, is:

The maximum value of the function $f(x)=(x-1)(x-2)(x-3)$ is:

Below is a figure indicating a sample space $S$ and the probability of occurrences of events $A$ and $B$. Which colored section of the portion will indicate the probability of events $B$ and $A$ occurring simultaneously?

Let $R$ be the relation on the set $\mathbb{R}$ of all real numbers defined by $aRb$ if $|a-b|\le 1$. Then $R$ is:

The value of $\sin \left[2{\cos }^{-1}\frac{\sqrt{5}}{3}\right]$ is: