Browse Questions

# The probability that $\sin^{-1} ( \sin \: x)+ \cos^{-1} ( \cos\: y)$ is an integer $x,y \in \{ 1,2,3,4 \}$ is

$\begin {array} {1 1} (A)\;\large\frac{1}{6} & \quad (B)\;\large\frac{3}{16} \\ (C)\;\large\frac{15}{16} & \quad (D)\;None\: of \: these \end {array}$

For $\sin^{-1} ( \sin\: x)+ \cos^{-1} ( \cos \: y)$ to be an integer $x$ should lie between
$\bigg[ -\large\frac{\pi}{2}, \large\frac{\pi}{2} \bigg]$
and $y$ should lie between $[ 0, \pi ]$
$\Rightarrow x = 1\: and \: y=1,2,3$
Required probability = $\large\frac{3}{16}$
Ans : (B)