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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Probability
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The probability that $ \sin^{-1} ( \sin \: x)+ \cos^{-1} ( \cos\: y)$ is an integer $ x,y \in \{ 1,2,3,4 \} $ is

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

 

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1 Answer

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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)

 

answered Jan 8, 2014 by thanvigandhi_1
 

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