A) \[2/\sqrt{2}\]
B) \[1\]
C) \[1/2\]
D) \[1/3\]
Correct Answer: C
Solution :
\[{{\cos }^{-1}}\sqrt{p}+{{\cos }^{-1}}\sqrt{1-p}+{{\cos }^{-1}}\sqrt{1-q}=\frac{3\pi }{4}\] \[{{\cos }^{-1}}\sqrt{p}+{{\sin }^{-1}}\sqrt{p}+{{\cos }^{-1}}\sqrt{1-q}=\frac{3\pi }{4}\] \[\frac{\pi }{2}+{{\cos }^{-1}}\sqrt{1-q}=\frac{3\pi }{4}\] \[{{\cos }^{-1}}\sqrt{1-q}=\frac{3\pi }{4}-\frac{\pi }{2}=\frac{3\pi -2\pi }{4}=\frac{\pi }{4}\] \[\sqrt{1-q}=1/\sqrt{2}\Rightarrow 1-q=1/2\Rightarrow q=1/2.\]
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