A) 0
B) 1
C) 3
D) 6
Correct Answer: C
Solution :
[c] We know that \[0\le {{\cos }^{-1}}x\le \pi .\] Hence, from the question \[{{\cos }^{-1}}\lambda =\pi ,{{\cos }^{-1}}\mu =\pi ,{{\cos }^{-1}}\gamma =\pi \] [\[\because {{\cos }^{-1}}\lambda +{{\cos }^{-1}}\mu +{{\cos }^{-1}}\gamma =3\pi \] is possible only when each term attains its maximum.] \[\Rightarrow \lambda =\mu =\gamma =-1\Rightarrow \lambda \mu +\mu \gamma +\gamma \lambda =3.\]
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