A) \[\frac{5\pi }{6}\]
B) \[\frac{\pi }{6}\]
C) \[\frac{\pi }{4}\]
D) \[\frac{3\pi }{4}\]
Correct Answer: B
Solution :
\[3\sin P+4\cos Q=6\] ... (i) \[4\sin Q+3\cos P=1\] ... (ii) Squaring and adding (i) & (ii) we get sin \[(P+Q)=\frac{1}{2}\] \[\Rightarrow \,\,P+Q=\frac{\pi }{6}\] or \[\frac{5\pi }{6}\] \[\Rightarrow \,\,R=\frac{5\pi }{6}\] or \[\frac{\pi }{6}\] If \[R=\frac{5\pi }{6}\] then \[0<P,Q<\frac{\pi }{6}\] \[\Rightarrow \,\,\cos Q<1\] and \[\sin P<\frac{1}{2}\] \[\Rightarrow 3\sin P+4\cos Q<\frac{11}{2}\] So \[R=\frac{\pi }{6}\]
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