A) \[4\]
B) \[8\]
C) \[10\]
D) \[12\]
Correct Answer: B
Solution :
We know that, \[a\cos \theta +b\sin \theta =c\] has one solution only. \[|c|\le \sqrt{{{a}^{2}}+{{b}^{2}}}\] Then, for the given, equation, we must have \[|2k+1|\,\,\le \sqrt{74}\] \[\Rightarrow \] \[-\sqrt{74}<2k+1<\sqrt{74}\] \[\Rightarrow \] \[-8<2k+1<8\] \[\therefore \] \[k=-4,\,\,-3,\,\,-2,\,\,-1,\,\,0,\,\,1,\,\,2,\,\,3\] Thus, there are \[8\] values which will satisfy the above inequality
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