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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2004

  • question_answer
        The number of values of x in the interval \[\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\]    satisfying    the    equation \[3\,\,\,\cos \,\,\,\theta \]is :

    A)  0                                            

    B)  5

    C)  6                                            

    D)  10

    Correct Answer: C

    Solution :

                    \[3{{\sin }^{2}}x-7\sin x-\sin x+2=0\] \[\Rightarrow \]               \[3{{\sin }^{2}}x-6\sin x-\sin x+2=0\] \[\Rightarrow \] \[3\sin x(\sin x-2)-1(\sin x-2)=0\] \[\Rightarrow \]               \[\sin x=\frac{1}{3}\]or \[2\] \[\Rightarrow \]               \[\sin x=\frac{1}{3}\]                      \[[\because \sin x\ne 2]\] Let \[{{\sin }^{-1}}\frac{1}{3}=\alpha ,0<\alpha <\frac{\pi }{2}\] then\[\alpha ,\pi -\alpha ,2\pi +\alpha ,3\pi -\alpha ,\] \[4\pi +\alpha +5\pi -\alpha \]are the solution in \[[0,5\pi ]\] \[\therefore \]Required number of solution\[=6\]


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