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JEE Main & Advanced Sample Paper JEE Main Sample Paper-21

  • question_answer
    The equation  \[sin\text{ }x+2sin\text{ }2x+3sin\text{ }3x-\frac{8}{\pi }=0\] has at least  one root in

    A)  \[\left( 0,\frac{\pi }{2} \right)\]                

    B)  \[\left( \frac{\pi }{2},\pi  \right)\]

    C)  \[\left( \pi ,\frac{3\pi }{2} \right)\]                       

    D)  none of above

    Correct Answer: A

    Solution :

    Consider \[f(x)=\frac{8}{\pi }x+\cos x+\cos 2x+\cos 3x\] \[f(0)=f\left( \frac{\pi }{2} \right)\,=3\]?    \[\therefore \,\,f'(c)=0\] for some \[c\in \,(0,\,\,\pi /2)\]


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