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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2013

  • question_answer
        The number of solutions of\[\sum\limits_{r=1}^{5}{\cos rx}=5\]in the interval\[[0,2\pi ]\]is

    A)  0                            

    B)  1      

    C)  5                            

    D)  10

    Correct Answer: B

    Solution :

                    \[\because \] \[\sum\limits_{r=1}^{5}{\cos rx=5}\] \[\Rightarrow \]\[cos\text{ }x+cos\text{ }2x+cos\text{ }3x+cos\text{ }4x+cos\text{ }5x=5\]which is possible only, when     \[cos\text{ }x=cos\text{ }2x=cos\text{ }3x=cos\text{ }4x=cos\text{ }5x=1\]and is satisfied by\[x=0\]only. Hence, the number of solution = 1


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