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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 4

  • question_answer
    \[{{\sin }^{-1}}(\sin 1)+{{\sin }^{-1}}(\sin 2)+{{\sin }^{-1}}(\sin 3)+{{\sin }^{-1}}(\sin n)\] is a rational number, where n is a natural number. Number of such values of 'n' is

    A) 1    

    B) 2                      

    C) 3          

    D) 4

    Correct Answer: C

    Solution :

    [c] \[{{\sin }^{-1}}(\sin 1)=1,{{\sin }^{-1}}(\sin 2)=\pi -2\] \[{{\sin }^{-1}}(\sin 3)=\pi -3\] Hence, \[{{\sin }^{-1}}(\sin n)\] should be \[n-2\pi \]. \[\Rightarrow \,\,\,\,\,n=5,6,7,\] Hence, number of values of n is 3.       


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