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JEE Main & Advanced Mathematics Limits, Continuity and Differentiability Question Bank Self Evaluation Test - Continuity and Differentiability

  • question_answer
    If \[\left. \begin{align}   & f(x)=sin\text{ }x,when\,\,x\,\,is\,\,rational \\  & \,\,\,\,\,\,\,\,\,\,=\,\cos x,when\,\,x\,\,is\,\,irrational \\ \end{align} \right\}\]

    A) Discontinuous at \[x=n\pi +\pi /4\]

    B) Continuous at \[x=n\pi +\pi /4\]

    C) Discontinuous at all x

    D) None of these

    Correct Answer: B

    Solution :

    [b] The function can be continuous only at those points for which \[\sin x=\cos x\Rightarrow x=n\pi +\frac{\pi }{4}\]


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