JEE Main & Advanced Sample Paper JEE Main Sample Paper-19

  • question_answer 67) If\[y=A\sin \omega t\]then\[\frac{{{d}^{5}}y}{d{{t}^{5}}}=\]

    A) \[A{{\omega }^{5}}\cos \left( \omega t-\frac{\pi }{2} \right)\]    

    B) \[A{{\omega }^{5}}\sin \left( \omega t-\frac{\pi }{2} \right)\]

    C) \[A{{\omega }^{5}}\cos \left( \omega t+\frac{\pi }{2} \right)\]   

    D) \[A{{\omega }^{5}}\sin \left( \omega t+\frac{\pi }{2} \right)\]

    Correct Answer: D

    Solution :

    \[y=A\sin \omega t\].      \[\therefore \,\,\frac{dy}{dx}=A\omega \cos \omega t\]                 \[\frac{{{d}^{2}}y}{d{{x}^{2}}}=-A{{\omega }^{2}}\sin \omega t\]                 \[\frac{{{d}^{3}}y}{d{{x}^{3}}}=A{{\omega }^{3}}\cos \omega t\]                 \[\frac{{{d}^{4}}y}{d{{x}^{4}}}=+A{{\omega }^{4}}\sin \omega t\] \[\therefore \]  \[\frac{{{d}^{5}}y}{d{{x}^{5}}}=A{{\omega }^{5}}\cos \omega t=A{{\omega }^{5}}\sin \left( \omega t+\frac{\pi }{2} \right)\]

adversite



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