KVPY Sample Paper KVPY Stream-SX Model Paper-13

  • question_answer
    \[X=\{x\in R:\cos (\sin x)=\sin (\cos x)\}.\]The number of elements in X is

    A) 0

    B) 2

    C) 4

    D) Not finite

    Correct Answer: A

    Solution :

    We have, \[\cos (\sin x)=\sin (\cos x)\]
    \[\Rightarrow \]\[\sin \left( \frac{\pi }{2}\pm \sin x \right)=\sin (\cos x)\]
    \[\Rightarrow \]\[\cos x=n\pi +{{(-1)}^{n}}\left( \frac{\pi }{2}+\sin x \right),n\in I\]
    \[\Rightarrow \]\[\cos x\pm \sin x=nx+{{(-1)}^{n}}\frac{\pi }{2},n\in I\]
    As LHS \[\in [-\,\sqrt{2},\sqrt{2}],\]and it does not satisfies RHS.
    Hence, no solutions exists.

You need to login to perform this action.
You will be redirected in 3 sec spinner