2. Solved Papers
  3. J & K CET Engineering

J & K CET Engineering J and K - CET Engineering Solved Paper-2005

  • question_answer
    If \[y={{\cos }^{-1}}\cos (|x|-f(x)),\] where \[f(x)=\left\{ \begin{matrix}    1, & if & x>0  \\    -1, & if & x<0  \\    0, & if & x=0  \\ \end{matrix} \right.\] Then, \[{{(dy/dx)}_{x=\frac{5\pi }{4}}}\]is equal to

    A)  \[-1\]

    B)  \[1\]

    C)  \[0\]

    D)  can't be determined

    Correct Answer: B

    Solution :

    \[\therefore \]      \[y={{\cos }^{-1}}\cos (x-1),x>0\] \[\Rightarrow \] \[y=x-1,0\le x-1\le \pi \] \[\Rightarrow \] \[y=x-1,1\le x\le \pi +1\] \[\therefore \] \[y=x-1,1\le x\le \pi +1\] At \[x=\frac{5\pi }{4}\in [1,\,\pi +1]\] \[\Rightarrow \] \[\frac{dy}{dx}=1\] \[\Rightarrow \] \[{{\left( \frac{dy}{dx} \right)}_{x=\frac{5\pi }{4}}}=1\]


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