2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main Sample Paper-23

  • question_answer
    Let \[f(x)=\left\{ \begin{matrix}    \frac{\int\limits_{0}^{{{x}^{2}}}{\sin \sqrt{x}dx}}{{{x}^{3}}} & x>0  \\    k, & x=0  \\ \end{matrix} \right.\] If \[f(x)\] is continuous at \[x=0\] then k equals

    A)  \[\frac{1}{3}\]                                     

    B)  \[\frac{2}{3}\]

    C)  \[\frac{4}{3}\]                                     

    D)  does not exist.   

    Correct Answer: B

    Solution :

    \[k=\underset{x\to 0}{\mathop{Lim}}\,\,\frac{\int\limits_{0}^{{{x}^{2}}}{\sin \,\sqrt{x}dx}}{{{x}^{2}}}\,=\frac{2x\,\sin \,|x|}{3{{x}^{2}}}\,=\frac{2}{3}\]


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