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JEE Main & Advanced AIEEE Solved Paper-2011

  • question_answer
    The values of p and q for which the function \[f(x)=\left\{ \begin{align}   & \frac{\sin (p+1)x+sinx}{x},\,\,\,\,\,\,x  & q,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=0 \\  & \frac{\sqrt{x+{{x}^{2}}}-\sqrt{x}}{{{x}^{3/2}}},\,\,\,\,\,\,\,x>0 \\ \end{align} \right.\]  is continuous for all \[x\] in R, are.   AIEEE  Solved  Paper-2011

    A) \[p=\frac{1}{2},q=\frac{3}{2}\]                     

    B) \[p=\frac{1}{2},q=-\frac{3}{2}\]

    C) \[p=\frac{5}{2},q=\frac{1}{2}\]                     

    D) \[p=-\frac{3}{2},q=\frac{1}{2}\]

    Correct Answer: D

    Solution :

                 The given function \[f\] is continuous at \[x=0\] if \[\underset{h\to 2}{\mathop{\lim }}\,f(0-h)=f(0)=\underset{h\to 0}{\mathop{\lim }}\,f(0+h)\] \[\Rightarrow \,\,p+2=q=\frac{1}{2}\] \[\Rightarrow \,\,p=-\frac{3}{2},q=\frac{1}{2}\]


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