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JEE Main & Advanced Sample Paper JEE Main Sample Paper-32

  • question_answer
    Suppose that \[f\left( 0 \right)=-3\] and \[f\left( x \right)\le 5\] for all real values of x. Then the largest value which f(2) can attain is                                    

    A) \[7\]      

    B)                                    \[-7\]             

    C)          \[13\]             

    D)                                   \[8\]                

    Correct Answer: A

    Solution :

    Using LMVT in [0, 2]                 \[\therefore \,\frac{f(2)-f(0)}{2-0}=f'(c)\,\]where \[c\,\in \,(0,2)\] \[\Rightarrow \,\frac{f(2)+3}{2}\,\underline{<}\,5\] \[\Rightarrow \,\,f(2)\,\underline{<}\,7\]


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