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JEE Main & Advanced Sample Paper JEE Main Sample Paper-16

  • question_answer
    Let \[f(x)=2{{x}^{2}}-3(a+1){{x}^{2}}+6ax-12\]has maxima and minima at \[{{x}_{1}}\] and \[{{x}_{2}}\] respectively and if \[2{{x}_{1}}={{x}_{2}}\], then the value of 'a' is

    A)  1                                            

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

    C)  -1                                          

    D)  2

    Correct Answer: D

    Solution :

    \[f'(x)=6(x-1)(x-a)\] If \[a<1,\]then\[{{x}_{1}}=a\]is point of maxima and\[{{x}_{2}}=1\]is point of minima. Hence,\[a=\frac{1}{2}\] If \[a>1,\]then\[{{x}_{1}}=1\]is point of maxima and \[{{x}_{2}}=a\]is point of minima. Hence, a =2


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