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JEE Main & Advanced Sample Paper JEE Main Sample Paper-9

  • question_answer
    If a & b are randomly choosen from {1,2,3,....,9} with replacement, then the probability that function\[f(x)=\frac{{{x}^{3}}}{3}+\frac{a{{x}^{2}}}{2}+bx+c(C\in R)\]is  strictly increasing is

    A) \[\frac{19}{50}\]                                              

    B) \[\frac{19}{100}\]

    C) \[\frac{31}{50}\]                                              

    D) \[\frac{31}{100}\]

    Correct Answer: A

    Solution :

    \[f'(x)={{x}^{2}}+ax+b>0\Rightarrow {{a}^{2}}-4b<0\] \[b=1\Rightarrow a=1\] \[b=2\Rightarrow a=1,2\] \[b=3\Rightarrow a=1,2,3\] \[b=4\Rightarrow a=1,2,3\] \[b=5\Rightarrow a=1,2,3,4\] \[\begin{align}   & : \\  & : \\ \end{align}\]                 \[b=10\Rightarrow a=1,2,3,4,5,6\] \[\therefore \]total pairs = 38 Probability\[=\frac{19}{50}\]


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