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KVPY Sample Paper KVPY Stream-SX Model Paper-11

  • question_answer
    The number of all possible positive integral values of a for which the roots of the quadratic equation \[6{{x}^{2}}-11x+a=0\] are rational numbers is:

    A) 2

    B) 5

    C) 3

    D) 4

    Correct Answer: C

    Solution :

    D must be perfect square
    \[\Rightarrow \]   \[121-24a={{\lambda }^{2}}\]
    \[\Rightarrow \]   Maximum value of \[\alpha \] is 5
    \[\alpha =1\]\[\Rightarrow \] \[\lambda \notin I\]
    \[\alpha =2\]\[\Rightarrow \] \[\lambda \notin I\]      \[\Rightarrow \]3 integral values
    \[\alpha =3\]\[\Rightarrow \] \[\lambda \notin I\]
    \[\alpha =4\]\[\Rightarrow \] \[\lambda \notin I\]
    \[\alpha =5\]\[\Rightarrow \] \[\lambda \notin I\]


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