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CLAT Sample Paper CLAT Sample Paper-4

  • question_answer
    If \[(x-1)\] is a factor of \[A{{x}^{3}}+B{{x}^{2}}-36x+22\] and \[{{2}^{B}}={{64}^{A}},\] find A and B.

    A)  \[A=4,\,\,B=16\]

    B)  \[A=6,\,\,B=24\]

    C)  \[A=2,\,\,B=12\]     

    D)  \[A=8,\,B=16\]

    Correct Answer: C

    Solution :

    Since, \[(x-1)\] is a factor of \[A{{x}^{3}}+B{{x}^{2}}-36x+22\]. \[\therefore \] \[A{{(1)}^{3}}+{{(1)}^{2}}-36(1)+22=0\] \[\Rightarrow \] \[A+B=14\] ?(i) and \[{{2}^{B}}={{({{2}^{6}})}^{A}}\Rightarrow B=6A\] ?(ii) On solving Eqs. (i) and (ii), we get \[A=2,\,\,B=12\]


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