If the value of the determinant a    1    11    b    11    1    c is positive, then

If the value of the determinant a    1    11    b    11    1    c is positive, then

  1. A

    abc >1

  2. B

    abc>-8

  3. C

    abc < - 8

  4. D

    abc >-2

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    Solution:

    We have,

    Δ=a    1    11    b    11    1    c=abc(a+b+c)+2

        Δ>0    abc+2>a+b+c    abc+2>3(abc)1/3 A.M. > G.M. a+b+c3>(abc)1/3

    x3+2>3x, where x=(abc)1/3x33x+2>0(x1)2(x+2)>0x+2>0x>2(abc)1/3>2abc>8

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