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SSC Sample Paper Mock Test-20 SSC CGL Tear-II Paper-1

  • question_answer
    \[\frac{{{(a-b)}^{3}}+{{(b-c)}^{3}}+{{(c-a)}^{3}}}{6\,\,(a-b)(b-c)(c-a)}\]is equal to

    A) 5

    B)  3     

    C)  2

    D)  1

    Correct Answer: D

    Solution :

    Putting \[(a-b)=x,\]\[(b-c)=y\]and \[(c-a)=z,\] we get   \[x+y+z=0\] \[\therefore \]      \[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}=3xyz\] \[\therefore \] Given expression \[=\frac{{{x}^{3}}+{{y}^{3}}+{{z}^{3}}}{6xyz}=\frac{3xyz}{6xyz}=\frac{1}{2}\]


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