SSC CPO SI and ASI 2012 Paper

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Question : 102 of 200

Marks: +1, -0

The simplified value of

{ {1}/{3}×{1}/{3}×{1}/{3}+ {1}/{4}× {1}/{4} ×{1}/{4}+ {1}/{5} ×{1}/{5} ×{1}/{5}-3×{1}/{3} ×{1}/{4} ×{1}/{5}}/{ {1}/{3} × {1}/{3}+ {1}/{4} ×{1}/{4}+ {1}/{5} ×{1}/{5}- ( {1}/{3} ×{1}/{4}+ {1}/{4}× {1}/{5}+ {1}/{5} ×{1}/{3} )}

is

$51/60$
$47/60$
$13/60$
$49/60$

Solution:

(2)Let

{1}/{3}=x, {1}/{4}=y, {1}/{5}=z

So,

{x^{3}+y^{3}+z^{3}-3 x y z}/{x^{2}+y^{2}+z^{2}-x y-y z-x z}

= {(x+y+z) (x^{2}+y^{2}+z^{2}-x y-y z-x z )}/{x^{2}+y^{2}+z^{2}-x y-y z-x z}

=x+y+z

= {1}/{3}+ {1}/{4}+ {1}/{5}= {47}/{60}

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