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SSC CHSL 2023 PYQ — Question 59

SSC CHSL - 04 Aug 2023 - Shift 1 • Quantitative Aptitude • Q59

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Simplify: (3.321)3+(2.681)3+(1.245)3−e×3.321×2.681×1.245(3.321)2+(2.681)2+(1.245)2−(3.321×2.681)−(2.681×1.245)−(1.245×3.321)\frac{(3.321)^3+(2.681)^3+(1.245)^3-e\times3.321\times2.681\times1.245}{(3.321)^2+(2.681)^2+(1.245)^2-(3.321\times2.681)-(2.681\times1.245)-(1.245\times3.321)}=?

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Correct answer: C

Explanation

The correct answer is Option 3 i.e 7.247.

(3.321)3+(2.681)3+(1.245)3−3×3.321×2.681×1.245(3.321)2+(2.681)2+(1.245)2−(3.321×2.681)−(2.681×1.245)−(1.245×3.321)\frac{(3.321)^3+(2.681)^3+(1.245)^3-3\times3.321\times2.681\times1.245}{(3.321)^2+(2.681)^2+(1.245)^2-(3.321\times2.681)-(2.681\times1.245)-(1.245\times3.321)}

We know that,

a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)

⇒ (3.321+2.681+1.245)((3.321)2+(2.681)2+(1.245)2−(3.321×2.681)−(2.681×1.245)−(1.245×3.321))(3.321)2+(2.681)2+(1.245)2−(3.321×2.681)−(2.681×1.245)−(1.245×3.321)\frac{(3.321 + 2.681 + 1.245)((3.321)^2+(2.681)^2+(1.245)^2-(3.321\times2.681)-(2.681\times1.245)-(1.245\times3.321))}{(3.321)^2+(2.681)^2+(1.245)^2-(3.321\times2.681)-(2.681\times1.245)-(1.245\times3.321)}

⇒ (3.321 + 2.681 + 1.245) = 7.247