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SSC CHSL 2023 PYQ — Question 60

SSC CHSL - 08 Aug 2023 - Shift 2 • Quantitative Aptitude • Q60

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Simplify the given expression. 

(0.25)4+2×(0.25)2+1−(0.25)2(0.25)2+0.25+1{(0.25)^4+2×(0.25)^2+1-(0.25)^2}\over {(0.25)^2+0.25+1}

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 0.8125.

Given, (0.25)4+2×(0.25)2+1−(0.25)2(0.25)2+0.25+1{(0.25)^4+2×(0.25)^2+1-(0.25)^2}\over {(0.25)^2+0.25+1}

⇒ (0.25)4+(0.25)2+1(0.25)2+0.25+1{(0.25)^4+(0.25)^2+1}\over {(0.25)^2+0.25+1}

a4 + a2 + 1 = (a2 + a + a)(a2 - a + 1)

a4 + a2 + 1/(a2 + a + a) = a2 - a + 1

⇒ (0.25)2 - 0.25 + 1

⇒ 0.0625 - 0.25 + 1

⇒ 1.0625 - 0.25 = 0.8125