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SSC CGL 2025 PYQ — Question 73

SSC CGL - 13 Sep 2025 - Shift 2 • Quantitative Aptitude • Q73

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Evaluate the expression: (110−9)−(19−8)+(18−7)−(17−6)+(16−5)−(15−2)=?(\frac{1}{\sqrt{10}-\sqrt{9}})-(\frac{1}{\sqrt9-\sqrt{8}})+(\frac{1}{\sqrt{8}-\sqrt{7}})-(\frac{1}{\sqrt{7}-\sqrt{6}})+(\frac{1}{\sqrt{6}-\sqrt{5}})-(\frac{1}{\sqrt{5}-2})=?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. √10 - 2.

(110−9)−(19−8)+(18−7)−(17−6)+(16−5)−(15−2)(\frac{1}{\sqrt{10}-\sqrt{9}})-(\frac{1}{\sqrt9-\sqrt{8}})+(\frac{1}{\sqrt{8}-\sqrt{7}})-(\frac{1}{\sqrt{7}-\sqrt{6}})+(\frac{1}{\sqrt{6}-\sqrt{5}})-(\frac{1}{\sqrt{5}-2})

=(110−9)−(19−8)+(18−7)−(17−6)+(16−5)−(15−4)=(\frac{1}{\sqrt{10}-\sqrt{9}})-(\frac{1}{\sqrt9-\sqrt{8}})+(\frac{1}{\sqrt{8}-\sqrt{7}})-(\frac{1}{\sqrt{7}-\sqrt{6}})+(\frac{1}{\sqrt{6}-\sqrt{5}})-(\frac{1}{\sqrt{5}-\sqrt4})

= (√10 + √9) - (√9 + √8) + (√8 + √7) - (√7 + √6) + (√6 + √5) - (√5 + √4)

= √10 + √9 - √9 - √8 + √8 + √7 - √7 - √6 + √6 + √5 - √5 - √4

= √10 - √4

= √10 - 2