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SSC CGL 2025 PYQ — Question 73

SSC CGL - 18 Sep 2025 - Shift 2 • Quantitative Aptitude • Q73

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Identify the incorrect relationship(s) from the list below:

(i) 6+2=5+3\sqrt6 + \sqrt2 = \sqrt5 +\sqrt3
(ii) 6+2<5+3\sqrt6 + \sqrt2 < \sqrt5 +\sqrt3
(ii) 6+2>5+3\sqrt6 + \sqrt2 > \sqrt5 +\sqrt3

 

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Correct answer: C

Explanation

The correct answer is Option 3 i.e. (i) and (iii).

(6+2)2=6+2+212=8+43(\sqrt6 + \sqrt2)^2 = 6 + 2 + 2\sqrt{12} = 8 + 4\sqrt3

(5+3)2=5+3+215=8+215(\sqrt5 + \sqrt3)^2 = 5 + 3 + 2\sqrt{15} = 8 + 2\sqrt{15}

(4√3)2 = 48 and (2√15)2 = 60

So, 43<2154\sqrt3 < 2\sqrt{15}

Thus 6+2<5+3\sqrt6 + \sqrt2 < \sqrt5 + \sqrt3 ⇒ (ii) is correct, (i) and (iii) are incorrect.