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SSC CGL 2022 PYQ — Question 42

SSC CGL Tier II - Quant - 3 Feb 2022 • Quantitative Aptitude • Q42

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If 1+32−1−32=c\sqrt{1+\frac{\sqrt{3}}{2}}-\sqrt{1-\frac{\sqrt{3}}{2}}=c, such that c > 0, then find the value of c.

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 1.

 1+32−1−32=C\sqrt{1+\frac{\sqrt{3}}{2}}-\sqrt{1-\frac{\sqrt{3}}{2}}=C

On squaring both sides we get,

⇒ C2 = 1 + 32\frac{\sqrt3}{2} + 1 - 32\frac{\sqrt3}{2} - 2 × (1+32)×(1−32)\sqrt{(1 + \frac{\sqrt3}{2}) \times (1 - \frac{\sqrt{3}}{2})}

⇒ C2 = 2 - 1

⇒ C2 = 1

⇒ C = +1 , -1

As c > 0, c = 1