SarkariPYQ

SSC CGL 2022 PYQ — Question 1

SSC CGL Tier II - Quant - 29 Jan 2022 • Quantitative Aptitude • Q1

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If x =  1+32−1−32\sqrt{1+\frac{\sqrt{3}}{2}}-\sqrt{1-\frac{\sqrt{3}}{2}} , then the value of 3−x3+x\frac{\sqrt{}3-x}{\sqrt{}3+x}(corrected to two decimal places) is:

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 0.27

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

On squaring both sides we get,

x2 = 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})}

x2 = 2 - 1

x2 = 1

x = +1 , -1

⇒ √3−x√3+x\frac{√3-x}{√3+x} = 3−13+1\frac{\sqrt3 -1}{\sqrt3 + 1}

On rationalization,

⇒ (3 + 1 - 23\sqrt3)/(3 - 1)

⇒ 2 - 3\sqrt3

⇒ 2 - 1.73 = 0.27