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Column-I Column-II
A If $\log_{x} \log_{18} (\sqrt{2} + \sqrt{8}) = \frac{- 1}{2}$
Then the value of ‘x’ is equal to P 1
B The number of integral pair(s) (x, y) whose sum is equal to their product is Q 2
C $x = \frac{1}{\sqrt{2 - \sqrt{3}}}$ and $y = \frac{1}{\sqrt{2 + \sqrt{3}}}$ then the value of ${(x - y)}^{2}$ equals R 3
D Let $x = 1 + \frac{1}{2 + \frac{1}{1 + \frac{1}{2 + \frac{1}{1 + \frac{1}{2 + .............}}}}}$
Then the value of ${(2 x - 1)}^{2}$ equals S 4

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$A - P, B - Q, C - R, D - S$

$A - S, B - Q, C - R, D - S$

$A - S, B - Q, C - Q, D - R$

None of these

answer is A.

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Detailed Solution

$(A) \log_{x} \log_{18} (3 \sqrt{2}) = - \frac{1}{2} \Rightarrow \log_{18} 3 \sqrt{2} = \frac{1}{\sqrt{x}} \Rightarrow \frac{1}{2} = \frac{1}{\sqrt{x}} \Rightarrow x = 4 (B) x = 2 & y = 2 o r x = 0 o r y = 0 (C) x = \frac{1}{\sqrt{2 - \sqrt{3}}} = \sqrt{2 + \sqrt{3}} y = \frac{1}{\sqrt{2 + \sqrt{3}}} = \sqrt{2 - \sqrt{3}} {(x - y)}^{2} = 4 - 2 \sqrt{2 + \sqrt{3}} \times \sqrt{2 - \sqrt{3}} = 4 - 2 = 2$

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