COLUMN-I COLUMN-IIA)If a=3(8+27−8−27),b=(42)(30)+36, then the value of logab is equal toP)-1B)If a=(4+23−4−23),b=11+62−11−62 then the value of logab is equal to Q)1C)If a=3+22,b=3−22 , then the value of logab is equal toR)2D)If a=7+72−1,b=7−72−1 , then the value of logab is equal to S)32

A) a=3((7+1)−(7−1))=6b=1296=36 B) a=(3+1)−(3−1)=2 b=(3+2)−(3−2)=22C) a=2+1;b=2−1D) a=2+3; b=2−3

COLUMN-I COLUMN-IIA)If a=3(8+27−8−27),b=(42)(30)+36, then the value of logab is equal toP)-1B)If a=(4+23−4−23),b=11+62−11−62 then the value of logab is equal to Q)1C)If a=3+22,b=3−22 , then the value of logab is equal toR)2D)If a=7+72−1,b=7−72−1 , then the value of logab is equal to S)32

A) a=3((7+1)−(7−1))=6b=1296=36 B) a=(3+1)−(3−1)=2 b=(3+2)−(3−2)=22C) a=2+1;b=2−1D) a=2+3; b=2−3

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COLUMN-I COLUMN-II
A) If $a = 3 (\sqrt{8 + 2 \sqrt{7}} - \sqrt{8 - 2 \sqrt{7}}), b = \sqrt{(42) (30) + 36}$ , then the value of $\log_{a} b$ is equal to P) $- 1$
B) If $a = (\sqrt{4 + 2 \sqrt{3}} - \sqrt{4 - 2 \sqrt{3}}), b = \sqrt{11 + 6 \sqrt{2}} - \sqrt{11 - 6 \sqrt{2}}$ then the value of $\log_{a} b$ is equal to Q) 1
C) If $a = \sqrt{3 + 2 \sqrt{2}}, b = \sqrt{3 - 2 \sqrt{2}}$ , then the value of $\log_{a} b$ is equal to R) 2
D) If $a = \sqrt{7 + \sqrt{7^{2} - 1}}, b = \sqrt{7 - \sqrt{7^{2} - 1}}$ , then the value of $\log_{a} b$ is equal to S) $\frac{3}{2}$

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$A \to R; B \to S; C \to P; D \to P$

$A \to S; B \to R; C \to P; D \to P$

$A \to R; B \to P; C \to P; D \to S$

answer is A.

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Detailed Solution

A) $a = 3 ((\sqrt{7} + 1) - (\sqrt{7} - 1)) = 6$
$b = \sqrt{1296} = 36$
B) $a = (\sqrt{3} + 1) - (\sqrt{3} - 1) = 2$
$b = (3 + \sqrt{2}) - (3 - \sqrt{2}) = 2 \sqrt{2}$
C) $a = \sqrt{2} + 1; b = \sqrt{2} - 1$
D) $a = 2 + \sqrt{3}; b = 2 - \sqrt{3}$

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