Problem

Match the following:

Column I	Column II
(A) If $\alpha$ and $\beta$ are the roots of $ax^2 + bx + c = 0$ , where $a = 2^{\log_2 3} - 3^{\log_3 2}$ , $b = 1 + 2^{\sqrt{\log_2 3}} - 3^{\sqrt{\log_3 2}}$ , and $c = \log_2 \log_2 \sqrt{\sqrt{\sqrt{\sqrt{\sqrt{2}}}}}$ , then HM of $\alpha$ and $\beta$ is	(p) divisible by 2
(B) The sum of the solutions of the equation $x-1 ^{\log_2 x^2 - 2\log_x 4} = (x-1)^7$ is	(q) divisible by 4
(C) If $5(\log_y x + \log_x y) = 26$ , $xy = 64$ , then the value of $x-y$ is	(r) divisible by 6
	(s) divisible by 8
	(t) divisible by 10