XAT 2014 — QA & DI Question 13

Points P and Q have the same Y coordinate but their X coordinates differ by 6 units (Since the diameter = 6 units)

We have two possible cases:

Case 1:

$y=a^x=2a^{(x+6)}$

$a={(1/2)}^{\left(\frac{1}{6}\right)}$

Case 2:

$y=2a^x=a^{(x+6)}$

$a={\left(2\right)}^{\left(\frac{1}{6}\right)}$

But it is given that a < 1

∴ Case 2 can be discarded

Hence, option (a).