Xavier Aptitude Test 2014 Paper

Question : 71 of 103

Marks: +1, -0

Circle

C_1

has a radius of 3 units. The line segment PQ is the only diameter of the circle which is parallel to the X axis. P and Q are points on curves given by the equations y = a

^{x}

and y = 2a

^{x}

respectively, where a < 1. The value of a is:

1/ $6√2$
1/ $6√3$
1/ $3√6$
1/ $√6$
None of the above

Validate

Solution:

(a) Since PQ is the diameter and parallel to x-axis, there fore 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}}=2 {a}^{(\ {x}+6)} \⇒\ {a}=(1 / 2) ( {1}/{6}\ )

Case 2:

\ {y}=2 {a}^{\ {x}}=\ {a}^{(\ {x}+6)} \⇒{a}=(2)\ (\ {1}/{6}\ )

But it is given that a < 1
∴ Case 2 can not be possible.

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