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Question:

Each question is followed by two statements, A and B. Answer each question using the following instructions

Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.

Is $(\frac{1}{a^{2}} + \frac{1}{a^{4}} + \frac{1}{a^{6}} + . . .) > (\frac{1}{a} + \frac{1}{a^{3}} + \frac{1}{a^{5}} + . . .) ?$

A. −3 ≤ a ≤ 3
B. One of the roots of the equation 4x2 − 4x + 1 = 0 is a

Explanation:

R.H.S. and L.H.S. are infinite GP's with common ratio = $\frac{1}{a^{2}}$ .

∴ We need to find whether

$\frac{\frac{1}{a^{2}}}{1 - \frac{1}{a^{2}}} < \frac{\frac{1}{a}}{1 - \frac{1}{a^{2}}}$

$∴ \frac{1}{a^{2}} > \frac{1}{a}$ ...(i)

This statement (i) is always true for a < 1.

Using statement A alone:

It does not give any conclusion regarding value of a i.e. whether it is less than 1 or not.

So, statement A alone is not sufficient to answer the question.

Using statement B alone:

4a²− 4a + 1 = 0 …(ii)

∴ a = 1/2

So, statement B alone is sufficient to answer the question.

Hence, option (a).

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