The circuit diagram is as shown below.
According to question, when given pair of point in options are connected through a resistance
R, then equivalent resistance between point A and B
(RAB) remains unchanged. It is only possible when current does not flows through resistance
R and circuit become Wheatstone bridge as shown in the figure below,
At the balanced condition,
= The current flow in
CD branch will be zero.
Now by checking each option,
from option
(a), circuit is,
Now,
∵=⇒=⇒= Hence, option (a) is correct.
From option (b), circuit is
Now,
=⇒≠ So, option (b) is also incorrect.
From option (c) circuit is,
Now.
=⇒=⇒= So, option
(c) is also correct.
From option (d), circuit is