Step 1: Recall the diode rule.
An ideal diode conducts only when forward biased, that is when its anode (the $p$ side) is at a higher potential than its cathode (the $n$ side). Reverse biased, it is an open switch.
Step 2: Think series versus parallel.
In a single series loop a current can flow only if every diode in the loop is forward biased. One reverse biased diode breaks the whole loop.
Step 3: Scan the four circuits.
We look for the arrangement where the only available path is blocked by a reverse biased diode.
Step 4: Identify the blocked loop.
In circuit (a) the diodes are placed so that the conducting path meets a diode whose $n$ side faces the higher potential terminal of the $1\,\text{V}$ source. That diode is reverse biased.
Step 5: Trace the consequence.
With this diode acting as an open switch and no parallel bypass, no charge can circulate, so the ammeter current is zero.
Step 6: Contrast the rest.
The other circuits offer at least one forward biased route, so they carry current and the meter deflects. Hence (a), option (B). \[ \boxed{\text{circuit (a)}} \]