Diode question conducting/cutoff
D2 has 3V on its cathode and for it to conduct there has to be more than 3V on its anode. By simple inspection, the cathode voltage cannot be greater than 3V therefore D2 is not conducting.

D1 has 1V on it's cathode and because D2 is not conducting we can forget about it as having any significant role in the circuit. Therefore the remaining supply voltage being 3V via a resistor to D1's anode means D1 has to be be forward biased and conducting.

Why would D1's anode (the net labelled "V") be 1V? It won't be - it will be somewhere between 1V and 3V - it has to be greater than 1V because D1 has to be conducting and the forward volt drop for a forward conducting diode will be somewhere between 0.2V and 1V (a wide range of diodes and possible currents are included in this estimation).

So if the person giving you the question believes the voltage at "V" is only 1V they are misled - liklihood being, that for a silicon diode it will be about 1.5V to 1.7V.