Given: A and B are input terminals.
Logic 1=>5V
Logic 0=<1V
Which logic gate operation, the following circuit does?

A) AND gate
B) OR gate
C) XOR gate
D) NOR gate

Hint: When both the diodes are ON, the diodes won’t allow current to flow in the circuit and when either of the diodes is ON, the current will take the path of least resistance. Check the potential drop across the larger resistor for all the 4 ON OFF possibilities for A and B.

Complete step by step answer
Let’s take the case when both A and B are ON first. The diodes won’t allow the current to flow through the smaller resistors and all the potential drop of 6V will occur across the larger resistor. So if both the diodes are on, the logic is 1.
When either of the diodes if OFF, the current will flow through the branch which is ON since the branches containing both A and B have very low resistance ($50\,\Omega < < 10k\Omega $) and so all the current will flow through that branch and the potential drop across the larger resistance will hence be zero. So if either of the diodes is ON, the logic is 0.
If both the diodes A and B are OFF, the current will flow through both the branches since both have lower resistances and hence again no potential drop will occur across the larger resistance and the logic will be 0.
Hence we only get a logic of 1 if both the diodes are ON and 0 in all other cases which correspond to the AND gate i.e. option (A).

Note
To solve such problems, we should always check out the response of the circuit in all possible configurations of points A and B. Since the difference in the resistance values is very large, when either of the points A or B are ON, almost no current will flow through the $10\,k\Omega $ resistor so we don’t need to calculate the potential drop across it since it will be negligible and we can assume the output to have logic 0.