The question says
A micro program control unit is required to generate a total of 25 control signals. Assume that during any micro instruction, at most two control signals are active
Here at most means the number of signals that can be active at a time can be 1 or 2 and we also have to consider the case when no signals are active.
As minimum number of bits is asked so we will go for vertical micro programming. There are 25 control signals any 2 at most can be active so no. of ways this can happen =
$^nC_0\ +\ ^nC_1\ +\ ^nC_2 $ here n = 5 so we get the value as 326 ways.
Now, 9 0s will represent no signal Let us try to divide the rest 325 ways on the basis of number of signals active (1 or 2) at a time.
Let's say we are using first and second bit to represent 1 active and 2 active signal.
CASE 1: Let us consider the first 2 bits as 10 represent "1 signal is active at a time" and 11 represents "2 signals are active at a time ". Now we can see that we are left with 7 bits so no. of control signals in which 1 signal is active is $2^7 = 128$. Similarly, no. of control signals with 2 signals active at a time is also $128$. But the number of control signals we get for "2 signals are active at a time " is 300. so, we cannot use this process.
CASE 2: Let us consider 01XXXXXXX for "1 signal is active at a time" and 1XXXXXXXX for "2 signals are active at a time ". Even in this case we are getting the number of control signals for which 2 signals are active as $2^8 = 256$. So, we can see that we need to add an extra bit in order to differentiate between the two types (1 and 2) of control signals.
So, answer is (C) 10 bits