Q.67 Let p, q, r and s be distinct real numbers. Max(a,b) = larger number between a and b, and Min(a,b) = smaller number between a and b. If N = Max[Min(p,q), Min(r,s)] and S = Min[Max(p,r), Max(q,s)], which of the following is definitely true? a N ≤ S, for all values of p, q, r and s b N ≥ S, for all values of p, q, r and s c N ≠ S, for all values of p, q, r and s d No specific relation exists between N and S

Consider the following case: p = 1, q = 4, r = 3 and s = 2. In this case, N = max(min(1,4),min(3,2)) = max (1,2) = 2
S = min(max(1,3),max(4,2)) = min(3,4) = 3. So, in this case N < S => option b) is wrong

Let p = 1, q = 2, r = 3, s = 4
N = 3. S = 3. So, option c) is wrong

For any combination of values, the max value that N can take is the second highest number. In this case, the highest and the second highest values should between r and s or p and q. In both these cases, the value of S is also the second highest number in the group. So, N <= S.
This can be better understood by taking an example: p = 1, q = 2, r = 3 and s = 4. N = 3 and S = 3

So, option a) is the correct answer.