Computer Sciences > Gate 2015 Set-2 > Number System
If p, q, r, s are distinct integers such that:

f(p, q, r, s) = max (p, q, r, s)
g(p, q, r, s) = min (p, q, r, s)
h(p, q, r, s) = remainder of (p × q) / (r × s) if (p × q) > (r × s) OR remainder of (r × s) / (p × q) if (r × s) > (p × q)
Also a function fgh (p, q, r, s) = f(p, q, r, s) × g(p, q, r, s) × h(p, q, r, s).

Also the same operation are valid with two variable functions of the form f(p, q).

What is the value of fg(h(2, 5, 7, 3), 4, 6, 8)?

Correct : 8

Given functions:
f(p, q, r, s) = max(p, q, r, s)
g(p, q, r, s) = min(p, q, r, s)
h(p, q, r, s) = remainder when larger product is divided by smaller product

We need to find: fg(h(2, 5, 7, 3), 4, 6, 8)

Let me start from the innermost function h(2, 5, 7, 3):
First, calculating the products:
p × q = 2 × 5 = 10
r × s = 7 × 3 = 21

Since (r × s) > (p × q), which means 21 > 10
h(2, 5, 7, 3) = remainder of 21 ÷ 10
h(2, 5, 7, 3) = 1

Now I need to find fg(1, 4, 6, 8):
Here fg means f × g (multiplication of f and g functions)

Calculating f(1, 4, 6, 8):
f(1, 4, 6, 8) = max(1, 4, 6, 8) = 8

Calculating g(1, 4, 6, 8):
g(1, 4, 6, 8) = min(1, 4, 6, 8) = 1

Therefore:
fg(1, 4, 6, 8) = f(1, 4, 6, 8) × g(1, 4, 6, 8)
fg(1, 4, 6, 8) = 8 × 1
fg(1, 4, 6, 8) = 8

Answer: fg(h(2, 5, 7, 3), 4, 6, 8) = 8

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