UPSC CDS 1 2022 Math Paper

Given:
A is the arithmetic mean of p and q
G is the geometric mean of p and q
And p>q
Concept Used:
For andy two numbers A.M ≥ G.M
Calculation:
For any two positive numbers p and q
A≥G
So, options 1) and 3) both can be the answer
But for option 3)
We have to take p=q
Now, if we put p=q in A≥G
i.e in (p+q)∕2≥√pq, we get
2p∕2≥√p2
⇒p≥p
‌ i.e ‌p=p
But According to the question we have
p>q
∴ The only 1) option will be correct.