Consider the following inequalities:

1.  where a > b > 0

2.  only when a > b > 0

Which of the above is/are correct?

Calculation:

Statement:1     where a > b > 0

Let a = 2 and b = 1

⇒ 

⇒  which is correct.

Hence, statement 1 is correct.

Statemnt:2    only when a > b > 0

Let a = 2 and b = 1

⇒ 

⇒  Which is also correct.

This inequality also holds for a = 1 and b = 2 i.e.

Statement 2 is correct for b > a > 0 as well.

But according to statement 2, inequality will be correct only if a > b > 0

So, statement 2 is incorrect.

Hence, statement (1) is correct but (2) statement (2) is incorrect.

Mistake PointsPlease note the language of  the second statement

"only when a > b > 0"

We have proved thet, statement is correct for 

a = 2 & b = 1 (i.e. a > b > 0) and b = 2 & a = 1 (i.e. b > a > 0)

Hence, due to only word, statement 2 will become incorrect.