Consider the following statements :

1. Lions do not have a particular breeding season.

2. Unlike most other big cats, cheetahs do not roar.

3. Unlike male lions, male leopards do not proclaim their territory by scent marking.

Which of the statements given above are correct?

The correct option is 1 and 2 only.

Let us analyze each statement step-by-step to understand why they are correct or incorrect:

Statement 1: Lions do not have a particular breeding season.
This statement is correct. Unlike many other wild animals, lions do not have a specific annual breeding season. Female lions (lionesses) are polyestrous and can come into heat at any time of the year. Consequently, cubs can be born in any month, although there can sometimes be peaks in breeding activity within a pride, especially after a pride takeover by new dominant males.

Statement 2: Unlike most other big cats, cheetahs do not roar.
This statement is correct. The ability to roar is determined by the structure of the hyoid apparatus and the vocal cords. Big cats belonging to the genus Panthera (such as lions, tigers, leopards, and jaguars) have a flexible hyoid apparatus that allows them to roar. Cheetahs (genus Acinonyx), along with snow leopards and cougars, have a completely ossified (rigid) hyoid apparatus, which prevents them from roaring. Instead, cheetahs communicate using sounds like purring, chirping, hissing, and growling.

Statement 3: Unlike male lions, male leopards do not proclaim their territory by scent marking.
This statement is incorrect. Both male lions and male leopards actively proclaim and defend their territories using scent marking. Leopards use urine spraying, cheek rubbing, claw scraping on trees, and feces to mark their home ranges and communicate their presence to other leopards. Therefore, the assertion that leopards do not perform scent marking is false.

Conclusion:
Since statements 1 and 2 are correct and statement 3 is incorrect, the correct option is "1 and 2 only".