Explanation:
Asymmetric carbon atom is a carbon atom that is attached to four different types of atoms or groups. Such a carbon atom is also called a chiral carbon atom.

Out of the given molecules, only option 'A' contains an asymmetric carbon atom. Let's see why -

CH₃CHClCOOH
This molecule has two carbon atoms, but none of them are chiral. The carbon atom attached to -COOH group has two methyl groups, one hydrogen atom and one chlorine atom, which are not different from each other.

CH₃CH₂COOH
This molecule also has two carbon atoms, but none of them are chiral. The carbon atom attached to -COOH group has two methyl groups and one ethyl group, which are not different from each other.

ClCH₂CH₂COOH
This molecule has three carbon atoms, but none of them are chiral. The carbon atom attached to -COOH group has two hydrogen atoms, one chlorine atom and one ethyl group, which are not different from each other.

Cl₂CHCOOH
This molecule has two carbon atoms, but none of them are chiral. Both carbon atoms have two chlorine atoms and one -COOH group attached to them, which are not different from each other.

CH₃CHClCOOH
This molecule has two carbon atoms, and the carbon atom attached to -COOH group is chiral. It has one hydrogen atom, one chlorine atom, one methyl group and one -COOH group attached to it, which are different from each other. Therefore, this molecule contains an asymmetric carbon atom.

Assymetric carbon means chiral carbon....ie the carbon which contains four different groups....here in option a the carbon contains 4 different groups ....so it is asyymetric carbon ..