Stereochemistry - GATE Chemistry MCQ

In the given compound, all substituent in cis position (above the plane). So, all group must be in up side.

  
Compound A/B are configuration enantiors. 

In the below given diagram of trans-1,3-dichlorohexane the chlorines cannot be positioned diaxial or diequatorial but can only be axial and equatorial or vice versa. Additionally, if they were diastereomers or structural isomers, then they could be separated by physical means.

Total number of isomer = 3

In A, C, and D, the plane of symmetry is there, so the only chiral molecule is option B.

In identifying stereogenic centers, any quaternary or tertiary carbons would be a good place to look. There are no quaternary carbons, and all the tertiary carbons are part of a benzene ring structure.

3-Methyl pentane shows optical activity as shown below:

The given compound, 1,2-dimethylcyclobutane has two chiral centers, and hence, has maximum of 22=4 stereoisomers. However, as shown in the scheme below, the cis-isomer has a plane of symmetry, and as a consequence, it is a meso-isomer:
 

However, trans-isomer can exists in two forms: (1R,2R)-1,2-dimethylcyclobutane and (1S,2S)-1,2-dimethylcyclobutane (see Scheme A$\mathbf{A}$).

The two isomers given in the question are both trans-isomers. Thus, they woul be either identical or enanthiomers as shown in the Scheme A$\mathbf{A}$ (cannot be diastereomers). Although, the OP's visualization is correct and can use to identify simple molecule like this, it is hard to visualize if presented complex molecule. The best way to identify stereoisomers are assign their appropriate (R/S)-configurations as I have done for OP's structures (see Scheme B$\mathbf{B}$).

Accordingly, both structures are (1R,2R)-1,2-dimethylcyclobutane. Thus, the compounds are identical.