At 300 K, the density of a certain gaseous molecule at 2 bar is double to that of dinitrogen (N2) at 4 bar. The molar mass of the gaseous molecule is :

For unknown gas : PM = ρRT
2 bar × M = ρunknownRT .. (1)
For nitrogen gas : 4 bar × 28 g/mol = ρnitrogenRT .. (2)
But, ρunknown = 2ρnitrogen
Substitute this in equation (1)
2 bar × M = 2ρnitrogenRT .. (3)
Divide equation (3) with equation (2)
(2 bar × M) / (4 bar × 28 g/mol) = (2ρnitrogenRT) / (ρnitrogenRT)
M / (2 × 28 g/mol) = 2
M = 4 × 28 g/mol = 112 g/mol
The molar mass of the gaseous molecule is 112 g/mol
Therefore, the correct option is A.