​ At which of the four conditions, the density of nitrogen will be the largest? STP 273 K and 2 atm 546 K and 1 atm 546 K and 2 atm

Dear Student

Since the density is equal to $\rho = \frac{P.Mw}{RT} [ P = pressure, Mw = molecular weight]$
So maximum density of nitrogen can be obtained at maximum pressure or lowest temperature.

So, in the given option (1) is correct at STP where the pressure is 1 atm and temperature is 273 K 

Regards