The wavelength of the monochromatic beam is given as,
The value of the width of the slit is,
The distance of the slit from the screen is,
Thus, the distance of the dark band from the center is,
For the first dark band,
m=0,
Substituting all the known values,
The value of the distance of the dark band becomes,
Thus, the first dark band is 5.4 mm away from the center of the screen.
Hence, the correct answer is 5.4 mm.