I can't apply selected color in CMYK mode but can apply RGB mode.
Yes, the CMYK colour space is smaller than the RGB space. So when you move from RGB to CMYK your colours are mapped to the nearest printable colour. To generalize, the RGB space has more very saturated "bright" colours. For in depth info, read up on 'additive' (RGB) and 'subtractive' (CMYK) colour.