$K$ and $Ca$ have atomic numbers $19$ and $20$ respectively,and they belong to the same period.
$(a)$ Which among them would have a smaller atomic size?
$(b)$ Which one would be more electropositive?
$(c)$ To which group would each of them belong?

(N/A) $Ca$ has a smaller atomic size. As we move from left to right across a period,the atomic size decreases because the effective nuclear charge increases,pulling the electrons closer to the nucleus.
$(b)$ $K$ is more electropositive. Electropositive character (metallic character) decreases across a period from left to right because the effective nuclear charge increases,making it harder to lose electrons.
$(c)$ $K$ belongs to group $1$ (Alkali Metals). $Ca$ belongs to group $2$ (Alkaline Earth Metals).