$(a)$ State the main characteristics of elements on which the modern periodic table is based.
$(b)$ No fixed position can be assigned to hydrogen in the periodic table. Why?

(N/A) The modern periodic table is based on the atomic number of elements and the electronic configuration (number of valence electrons).
$(b)$ Hydrogen shows dual behavior:
$1.$ Like alkali metals,it has one valence electron and forms positive ions $(H^+)$ by losing an electron.
$2.$ Like halogens,it is a non-metal,exists as a diatomic molecule $(H_2)$,and forms covalent compounds by sharing electrons.
Due to these properties resembling both groups,it cannot be assigned a fixed position.