The correct options are
A The value of electron gain enthalpy of an element can be negative or positive
B Metallic charecter of the elements increases down the group and decreases across the period
C Ionization enthalpy of an atom is equal to electron gain enthalpy of it's unipositive cation in terms of magnitude.
D The Cl− and Ca2+ are iso- electronic species but first has larger size than second
Electron gain enthalpy of an element is defined as energy released when a neutral gaseous atom accepts an extra electron to form the gaseous negative ion.
The process of adding an electron to the atom can be positive or negative.
Energy is released when an electron is added. So, the E. G. E is negative. Similarly, when electron is added to noble gases or any other elements having stable half filled or fully filled configurations, E.G E is positive.
Metallic charecter decreases down because the outermost electrons move further away from the nucleus due to addition of an extra shell. So, electrons can be easily removed, therefore metallic charecter will increase Effective nuclear charge acting on the valence shell electrons increases across a period, the tendency to lose electrons will decrease therefore the metallic charecter decreases.
Ionization enthalpy is equal to electron gain enthalpy magnitude wise as the process is exact reverse.
Anions are formed when atoms accepts electron where as cations are formed when electrons are lost so, in case of isoelectronic species, cations will expireince more effective nuclear charge. Hence their size will be less.