Solution

The statements (I), (III) and (IV) are correct.

As the s-character of a hybrid orbital decreases,

(I) the bond angle decreases. The bond angles for $$ sp $$, $$sp^{2}$$ and $$ sp^{3} $$ hybrid orbitals are $$180^{0}$$ , $$ 120^{0} $$ and $$109^{0}$$ respectively.

(II) the bond strength decreases. Triple bond ($$sp$$ hybridisation) is stronger than double bond ($$sp^{2}$$ hybridisation) which in turn is stronger than single bond ($$sp^{3}$$ hybridisation).

(III) the bond length increases. Triple bond ($$ sp $$ hybridisation) is shorter than double bond ($$sp^{2}$$ hybridisation) which in turn is shorter than single bond ($$sp^{3}$$ hybridisation).

(IV) the size of orbital increases. s orbital is smaller than p orbital. Hence, $$ sp $$ hybrid orbitals are smaller than $$sp^{2}$$ hybrid orbitals which in turn are smaller than $$sp^{3}$$ hybrid orbitals.

Hence , option A is correct .