What are the maximum and minimum oxidation numbers of N, S and Cl?

Hint :Oxidation state of an element tells us about the tendency of the element to lose electrons. The oxidation state also tells us about if the element has actually lost electrons or it has gained electrons. If the state is positive then it gains that many electrons and negative then it has stained that number of electrons.

Complete Step By Step Answer:
Oxidation state of an element tells us about the number of electrons an element can gain or lose.
Oxidation state is related to the element’s capability to lose or gain electrons. The tendency of losing electrons depends on the number of electrons in its last shell. If they are less than half of the electrons the last orbital can accommodate, then it has a greater tendency to lose electrons. If the last orbital has more than half of the electrons to be present in the last orbital then we can say that it has greater tendency to lose electrons.
Now the elements we have got are nitrogen, sulphur and chlorine.
Nitrogen- nitrogen has five electrons in its outermost orbital and all are unpaired and as we know the most stable state of an element is when all the electrons are paired or all the electrons are unpaired. Nitrogen is in a stable state, so it can lose and gain both. The maximum and minimum oxidation states therefore will be $ + 5\,and\, - 3 $ respectively. It needs just three electrons to complete its shell and only needs to lose five electrons to reach its previous noble element.
Sulphur- now sulphur has six electrons in its outermost orbital, therefore it can lose and gain as well, it loses six electrons in the presence of greater electronegative elements and gains electrons from lesser electronegative elements. Therefore, the oxidation states it can possess, maximum and minimum are $ + 6\,and\, - 2 $ , respectively.
Chlorine- now chlorine has seven electrons in its outermost orbital, therefore it can lose and gain as well, it loses seven electrons in the presence of greater electronegative elements and gains electrons from lesser electronegative elements. Therefore, the oxidation states it can possess, maximum and minimum are $ + 7\,and\, - 1 $ , respectively.

Note :
The halogens are the most electronegative of the periodic table. They don’t generally possess negative oxidation states until and unless their size is large like that or chlorine. The electronegativity increases from left to right of the periodic table.