This problem is based on writing ionic equations and determining oxidation states of elements.
In order to write the complete ionic equation, first write the balanced molecular equation. Then show the aqueous compounds dissociated into ions. Insoluble salts, weak acids and bases are written in form of their molecular formula.
Then cancel out the ions that are common on both the sides to get the net ionic equation.
Ionic equations are chemical equations in which the electrolytes that dissociate completely in aqueous solution are written as dissociated ions. The symbol aq is written in front of the ions to show that they are in aqueous solutions.
The oxidation state or the oxidation number of an element is equal to the number of electrons that an atom gains, loses or shares when combines with other atoms to form a compound.
To determine the oxidation state of an element there are certain points to remember.
Oxidation state of an uncombined atom is 0. The sum of oxidation states of all atoms in a neutral compound is 0 and in an ion is equal to the ionic charge. In an oxidation reduction reaction if the oxidation number of an element increases, then it shows that is oxidized, and if the oxidation number decreases, it shows that the element is reduced.
(1)
In the reaction,
consists of
and
,
consists of
and
.
In this reaction there is double displacement of ions. So,
and
forms
and
and
forms water. So, the chemical equation for this reaction is as follows:

In this equation,
and
are balanced, but there are two
and two
on left side, and only two hydrogen and one oxygen atoms on right hand side.
So, put the coefficient two before
to get the balanced molecular equation as follows:

In the reaction,

Barium hydroxide and sulphuric acid are soluble in water,and barium sulphate is a solid that is insoluble.Water is in liquid state.
Thus the complete chemical equation with physical states of the substances is

In this chemical equation, barium hydroxide and sulphuric acid are aqueous.
So replacing these by their dissociated ions in the chemical equation,we get the complete ionic equation.

As there are no common ions on the two sides, the complete ionic equation is the net ionic equation.
Thus, the net ionic equation is as follows:

(2.i)
The sum of oxidation states of all atoms in an ion is equal to the ionic charge. In
,the charge on ion is
. In
,there are two carbons and four oxygen atoms. Oxidation state of oxygen is 
Thus, oxidation state is calculated as follows:

Thus, oxidation state of carbon is
in
.
(2.ii)
Oxidation state of
is
and Oxidation state of
is
.
and
are neutral.
Thus for
, the oxidation state is calculated as follows:

For
, the oxidation state is calculated as follows:

Thus oxidation state of
decreases from
in
to
in
.
The net ionic equation is as follows:

The oxidation state of carbon is
in
.
The
is reduced in the reaction.
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