For the reduction of `NO_(3)^(c-)` ion in an aqueous solution, `E^(c-)` is `+0.96V`, the values of `E^(c-)` for some metal ions are given below `:`
`i.V^(2+)(aq)+2e^(-)rarr V, " "E^(c-)=-1.19V`
`ii. Fe^(3+)(aq)+3e^(-) rarr Fe, " "E^(c-)=-0.04V`
`iii. Au^(3+)(aq)+3e^(-) rarr Au, " "E^(c-)=+1.40V`
`iv. Hg^(2+)(aq)+2e^(-) rarr Hg, " "E^(c-)=+0.86V`
The pair`(s)` of metals that is `//` are oxidized by `NO_(3)^(c-)` in aqueous solution is `//` are

Explanation

To determine which pairs of metal ions are oxidized by the `NO3^-` ion in an aqueous solution, we need to compare the standard reduction potentials (E°) of the metal ions with that of the `NO3^-` ion.

### Step-by-Step Solution:

1. **Identify the Standard Reduction Potential of `NO3^-`:**
The standard reduction potential for the reduction of `NO3^-` is given as:
\[ E^\circ(\text{NO}_3^-/\text{NO}) = +0.96 \, \text{V} \]

2. **List the Standard Reduction Potentials of the Given Metal Ions:**
The standard reduction potentials for the metal ions provided are:
- \( V^{2+} + 2e^- \rightarrow V \), \( E^\circ = -1.19 \, \text{V} \)
- \( Fe^{3+} + 3e^- \rightarrow Fe \), \( E^\circ = -0.04 \, \text{V} \)
- \( Au^{3+} + 3e^- \rightarrow Au \), \( E^\circ = +1.40 \, \text{V} \)
- \( Hg^{2+} + 2e^- \rightarrow Hg \), \( E^\circ = +0.86 \, \text{V} \)

3. **Compare the Standard Reduction Potentials:**
To find which metal ions can be oxidized by `NO3^-`, we need to identify those with standard reduction potentials less than `+0.96 V` (since a higher reduction potential means a stronger oxidizing agent).

- For \( V^{2+} \): \( -1.19 \, \text{V} < 0.96 \, \text{V} \) (can be oxidized)
- For \( Fe^{3+} \): \( -0.04 \, \text{V} < 0.96 \, \text{V} \) (can be oxidized)
- For \( Au^{3+} \): \( +1.40 \, \text{V} > 0.96 \, \text{V} \) (cannot be oxidized)
- For \( Hg^{2+} \): \( +0.86 \, \text{V} < 0.96 \, \text{V} \) (can be oxidized)

4. **Identify the Pairs of Metals:**
The metal ions that can be oxidized by `NO3^-` are:
- \( V^{2+} \)
- \( Fe^{3+} \)
- \( Hg^{2+} \)

5. **Conclusion:**
The pairs of metals that can be oxidized by `NO3^-` in aqueous solution are:
- \( V^{2+} \) and \( Fe^{3+} \)
- \( V^{2+} \) and \( Hg^{2+} \)
- \( Fe^{3+} \) and \( Hg^{2+} \)

### Final Answer:
The pairs of metals that are oxidized by `NO3^-` in aqueous solution are \( V^{2+}, Fe^{3+} \) and \( Hg^{2+} \).