Aniline when diazotized in cold and then treated with dimethyl aniline gives a coloured product. Its structure would be

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Explanation

To solve the problem of determining the structure of the colored product formed when aniline is diazotized and then treated with dimethyl aniline, we can follow these steps:

### Step 1: Diazotization of Aniline
- **Aniline Structure**: Aniline (C6H5NH2) consists of a benzene ring with an amino group (-NH2).
- **Diazotization Reaction**: Aniline is treated with sodium nitrite (NaNO2) in the presence of hydrochloric acid (HCl) at a low temperature (0-5°C). This process converts the amino group into a diazonium group (-N2+).

**Reaction**:
\[ \text{C6H5NH2} + \text{NaNO2} + \text{HCl} \rightarrow \text{C6H5N2Cl} + \text{NaCl} + \text{H2O} \]

Here, C6H5N2Cl is the diazonium salt.

### Step 2: Reaction with Dimethyl Aniline
- **Dimethyl Aniline Structure**: Dimethyl aniline has two methyl groups attached to the nitrogen atom (C6H4(N(CH3)2)).
- **Coupling Reaction**: The diazonium salt reacts with dimethyl aniline to form a colored azo compound. In this reaction, the diazonium group (-N2+) couples with the dimethyl aniline, replacing a hydrogen atom and forming an azo bond (-N=N-).

**Reaction**:
\[ \text{C6H5N2Cl} + \text{C6H4(N(CH3)2)2} \rightarrow \text{C6H4(N(CH3)2)N=N-C6H4} + \text{HCl} \]

### Step 3: Structure of the Product
- The final product is an azo dye, specifically N,N-dimethyl-4-aminobenzenesulfonamide, which has the azo (-N=N-) linkage between the benzene rings.
- The structure can be represented as:

\[ \text{C6H4(N(CH3)2)N=N-C6H4(NH2)} \]

### Conclusion
The colored product formed from the reaction of diazotized aniline and dimethyl aniline is an azo compound, specifically N,N-dimethyl-4-aminobenzenesulfonamide.