To solve the problem, we need to analyze the resistances of the wire samples A, B, C, and D, and determine the relationship between their resistivities based on the given resistances.
### Step-by-Step Solution:
1. **Understand the Resistance Formula**:
The resistance \( R \) of a wire is given by the formula:
\[
R = \frac{\rho L}{A}
\]
where \( \rho \) is the resistivity of the material, \( L \) is the length of the wire, and \( A \) is the cross-sectional area. Since all samples have the same length and area, the resistance is directly proportional to the resistivity.
2. **List the Given Resistances**:
- Resistance of sample A, \( R_A = 10 \, \Omega \)
- Resistance of sample B, \( R_B = 15 \, \Omega \)
- Resistance of sample C, \( R_C = 18 \, \Omega \)
- Resistance of sample D, \( R_D = 5 \, \Omega \)
3. **Determine the Order of Resistivity**:
Since resistance is directly proportional to resistivity, we can establish the following order based on the resistances:
- Highest resistance corresponds to highest resistivity.
- Therefore, the order of resistivity from highest to lowest is:
\[
\rho_C > \rho_B > \rho_A > \rho_D
\]
This translates to:
- \( R_C = 18 \, \Omega \) (highest resistivity)
- \( R_B = 15 \, \Omega \)
- \( R_A = 10 \, \Omega \)
- \( R_D = 5 \, \Omega \) (lowest resistivity)
4. **Analyze the Statements**:
Now we need to evaluate the statements provided in the question to find the incorrect one:
- **Statement 1**: The resistivity of material C is less than that of material A. (Incorrect)
- **Statement 2**: The resistivity of material A is twice that of material D. (Correct)
- **Statement 3**: The resistivity of A is thrice that of resistivity of D. (Incorrect)
- **Statement 4**: The resistivity of material C is greater than that of material B. (Correct)
5. **Identify the Incorrect Statement**:
From the analysis, we see that:
- Statement 1 is incorrect because \( \rho_C > \rho_A \).
- Statement 3 is also incorrect because \( \rho_A \) is double \( \rho_D \), not thrice.
Thus, the incorrect statements are Statements 1 and 3. However, if we are to choose one, we can highlight Statement 3 as a clear falsehood.
### Conclusion:
The incorrect statement is:
- **The resistivity of A is thrice that of resistivity of D.**
