Identify the incorrectly matched set ffrom the following

Options

A. Set - A : Wavelength `(lambda)` , SET - B : Nanometre
B. Set A : Frequency `(upsilon)` , Set B : Hertz
C. Set A : Wave number , Set B : `"metre"^(-1)`
D. Set A : Velocity (C ), Set B : ergs

Answer

To identify the incorrectly matched set from the given options, we will analyze each option one by one, focusing on the physical quantity and its corresponding unit.

### Step-by-Step Solution:

1. **Option A: Wavelength**
- **Physical Quantity**: Wavelength (denoted by λ)
- **Given Unit**: Nanometer (nm)
- **Analysis**: Wavelength is a measure of length, and nanometer is indeed a unit of length. Therefore, this option is correctly matched.

2. **Option B: Frequency**
- **Physical Quantity**: Frequency (denoted by ν)
- **Given Unit**: Hertz (Hz)
- **Analysis**: Frequency is defined as the number of occurrences of a repeating event per unit time, and its unit is Hertz (1 Hz = 1 s⁻¹). This option is also correctly matched.

3. **Option C: Wave Number**
- **Physical Quantity**: Wave number (denoted by 𝜈̅)
- **Given Unit**: Meter inverse (m⁻¹)
- **Analysis**: Wave number is defined as the number of wavelengths per unit distance, which is the inverse of wavelength. The SI unit of wavelength is meters, hence the unit of wave number is indeed meter inverse. This option is correctly matched as well.

4. **Option D: Velocity**
- **Physical Quantity**: Velocity (denoted by v)
- **Given Unit**: Ergs
- **Analysis**: Velocity is defined as the displacement per unit time, typically measured in meters per second (m/s) or centimeters per second (cm/s). Ergs, however, is a unit of energy, not velocity. Therefore, this option is incorrectly matched.

### Conclusion:
The incorrectly matched set is **Option D: Velocity with the unit Ergs**.