The following can be arranged in decreasing order of wave number
A. AM radio
B. TV and FM radio
C. Microwave
D. Short radio wave

Options

A. `AgtBgtDgtC`
B. `CgtDgtBgtA`
C. `AgtBgtCgtD`
D. `DgtCgtBgtA`

Answer

To solve the problem of arranging the given electromagnetic waves in decreasing order of wave number, we need to understand the relationship between wave number (k), wavelength (λ), and frequency (ν).

### Step-by-Step Solution:

1. **Understand Wave Number**:
The wave number (k) is defined as:
\[ k = \frac{2\pi}{\lambda} \]
where λ is the wavelength. This means that wave number is inversely proportional to wavelength.

2. **Identify Wavelengths of Each Wave Type**:
- **AM Radio**: Typically has a longer wavelength (around 100 m to 1 km).
- **FM Radio and TV**: Have shorter wavelengths than AM radio (around 1 m to 3 m).
- **Microwave**: Has even shorter wavelengths (around 1 mm to 1 m).
- **Short Radio Wave**: These have wavelengths that can range from about 10 m to 100 m, but are generally shorter than AM radio waves.

3. **Arrange Waves by Wavelength**:
From the above information, we can arrange the waves in order of decreasing wavelength:
- AM Radio (longest wavelength)
- Short Radio Wave
- FM and TV Radio
- Microwave (shortest wavelength)

4. **Convert Wavelength Order to Wave Number Order**:
Since wave number is inversely related to wavelength, we can now convert the wavelength order to wave number order:
- Microwave (highest wave number)
- Short Radio Wave
- FM and TV Radio
- AM Radio (lowest wave number)

5. **Final Arrangement**:
Thus, the decreasing order of wave number is:
\[ \text{Microwave (C)} > \text{Short Radio Wave (D)} > \text{FM and TV Radio (B)} > \text{AM Radio (A)} \]

### Conclusion:
The final answer in terms of the options provided is:
\[ C > D > B > A \]