L, C and R represent the physical quantities, inductance, capacitance and resistance respectively. The combination(s) which have the dimensions of frequency are

Options

A. `(1)/(RC)`
B. `(R)/(L)`
C. `(1)/(sqrt(LC))`
D. `(C)/(L)`

Explanation

To determine which combinations of inductance (L), capacitance (C), and resistance (R) have the dimensions of frequency, we need to analyze the dimensions of each quantity and their combinations.

### Step-by-Step Solution:

1. **Understanding Dimensions of L, C, and R**:
- Inductance (L) has the dimension: \([L] = [M^1 L^2 T^{-2} A^{-2}]\)
- Capacitance (C) has the dimension: \([C] = [M^{-1} L^{-2} T^4 A^2]\)
- Resistance (R) has the dimension: \([R] = [M^1 L^2 T^{-3} A^{-2}]\)

2. **Finding the Dimension of Frequency**:
- Frequency (f) is defined as the reciprocal of the time period (T), hence its dimension is: \([f] = [T^{-1}]\).

3. **Analyzing the Combinations**:
- **Combination 1: \( \frac{1}{CR} \)**
- Calculate the dimension:
\[ [CR] = [C][R] = [M^{-1} L^{-2} T^4 A^2] \cdot [M^1 L^2 T^{-3} A^{-2}] = [M^0 L^0 T^1 A^0] = [T] \]
- Therefore, \( \frac{1}{CR} \) has the dimension:
\[ \left[\frac{1}{CR}\right] = [T^{-1}] \]
- This matches the dimension of frequency.

- **Combination 2: \( \frac{L}{R} \)**
- Calculate the dimension:
\[ \frac{L}{R} = \frac{[L]}{[R]} = \frac{[M^1 L^2 T^{-2} A^{-2}]}{[M^1 L^2 T^{-3} A^{-2}]} = [T] \]
- Therefore, \( \frac{L}{R} \) has the dimension:
\[ \left[\frac{L}{R}\right] = [T] \]
- Thus, \( \frac{1}{\frac{L}{R}} = \frac{R}{L} \) has the dimension:
\[ [T^{-1}] \]
- This also matches the dimension of frequency.

- **Combination 3: \( \sqrt{CR \cdot LR} \)**
- Calculate the dimension:
\[ CR \cdot LR = [C][R][L][R] = [M^{-1} L^{-2} T^4 A^2] \cdot [M^1 L^2 T^{-3} A^{-2}] \cdot [M^1 L^2 T^{-2} A^{-2}] \]
\[ = [M^{1-1} L^{2-2} T^{4-3-2} A^{2-2}] = [M^0 L^0 T^{-1} A^0] = [T^{-1}] \]
- Therefore, \( \sqrt{CR \cdot LR} \) has the dimension:
\[ [T^{-1}] \]
- This matches the dimension of frequency.

- **Combination 4: \( \frac{C}{L} \)**
- Calculate the dimension:
\[ \frac{C}{L} = \frac{[C]}{[L]} = \frac{[M^{-1} L^{-2} T^4 A^2]}{[M^1 L^2 T^{-2} A^{-2}]} = [M^{-2} L^{-4} T^6 A^4] \]
- This does not match the dimension of frequency.

4. **Conclusion**:
- The combinations that have the dimensions of frequency are:
- \( \frac{1}{CR} \)
- \( \frac{L}{R} \)
- \( \sqrt{CR \cdot LR} \)

### Final Answer:
The combinations that have the dimensions of frequency are:
- \( \frac{1}{CR} \)
- \( \frac{L}{R} \)
- \( \sqrt{CR \cdot LR} \)