L, C and R represent the physical quantities inductance, capacitance and resistance respectively. The combinations which have the dimensions of frequency are-

Options

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

Answer

To find the combinations of inductance (L), capacitance (C), and resistance (R) that have the dimensions of frequency, we need to analyze the dimensions of each of these quantities and their combinations.

### Step 1: Understand the Dimensions
1. **Inductance (L)**: The dimension of inductance is given by \([L] = [M^1 L^2 T^{-2} A^{-2}]\).
2. **Capacitance (C)**: The dimension of capacitance is given by \([C] = [M^{-1} L^{-2} T^4 A^2]\).
3. **Resistance (R)**: The dimension of resistance is given by \([R] = [M^1 L^2 T^{-3} A^{-2}]\).

### Step 2: Find the Dimensions of Frequency
Frequency (f) has the dimension given by:
\[ [f] = [T^{-1}] \]

### Step 3: Analyze the Combinations
Now, we will analyze the combinations of L, C, and R to see which ones yield the dimension of frequency.

#### Combination 1: \( \frac{1}{RC} \)
- Dimensions of \(RC\):
\[ [R] = [M^1 L^2 T^{-3} A^{-2}], \quad [C] = [M^{-1} L^{-2} T^4 A^2] \]
\[ [RC] = [M^1 L^2 T^{-3} A^{-2}] \cdot [M^{-1} L^{-2} T^4 A^2] = [M^0 L^0 T^1 A^0] = [T^1] \]
Thus,
\[ \frac{1}{RC} = [T^{-1}] \quad \text{(has dimensions of frequency)} \]

#### Combination 2: \( \frac{1}{\sqrt{LC}} \)
- Dimensions of \(LC\):
\[ [L] = [M^1 L^2 T^{-2} A^{-2}], \quad [C] = [M^{-1} L^{-2} T^4 A^2] \]
\[ [LC] = [M^1 L^2 T^{-2} A^{-2}] \cdot [M^{-1} L^{-2} T^4 A^2] = [M^0 L^0 T^2 A^0] = [T^2] \]
Thus,
\[ \sqrt{LC} = [T] \quad \Rightarrow \quad \frac{1}{\sqrt{LC}} = [T^{-1}] \quad \text{(has dimensions of frequency)} \]

#### Combination 3: \( \frac{R}{L} \)
- Dimensions of \( \frac{R}{L} \):
\[ [R] = [M^1 L^2 T^{-3} A^{-2}], \quad [L] = [M^1 L^2 T^{-2} A^{-2}] \]
\[ \frac{R}{L} = \frac{[M^1 L^2 T^{-3} A^{-2}]}{[M^1 L^2 T^{-2} A^{-2}]} = [T^{-1}] \quad \text{(has dimensions of frequency)} \]

### Conclusion
The combinations that have the dimensions of frequency are:
1. \( \frac{1}{RC} \)
2. \( \frac{1}{\sqrt{LC}} \)
3. \( \frac{R}{L} \)

Thus, the correct options are A, B, and C.