If the dimensions of `B^(2)l^(2)C` are `[M^(a)L^(b)T^(c)]`, then the value of `a+b+c` is
[Here `B,l` and `C` represent the magnitude of magnetic field, length and capacitance respectively]

Answer

To solve the problem, we need to find the dimensions of \( B^2 l^2 C \) and express them in the form \( [M^a L^b T^c] \). Here, \( B \) is the magnetic field, \( l \) is length, and \( C \) is capacitance.

### Step 1: Determine the dimensions of each variable

1. **Magnetic Field \( B \)**:
The dimension of the magnetic field \( B \) is given by:
\[ [B] = [M^1 L^0 T^{-2} A^{-1}] \]
where \( A \) is the unit of electric current.

2. **Length \( l \)**:
The dimension of length \( l \) is:
\[ [l] = [L^1] \]

3. **Capacitance \( C \)**:
The dimension of capacitance \( C \) is:
\[ [C] = [M^{-1} L^{-2} T^4 A^2] \]

### Step 2: Calculate the dimensions of \( B^2 l^2 C \)

Now, we will calculate the dimensions of \( B^2 l^2 C \):
\[ [B^2] = [B]^2 = [M^1 L^0 T^{-2} A^{-1}]^2 = [M^2 L^0 T^{-4} A^{-2}] \]
\[ [l^2] = [l]^2 = [L^1]^2 = [L^2] \]
\[ [C] = [M^{-1} L^{-2} T^4 A^2] \]

Now, we can combine these dimensions:
\[ [B^2 l^2 C] = [B^2] \cdot [l^2] \cdot [C] \]
Substituting the dimensions we calculated:
\[ [B^2 l^2 C] = [M^2 L^0 T^{-4} A^{-2}] \cdot [L^2] \cdot [M^{-1} L^{-2} T^4 A^2] \]

### Step 3: Combine the dimensions

Now, we combine the dimensions step-by-step:
1. For mass \( M \):
\[ M^{2} \cdot M^{-1} = M^{2 - 1} = M^{1} \]
2. For length \( L \):
\[ L^{0} \cdot L^{2} \cdot L^{-2} = L^{0 + 2 - 2} = L^{0} \]
3. For time \( T \):
\[ T^{-4} \cdot T^{4} = T^{-4 + 4} = T^{0} \]
4. For current \( A \):
\[ A^{-2} \cdot A^{2} = A^{-2 + 2} = A^{0} \]

Thus, the combined dimensions of \( B^2 l^2 C \) are:
\[ [B^2 l^2 C] = [M^1 L^0 T^0 A^0] = [M^1] \]

### Step 4: Identify \( a, b, c \)

From the combined dimensions:
- \( a = 1 \)
- \( b = 0 \)
- \( c = 0 \)

### Step 5: Calculate \( a + b + c \)

Now, we can find \( a + b + c \):
\[ a + b + c = 1 + 0 + 0 = 1 \]

### Final Answer
The value of \( a + b + c \) is \( 1 \).

---