Among the following, what is the total number of compounds having zero oxidation state of the underlined elements?
a. `ul(S)O_(3)^(2-)`
b. `H_(2)ul(C )O`
c. `ul(C )H_(2)Cl_(2)`
d. `Na_(2)ul(cl_(2))`
e. `ul(O)_(3)`

Explanation

To find the total number of compounds with zero oxidation state of the underlined elements, we will calculate the oxidation states of the specified elements in each compound step by step.

### Step 1: Analyze the first compound `ul(S)O_(3)^(2-)`
- The compound is `SO3^(2-)`.
- Let the oxidation state of sulfur (S) be \( X \).
- The oxidation state of oxygen (O) is \(-2\).
- The equation for the overall charge is:
\[ X + 3(-2) = -2 \]
Simplifying this gives:
\[ X - 6 = -2 \implies X = +4 \]
- **Oxidation state of S = +4** (not zero).

### Step 2: Analyze the second compound `H_(2)ul(C)O`
- The compound is `H2CO`.
- Let the oxidation state of carbon (C) be \( X \).
- The oxidation state of hydrogen (H) is \( +1 \) and oxygen (O) is \(-2\).
- The equation for the overall charge is:
\[ 2(+1) + X + (-2) = 0 \]
Simplifying this gives:
\[ 2 + X - 2 = 0 \implies X = 0 \]
- **Oxidation state of C = 0**.

### Step 3: Analyze the third compound `ul(C)H_(2)Cl_(2)`
- The compound is `CH2Cl2`.
- Let the oxidation state of carbon (C) be \( X \).
- The oxidation state of hydrogen (H) is \( +1 \) and chlorine (Cl) is \(-1\).
- The equation for the overall charge is:
\[ 2(+1) + X + 2(-1) = 0 \]
Simplifying this gives:
\[ 2 + X - 2 = 0 \implies X = 0 \]
- **Oxidation state of C = 0**.

### Step 4: Analyze the fourth compound `Na_(2)ul(Cl_(2))`
- The compound is `Na2Cl2`.
- Let the oxidation state of chlorine (Cl) be \( X \).
- The oxidation state of sodium (Na) is \( +1 \).
- The equation for the overall charge is:
\[ 2(+1) + 2X = 0 \]
Simplifying this gives:
\[ 2 + 2X = 0 \implies 2X = -2 \implies X = -1 \]
- **Oxidation state of Cl = -1** (not zero).

### Step 5: Analyze the fifth compound `ul(O)_(3)`
- The compound is `O3`.
- Let the oxidation state of oxygen (O) be \( X \).
- Since it is a neutral molecule:
\[ 3X = 0 \implies X = 0 \]
- **Oxidation state of O = 0**.

### Summary of Oxidation States:
1. `SO3^(2-)`: S = +4
2. `H2CO`: C = 0
3. `CH2Cl2`: C = 0
4. `Na2Cl2`: Cl = -1
5. `O3`: O = 0

### Total Count of Compounds with Zero Oxidation State:
- The compounds with zero oxidation states are:
- `H2CO` (C = 0)
- `CH2Cl2` (C = 0)
- `O3` (O = 0)

Thus, the total number of compounds having zero oxidation state is **3**.

### Final Answer:
**3**