The correct sequence of the oxidation state of underlined elements is
`Na_(2)[ul(Fe)(CN)_(5)NO],K_(2)ul(Ta)F_(7),Mg_(2)ul(P)_(2)O_(7),Na_(2)ul(S)_(4)O_(6),ul(N)_(3)H`

Options

A. `+3, +5, +5, +2.5, -(1)/(3)`
B. `+5, +3, +5, +3, +(1)/(3)`
C. `+3, +3, +5, +5, -(1)/(3)`
D. `+5,+5, +3, +2.5,+(1)/(3)`

Explanation

To determine the correct sequence of the oxidation states of the underlined elements in the given compounds, we will calculate the oxidation states step by step for each compound.

### Step 1: Calculate the oxidation state of Iron (Fe) in Na₂[Fe(CN)₅NO]

1. **Identify the oxidation states of known elements:**
- Sodium (Na) has an oxidation state of +1.
- Carbon (C) in cyanide (CN) has an oxidation state of +4, while nitrogen (N) has an oxidation state of -3. Thus, CN as a whole has an oxidation state of -1.
- The oxidation state of NO (nitric oxide) is 0.

2. **Set up the equation:**
\[ 2(+1) + x + 5(-1) + 0 = 0 \]
\[ 2 + x - 5 = 0 \]
\[ x - 3 = 0 \implies x = +3 \]

### Step 2: Calculate the oxidation state of Tantalum (Ta) in K₂TaF₇

1. **Identify the oxidation states of known elements:**
- Potassium (K) has an oxidation state of +1.
- Fluorine (F) has an oxidation state of -1.

2. **Set up the equation:**
\[ 2(+1) + x + 7(-1) = 0 \]
\[ 2 + x - 7 = 0 \]
\[ x - 5 = 0 \implies x = +5 \]

### Step 3: Calculate the oxidation state of Phosphorus (P) in Mg₂P₂O₇

1. **Identify the oxidation states of known elements:**
- Magnesium (Mg) has an oxidation state of +2.
- Oxygen (O) has an oxidation state of -2.

2. **Set up the equation:**
\[ 2(2) + 2x + 7(-2) = 0 \]
\[ 4 + 2x - 14 = 0 \]
\[ 2x - 10 = 0 \implies 2x = 10 \implies x = +5 \]

### Step 4: Calculate the oxidation state of Sulfur (S) in Na₂S₄O₆

1. **Identify the oxidation states of known elements:**
- Sodium (Na) has an oxidation state of +1.
- Oxygen (O) has an oxidation state of -2.

2. **Set up the equation:**
\[ 4x + 2(+1) + 6(-2) = 0 \]
\[ 4x + 2 - 12 = 0 \]
\[ 4x - 10 = 0 \implies 4x = 10 \implies x = +2.5 \]

### Step 5: Calculate the oxidation state of Nitrogen (N) in N₃H

1. **Identify the oxidation states of known elements:**
- Hydrogen (H) has an oxidation state of +1.

2. **Set up the equation:**
\[ 3x + 3(+1) = 0 \]
\[ 3x + 3 = 0 \]
\[ 3x = -3 \implies x = -1 \]

### Summary of Oxidation States
- Iron (Fe) = +3
- Tantalum (Ta) = +5
- Phosphorus (P) = +5
- Sulfur (S) = +2.5
- Nitrogen (N) = -1

### Final Sequence of Oxidation States
The correct sequence of the oxidation states of the underlined elements is:
1. Fe: +3
2. Ta: +5
3. P: +5
4. S: +2.5
5. N: -1

### Conclusion
The correct order of oxidation states is: +3, +5, +5, +2.5, -1.