The number of correct option is
(a) `P_(2)O_(5) gtZnO gtMgO gt Na_(2)O_(2)` (acidic strenght)
(b) `TI_(2)O_(3) gt TI_(2)O gtGa_(2)O_(3) gt AI_(2)O_(3) ` (basic strenght)
( c) `MnO gt P_(2)O_(5) gt CrO_(3) gt Mn_(2)O_(7)` (ionic character)
(d) `H_(2)OgtHF gtNH_(3)` (melting point)
(e) `H_(2)O gtHF gtNH_(3)` (boiling point) .

Explanation

To solve the question, we need to analyze each option regarding the properties of the compounds mentioned. Let's break it down step by step.

### Step 1: Analyze Option (a)
**Statement:** `P_(2)O_(5) gt ZnO gt MgO gt Na_(2)O_(2)` (acidic strength)

**Explanation:**
- As we move from left to right across a period, the acidic strength of oxides generally increases due to the increase in non-metallic character.
- In this case, `P_(2)O_(5)` is a non-metal oxide and is highly acidic.
- `ZnO` is amphoteric, while `MgO` is basic, and `Na_(2)O_(2)` is a basic peroxide.
- Therefore, the order of acidic strength is correct: `P_(2)O_(5) > ZnO > MgO > Na_(2)O_(2)`.

**Conclusion:** Option (a) is correct.

### Step 2: Analyze Option (b)
**Statement:** `Tl_(2)O_(3) gt Tl_(2)O gt Ga_(2)O_(3) gt Al_(2)O_(3)` (basic strength)

**Explanation:**
- Basic strength of oxides generally increases down a group due to increased metallic character.
- However, comparing `Tl_(2)O` (where Tl is in +1 oxidation state) and `Tl_(2)O_(3)` (where Tl is in +3 oxidation state), the oxide with the lower oxidation state (Tl in +1) is more basic.
- Thus, `Tl_(2)O` should be more basic than `Tl_(2)O_(3)`, making the order incorrect.

**Conclusion:** Option (b) is incorrect.

### Step 3: Analyze Option (c)
**Statement:** `MnO gt P_(2)O_(5) gt CrO_(3) gt Mn_(2)O_(7)` (ionic character)

**Explanation:**
- According to Fajan's rule, the covalent character increases with the charge on the cation.
- `MnO` has Mn in +2 oxidation state, `P_(2)O_(5)` has P in +5, `CrO_(3)` has Cr in +6, and `Mn_(2)O_(7)` has Mn in +7.
- As the oxidation state increases, the covalent character increases, leading to a decrease in ionic character.
- Therefore, the order is correct: `MnO > P_(2)O_(5) > CrO_(3) > Mn_(2)O_(7)`.

**Conclusion:** Option (c) is correct.

### Step 4: Analyze Option (d)
**Statement:** `H_(2)O gt HF gt NH_(3)` (melting point)

**Explanation:**
- The melting point is influenced by hydrogen bonding.
- Water forms four hydrogen bonds per molecule, HF forms two, and NH3 forms one.
- Thus, the order of melting points is: `H_(2)O > HF > NH_(3)`.

**Conclusion:** Option (d) is correct.

### Step 5: Analyze Option (e)
**Statement:** `H_(2)O gt HF gt NH_(3)` (boiling point)

**Explanation:**
- Similar to melting points, boiling points are also influenced by hydrogen bonding.
- The same reasoning applies: `H_(2)O` has the strongest hydrogen bonding, followed by `HF`, and then `NH3`.
- Hence, the order of boiling points is also: `H_(2)O > HF > NH_(3)`.

**Conclusion:** Option (e) is correct.

### Final Count of Correct Options
After analyzing all options:
- Correct options: (a), (c), (d), (e)
- Incorrect option: (b)

**Total Correct Options:** 4

### Final Answer:
The number of correct options is **4**.

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