Which of the following statements are correct?
`(I)` `N_(2)H_(4)` is pyramidal about each N atom.
`(II)` `NH_(2)OH` is pyramidal about the N atom and bent about the O atom.
`(III)` `CH_(3)COCl` is trigonal planar about the carbon atom ( attached to O and Cl).

Explanation

To determine which of the statements about the given compounds are correct, we will analyze each statement one by one.

### Step 1: Analyze Statement I
**Statement I:** `N2H4` is pyramidal about each N atom.

- **Structure of Hydrazine (N2H4):**
- The molecular structure of hydrazine consists of two nitrogen atoms, each bonded to two hydrogen atoms.
- Each nitrogen atom has one lone pair of electrons.

- **Hybridization:**
- Each nitrogen atom in hydrazine is sp³ hybridized due to the presence of three regions of electron density (two N-H bonds and one lone pair).

- **Geometry:**
- The presence of a lone pair on each nitrogen atom results in a pyramidal geometry around each nitrogen atom.

**Conclusion for Statement I:** True.

### Step 2: Analyze Statement II
**Statement II:** `NH2OH` is pyramidal about the N atom and bent about the O atom.

- **Structure of Hydroxylamine (NH2OH):**
- Hydroxylamine consists of a nitrogen atom bonded to two hydrogen atoms and one hydroxyl group (–OH).

- **Hybridization:**
- The nitrogen atom is sp³ hybridized (three regions of electron density: two N-H bonds and one lone pair).
- The oxygen atom is also sp³ hybridized (two lone pairs and one bond to hydrogen).

- **Geometry:**
- The nitrogen atom with one lone pair is pyramidal.
- The oxygen atom with two lone pairs is bent due to the repulsion of the lone pairs.

**Conclusion for Statement II:** True.

### Step 3: Analyze Statement III
**Statement III:** `CH3COCl` is trigonal planar about the carbon atom (attached to O and Cl).

- **Structure of Acetyl Chloride (CH3COCl):**
- The structure consists of a carbon atom bonded to three atoms: a methyl group (–CH3), a carbonyl group (C=O), and a chlorine atom (Cl).

- **Hybridization:**
- The carbon atom in the carbonyl group (C=O) is sp² hybridized (three regions of electron density: one C=O double bond and one C-Cl single bond, and one C-H bond).

- **Geometry:**
- An sp² hybridized carbon atom has a trigonal planar geometry.

**Conclusion for Statement III:** True.

### Final Conclusion
All three statements are correct.