Linear structure is assumed by:
(I) `NCO` (II)`CS_(2)` (III)`overset(+)(N)O_(2)` (IV)Solid `BeH_(2)`

Options

A. all four
B. (II), (III) and (IV)
C. (I), (II) and (III)
D. (II) and (III)

Answer

To determine which of the given compounds has a linear structure, we will analyze each option step by step.

### Step 1: Analyze NCO (Cyanate Ion)
1. **Draw the Lewis Structure**:
- Nitrogen (N) has 5 valence electrons, Carbon (C) has 4, and Oxygen (O) has 6.
- The total number of valence electrons = 5 + 4 + 6 = 15.
- The most stable structure involves a triple bond between N and C, and a double bond between C and O, resulting in the structure: N≡C-O.
- The negative charge can be placed on the oxygen atom.

2. **Determine the Geometry**:
- The N≡C-O structure is linear due to the triple bond between N and C, which does not allow for any angle deviation.

### Step 2: Analyze CS₂ (Carbon Disulfide)
1. **Draw the Lewis Structure**:
- Carbon (C) has 4 valence electrons, and each Sulfur (S) has 6.
- The total number of valence electrons = 4 + 2(6) = 16.
- The structure can be represented as: S=C=S, where carbon is in the center.

2. **Determine the Geometry**:
- The S=C=S structure is also linear due to the double bonds on either side of carbon.

### Step 3: Analyze NO₂⁺ (Nitronium Ion)
1. **Draw the Lewis Structure**:
- Nitrogen (N) has 5 valence electrons, and each Oxygen (O) has 6.
- The total number of valence electrons = 5 + 2(6) - 1 (for the positive charge) = 16.
- The structure is drawn as: O=N^+=O, with a double bond between N and each O.

2. **Determine the Geometry**:
- The O=N=O structure is linear due to the double bonds, which allows for a 180-degree bond angle.

### Step 4: Analyze BeH₂ (Beryllium Dihydride)
1. **Draw the Lewis Structure**:
- Beryllium (Be) has 2 valence electrons, and each Hydrogen (H) has 1.
- The total number of valence electrons = 2 + 2(1) = 4.
- The structure is represented as: H-Be-H.

2. **Determine the Geometry**:
- The H-Be-H structure is bent due to the presence of lone pairs on beryllium, resulting in an angle less than 180 degrees.

### Conclusion
From the analysis:
- **Linear Structures**: NCO, CS₂, NO₂⁺
- **Non-Linear Structure**: BeH₂

Thus, the compounds that assume a linear structure are **NCO, CS₂, and NO₂⁺**.

### Final Answer
The correct options that assume a linear structure are (I) NCO, (II) CS₂, and (III) NO₂⁺.