Step 1: Understanding the Concept:
The shape of a molecule follows from VSEPR theory. A molecule is linear when the central atom has two electron regions and no lone pair, so the bond angle is \(180^{\circ}\).
Step 2: Detailed Explanation of the keyed option:
In \(\text{CO}_2\) carbon forms two double bonds, \(\text{O=C=O}\), and has no lone pair. Two regions of electron density stay as far apart as possible, so the O-C-O angle is \(180^{\circ}\) and the molecule is linear (sp hybridised carbon).
Step 3: Why the other options are wrong.
\(\text{SO}_2\) has one lone pair on sulphur, which pushes the two S=O bonds into a bent shape of about \(119^{\circ}\). \(\text{BCl}_3\) has three bond pairs on boron and no lone pair, giving a trigonal planar shape with \(120^{\circ}\) angles. \(\text{NH}_3\) has three bond pairs and one lone pair on nitrogen, giving a pyramidal shape.
Final Answer:
Only carbon dioxide is linear, option (C).
\[ \boxed{\text{CO}_2 \text{ (C)}} \]