1. We need to count the species with linear geometry among:

$\mathrm{SO_2,\ BeCl_2,\ CO_2,\ N_3^-,\ NO_2,\ F_2O,\ XeF_2,\ NO_2^+,\ I_3^-,\ O_3}$

We evaluate each using VSEPR / known molecular geometry.

2. Check each species:

(i) $\mathrm{SO_2}$

• Central atom: S
• Electron geometry: trigonal planar (one lone pair on S)
• Molecular shape: bent/angular
• Not linear

(ii) $\mathrm{BeCl_2}$

• Central atom: Be
• Two bond pairs, no lone pair on Be
• Shape: linear
• Linear

(iii) $\mathrm{CO_2}$

• Central atom: C
• Two electron domains, no lone pair
• Shape: linear
• Linear

(iv) $\mathrm{N_3^-}$

• Azide ion
• Resonance-stabilized and known to be linear
• Linear

(v) $\mathrm{NO_2}$

• Neutral nitrogen dioxide has an odd electron
• Shape is bent
• Not linear

(vi) $\mathrm{F_2O}$

• Same as $\mathrm{OF_2}$
• Central atom O has two lone pairs
• Shape: bent
• Not linear

(vii) $\mathrm{XeF_2}$

• Central atom Xe
• Five electron pairs around Xe: $2$ bond pairs + $3$ lone pairs
• Trigonal bipyramidal electron arrangement; lone pairs occupy equatorial positions
• Molecular shape: linear
• Linear

(viii) $\mathrm{NO_2^+}$

• Nitronium ion
• Central atom N with two bonding regions, no lone pair
• Shape: linear
• Linear

(ix) $\mathrm{I_3^-}$

• Central atom I
• Five electron pairs: $2$ bond pairs + $3$ lone pairs
• Shape: linear
• Linear

(x) $\mathrm{O_3}$

• Ozone
• Central atom O with one lone pair
• Shape: bent
• Not linear

3. Linear species are:

$\mathrm{BeCl_2,\ CO_2,\ N_3^-,\ XeF_2,\ NO_2^+,\ I_3^-}$

Total number:

$6$

4. Comparison with stored answer:

• Derived answer = $6$
• Stored correct answer = $6$

They match.