1. Use combustion/Dumas data to infer the atom ratio

   Let the organic compound have formula $C_xH_yN_z$.

   On complete combustion:

   • $x$ carbon atoms give $x$ moles of $CO_2$
   • $y$ hydrogen atoms give $\dfrac{y}{2}$ moles of $H_2O$
   • $z$ nitrogen atoms give $\dfrac{z}{2}$ moles of $N_2$

   We are given that the compound evolves:

   • $6$ moles of $CO_2$
   • $4$ moles of $H_2O$
   • $1$ mole of $N_2$

2. Find number of C, H, and N atoms

   From $CO_2$: $x=6$

   From $H_2O$: $\frac{y}{2}=4 \Rightarrow y=8$

   From $N_2$: $\frac{z}{2}=1 \Rightarrow z=2$

3. Write the molecular formula

   Therefore, the formula is: $C_6H_8N_2$

4. Check options

   • A: $C_6H_8N$ ❌ (would give only $\tfrac{1}{2}$ mole $N_2$)
   • B: $C_6H_8N_2$ ✅
   • C: $C_{12}H_8N$ ❌ (would give $12$ moles $CO_2$)
   • D: $C_{12}H_8N_2$ ❌ (would give $12$ moles $CO_2$)

Hence the correct option is B.