Write the state of hybridisation of carbon in the following compounds and the shapes of each of the molecules:
$(a)$ $H_2C=O$
$(b)$ $CH_3F$
$(c)$ $HC \equiv N$

(N/A) $H_2C=O$: The carbon atom is bonded to two hydrogen atoms and one oxygen atom via a double bond. It has $3$ sigma bonds and $0$ lone pairs,resulting in $sp^2$ hybridisation. The shape is trigonal planar.
$(b)$ $CH_3F$: The carbon atom is bonded to three hydrogen atoms and one fluorine atom via single bonds. It has $4$ sigma bonds and $0$ lone pairs,resulting in $sp^3$ hybridisation. The shape is tetrahedral.
$(c)$ $HC \equiv N$: The carbon atom is bonded to one hydrogen atom via a single bond and one nitrogen atom via a triple bond. It has $2$ sigma bonds and $0$ lone pairs,resulting in $sp$ hybridisation. The shape is linear.