Hybrid orbital are formed by the overlapping of orbitals having almost same energy.
Single bond= one sigma bond = sp3 hybridization
Double bond = one sigma bond + one pie bond = sp2 hybridization
Triple bond = one sigma bond + two pie bond = sp hybridization
(a)

According to structure, C1 & C2 are making 4 sigma bonds(single bond) each with the help of one s hybrid orbital & 3 p hybrid orbital, hence C1& C2 are sp3 hybridised
(b)

Here C1 is making 4 sigma bond therefore it s sp3 hybridised , while C2 and C3 are making a double bond( 1 sigma + 1 pie bond ) therefore they both are sp2 hybridized.
(c)

Both the carbons C1 & C2 are making single bond(sigma bond),therefore they are sp3hybridized.
(d)

From the structure it is clear that C1 is making sigma bonds only, therefore it is sp3 hybridised.C2 is making a double bond therefore it is sp2 hybridised.
C1 is sp3 hybridized and C2 is sp2 hybridized.
(e)

Here C1 is making a sigma bond therefore it is in sp3 hybridization state, while C2 is making a double bond ,it is in sp2 hybridised state.
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