These are short and simple. :) I've included my answers, tell me if I am wrong please.

CH3 is attached to a carbon on a pentane ring. Is the hybridization of the carbon sp3?

NH connects a benzene ring to two benzene rings. Is the hybridization of the nitrogen sp2?

OH is attached to a carbon on a pentane ring. Is the hybridization of the oxygen sp? I had issues with this one.

On a benzene ring, what is the hybridization of a carbon that has a double bond on one side and a single bond on the other? Is it sp2?

For the first question, CH3 attached to a carbon on a pentane ring, the hybridization of the carbon can be determined using the concept of the "valence bond theory." In this theory, the carbon atom forms sigma (σ) bonds and can undergo hybridization to explain its bonding.

To determine the hybridization, you need to count the number of sigma bonds and lone pairs around the carbon atom. In this case, the carbon atom is attached to four sigma bonds (one to the pentane ring and three to the CH3 group). There are no lone pairs present.

The hybridization of an atom depends on the number of sigma bonds and lone pairs. When an atom is bonded to four sigma bonds and has no lone pairs, it is sp3 hybridized. Therefore, the correct answer is yes, the hybridization of the carbon attached to CH3 on the pentane ring is sp3.

For the second question, NH connecting a benzene ring to two benzene rings, the hybridization of the nitrogen can also be determined using the valence bond theory.

Again, count the number of sigma bonds and lone pairs around the nitrogen atom. In this case, the nitrogen atom forms three sigma bonds (two to the benzene rings and one connecting to the remaining part of the molecule). There is also one lone pair present.

When an atom is bonded to three sigma bonds and has one lone pair, it is sp2 hybridized. Therefore, the correct answer is yes, the hybridization of the nitrogen atom connecting the benzene rings in this molecule is sp2.

For the third question, OH attached to a carbon on the pentane ring, the hybridization of the oxygen can be determined similarly.

Count the number of sigma bonds and lone pairs around the oxygen atom. In this case, the oxygen atom forms one sigma bond with the carbon on the pentane ring and also contains two lone pairs.

When an atom is bonded to one sigma bond and has two lone pairs, it is sp2 hybridized. Therefore, the correct answer is no, the hybridization of the oxygen atom attached to the pentane ring is not sp, but sp2.

For the fourth question, on a benzene ring, if a carbon atom has a double bond on one side and a single bond on the other, its hybridization can be determined using the valence bond theory.

In this case, the carbon atom forms three sigma bonds (two single bonds with neighboring carbon atoms in the benzene ring and one double bond with another atom) and does not have any lone pairs.

When an atom is bonded to three sigma bonds and has no lone pairs, it is sp2 hybridized. Therefore, the correct answer is yes, the hybridization of the carbon atom with a double bond on one side and a single bond on the other in a benzene ring is sp2.