Question

Hyperconjugation involves overlap of the following orbitals:
A. $\sigma -\sigma$
B. $\sigma -p$
C. $p-p$
D. $\pi -\pi$

Answer 1

Hyperconjugation effect is one of the type of permanent effect in which localization of $\sigma$electrons of $C-H$ bond of an alkyl group directly attached to an atom of the unsaturated system or to an atom with an unshared p orbital.
Step by step solution: The main role of hyperconjugation is to stabilize the carbocation because it helps in the dispersal of positive charge. Higher the number of alkyl groups attached to a positively charged carbon atom then greater is the hyper conjugation interaction and stability of carbonation.
Hyper conjugation can also be known by the name $\sigma$ hyper conjugation. It generally involves the interaction of electrons in a sigma orbital with nearby non-bonding p or antibonding $\sigma *$or $\pi *$ orbitals to provide extended molecular orbitals which further increase the stability of the system. Rather than this sometimes low lying antibonding $\sigma *$ also interact with filled orbitals of lone pair character in which this type of conjugation is termed as negative hyperconjugation. Increase in electron delocalization increases the stability of the system which is associated with hyper conjugation.

Hence from the above discussion we can consider that hyperconjugation involves overlap of $\sigma -p$ orbitals, i.e. option B is the correct answer.

Note:
The main applications of hyperconjugation is it can be used to rationalize a variety of chemical processes which involves anomeric effect, gauche effect , beta silicon effect and also tells about the stability of substituted carbocations.