Answer:
(a) No. Ground-state carbon has only 2 half-filled orbitals that could be used for bonding.
(b) No. The bond angles would be incorrect as the p-orbitals are all perpendicular to each other (90°).
Step-by-step explanation:
See attachment for the ground-state and excited-state electron orbital diagrams of carbon.
A methane molecule has all four CH bonds the same length and at 109.5° from each other. Hybridization of the s and p orbitals to sp³ orbitals is necessary.