According to the VB theory the bonds formed in methane due to overlapping are:
A.$1\sigma s - s,3\sigma s - p$
B.$1\sigma s - p,3\sigma s - p$
C.$2\sigma s - s,2\sigma s - p$
D.$4\sigma s{p^3} - s$

Hint:
Valence bond theory was given by Heitler and London and was further developed by Pauling. Valence bond theory is based on the knowledge of atomic orbitals, electronic configuration of elements and their recombination to form hybrid orbitals.

Complete step by step answer:
Methane is an example of saturated hydrocarbon. It has the formula $C{H_4}$ . We know that in molecules hybridization takes place. Pauling introduced this concept.
The mixing of atomic orbitals to form new hybrid orbitals of nearly the same energy is called hybridization.
In methane the hydrogen atom has one electron and has the configuration $1{s^1}$ .
The carbon has six electrons with configuration $1{s^2}2{s^2}2{p^2}$ .
Now the three $2p$ orbitals of carbon mix with the $1s$ orbital to form four $s{p^3}$ hybrid orbitals of equivalent energy and shape. These four hybrid orbitals formed are at the four corners of the tetrahedron. They attain this shape because at this position the electronic repulsion is minimum. The angle between the hybrid orbitals in the $s{p^3}$ hybridization is $109.5^\circ $ .
So the correct option is A.

Additional information:
-The main features of hybridization are-
-The number of hybrid orbitals that are formed are equal to the number of atomic orbitals that get hybridized.
-The hybridized orbitals are equivalent in energy and shape.
-Hybrid orbitals form stable bonds as compared to the pure atomic orbitals.
-These hybrid orbitals are placed in the three dimensional space in the molecule in such a way that there is minimum electron repulsion between electron pairs and thus stable arrangement. Therefore the type of hybridization helps to predict the geometry of molecules.

Note:The valence bond theory explains the shape, the formation and directional properties of bonds in polyatomic molecules like $C{H_4},N{H_3},{H_2}O$ in terms of overlap and hybridization of molecules. The limitations of valence bond theory were corrected by the molecular orbital theory.