Isolobal pairs refer to two molecules or ions that have the same number of valence electrons and have similar structures, making them equivalent in terms of their electronic properties.

In the given pairs, we need to identify the ones that are isolobal.

(I) Mn(CO)5, CH3
- Mn(CO)5 has 18 valence electrons (5 from Mn, 5 x 2 from CO).
- CH3 has 8 valence electrons (4 from C, 1 from each H).
- These two molecules do not have the same number of valence electrons or similar structures, so they are not isolobal.

(II) Fe(CO)4, O
- Fe(CO)4 has 18 valence electrons (8 from Fe, 4 x 2 from CO).
- O has 6 valence electrons.
- These two molecules do not have the same number of valence electrons or similar structures, so they are not isolobal.

(III) Co(CO)3, R2Si
- Co(CO)3 has 16 valence electrons (9 from Co, 3 x 2 from CO).
- R2Si has 16 valence electrons (4 from Si, 6 from each R).
- These two molecules have the same number of valence electrons and similar structures (both have a central atom surrounded by three ligands), so they are isolobal.

(IV) Mn(CO)5, RS
- Mn(CO)5 has 18 valence electrons (5 from Mn, 5 x 2 from CO).
- RS has 16 valence electrons (6 from S, 5 from R).
- These two molecules do not have the same number of valence electrons or similar structures, so they are not isolobal.

(V) Mn(CO)4CH,
- Mn(CO)4CH has 18 valence electrons (5 from Mn, 4 x 2 from CO, 4 from C, 1 from H).
- Co(CO)3 has 16 valence electrons.
- These two molecules do not have the same number of valence electrons or similar structures, so they are not isolobal.

(VI) Co(CO)4, CH3
- Co(CO)4 has 18 valence electrons (9 from Co, 4 x 2 from CO).
- CH3 has 8 valence electrons (4 from C, 1 from each H).
- These two molecules do not have the same number of valence electrons or similar structures, so they are not isolobal.

Therefore, the number of isolobal pairs is 1, which is the pair (III) Co(CO)3, R2Si.