Solution:

Given,
Mass of solute (X) = 2g
Molar mass of X = 32g/mol
Mass of solvent (CS2) = 100g
Vapour pressure of CS2 = 854 Torr

Using the formula of mole fraction, we can calculate the mole fraction of the solute:

Mole fraction (X) = number of moles of X / total number of moles

Number of moles of X = Given mass of X / Molar mass of X
= 2/32
= 0.0625 mol

Number of moles of CS2 = Given mass of CS2 / Molar mass of CS2
= 100/76.14
= 1.313 mol

Total number of moles = 0.0625 + 1.313
= 1.3755 mol

Mole fraction (X) = 0.0625 / 1.3755
= 0.0455

Using the formula of Raoult's law, we can calculate the vapour pressure of the solution:

Vapour pressure of the solution = Vapour pressure of the solvent x Mole fraction of the solvent

Vapour pressure of the solution = 854 x 0.9545
= 815.9 Torr

Now, let's determine the molecular formula of the solute:

We know that the vapour pressure of a solution depends on the number of solute particles present in the solution. More the number of particles, lower will be the vapour pressure of the solution.

The solute X has a molar mass of 32g/mol. Therefore, the molecular formula of X can be X, X2, X4, X8, etc.

If the molecular formula of X is X, then the number of solute particles present in the solution will be equal to the number of moles of X. But we have already calculated the number of moles of X to be 0.0625 mol. Therefore, the vapour pressure of the solution would have been higher than 854 Torr. Hence, the molecular formula of X cannot be X.

If the molecular formula of X is X2, then the number of solute particles present in the solution will be twice the number of moles of X. Therefore, the vapour pressure of the solution would be lower than 854 Torr, but it would still be higher than 815.9 Torr. Hence, the molecular formula of X cannot be X2.

Similarly, we can eliminate the options X4 and X8 as well. The only possible molecular formula of X is X4, which means that the solute X is a tetramer.

Therefore, the correct answer is option (C) X4.