Correct Answer  Option 4 : ML
^{2}T
^{2}K
^{1}
Concept:

Gas constant(R): It is the constant of proportionality that relates the energy scale in physics to the temperature scale, when a mole of particles at the stated temperature is being considered.
 As a consequence, the value of the gas constant is also exactly defined, at precisely 8.3144 J/molK.

Ideal gas: It is a hypothetical gas, consisting of molecules that are having negligible volume and their collision is perfectly elastically (means no loss of energy) and obeys gas law.
The gas law P V = n R T
Where P = pressure of the gas, V = volume of the gas, n = moles of the gas, R = 8.31 J/molK (Universal gas constant), and T = temperature of the gas.
Explanation:
We have the gas law
P V = n R T
⇒ Pressure × Volume = Total moles × Temperature × Gas Constant
∴ Gas Constant = Pressure × Volume × [Total moles × Temperature]^{1 .} . . . . (1)
The dimensional formula of temperature and volume = [M^{0} L^{0} T^{0} K^{1}] and [M^{0} L^{3 }T^{0}] . . . . (2)
Since, Pressure = Force × [Area]^{1}
P = M × a × [Area]^{1} = [M × LT^{2} × L^{2}]
∴ the dimensions of pressure = [M^{1} L^{1} T^{2}] . . . . (3)
On substituting equation (2) and (3) in equation (1) we get,
Gas Constant = Pressure × Volume × [Total moles × Temperature]1
Or, G = [M^{1} L^{1} T^{2}] × [L^{3}] × [K^{1}]^{1} = [M^{1} L^{2} T^{2} K^{1}].
Therefore, the gas constant is dimensionally represented as [M^{1} L^{2 }T^{2} K^{1}].