Step 1: Understanding the ionic conductance at infinite dilution.
The equivalent conductance at infinite dilution for a salt like BaCl\(_2\) is the sum of the ionic conductances of the ions:
\[
\Lambda^0_{BaCl_2} = \Lambda^0_{Ba^{2+}} + \Lambda^0_{Cl^-}
\]
Step 2: Substituting the given values.
Given
\( \Lambda^0_{Ba^{2+}} = 127 \, \text{ohm}^{-1}\text{cm}^2 \) and,
\( \Lambda^0_{Cl^-} = 76 \, \text{ohm}^{-1}\text{cm}^2 \),
we add them:
\[
\Lambda^0_{BaCl_2} = 127 + 76 = 203 \, \text{ohm}^{-1}\text{cm}^2
\]
Step 3: Conclusion.
The correct answer is (2) 203