To solve this problem, we need to match the items in Column I with the correct expressions in Column II. Let's analyze each item:$\\$(A) Root mean square speed of gas molecules:$\\$The formula for root mean square speed $(v_{rms})$ is given by $v_{rms} = \sqrt{\frac{3RT}{M}}. \\$This matches with (Q).$\\$(B) Pressure exerted by ideal gas:$\\$The pressure $(P)$ exerted by an ideal gas is given by $P = \frac{1}{3} nmv^2. \\$This matches with (P).$\\$(C) Average kinetic energy of a molecule:$\\$The average kinetic energy $(KE_{avg})$ of a molecule is given by $KE_{avg} = \frac{3}{2} k_B T. \\$This matches with (S).$\\$(D) Total internal energy of 1 mole of a diatomic gas:$\\$For a diatomic gas, the total internal energy $(U)$ is given by $U = \frac{5}{2} RT. \\$This matches with (R).$\\$Now, let's match the options:$\\$Option 1: $(A)-(R), (B)-(P), (C)-(S), (D)-(Q) \quad$(Incorrect)$\\$Option 2: $(A)-(Q), (B)-(R), (C)-(S), (D)-(P) \quad$(Incorrect)$\\$Option 3: $(A)-(Q), (B)-(P), (C)-(S), (D)-(R) \quad$(Correct)$\\$Option 4: $(A)-(R), (B)-(Q), (C)-(P), (D)-(S) \quad$(Incorrect)$\\$Therefore, the correct option is Option 3.