**Column 1** **-----** **Column 2**

(A)GMeMs---- (p)[M2L2T-3]
(B)3RT/M-----(q)[ML3T-2]
(C)F2/q2B2--- (r)[L2T-2 ]
(D)GMe/Re----(s)none? Explain in details.

**Explanation:**

To match the given values in Column 1 with the corresponding values in Column 2, we need to understand the units and their respective dimensions.

**1. (A) GMeMs - (p) [M2L2T-3]**

In this case, "GMeMs" represents the gravitational constant (G) multiplied by the mass of one object (M) and the mass of another object (M), resulting in the dimension [M2]. Since it involves mass, it is represented by the unit [M]. Additionally, the dimensions for length (L) and time (T) are raised to the power of 2 and -3, respectively. Hence, the correct match is (A) - (p).

**2. (B) 3RT/M - (q) [ML3T-2]**

In this case, "3RT/M" represents the product of the ideal gas constant (R) multiplied by the temperature (T) and divided by the molar mass (M). The ideal gas constant (R) has dimensions [ML2T-2K-1]. Multiplying it by temperature (T) [T] and dividing by molar mass (M) [M] results in the dimension [ML3T-2]. Hence, the correct match is (B) - (q).

**3. (C) F2/q2B2 - (r) [L2T-2]**

In this case, "F2/q2B2" represents the squared force (F) divided by the squared charge (q) and squared magnetic field (B). The dimensions for force (F) are [MLT-2]. Dividing it by the squared charge (q) [C-2] and squared magnetic field (B) [M-2T-2] results in the dimension [L2T-2]. Hence, the correct match is (C) - (r).

**4. (D) GMe/Re - (s) none? Explain in detail.**

In this case, "GMe/Re" represents the product of the gravitational constant (G) multiplied by the mass of the Earth (Me) and divided by the radius of the Earth (Re). The gravitational constant (G) has dimensions [M-1L3T-2]. Multiplying it by the mass of the Earth (Me) [M] and dividing by the radius of the Earth (Re) [L] does not result in any specific dimension. This is because the division of mass by length does not yield any consistent unit or dimension. Therefore, there is no correct match for (D) in Column 2.

In summary:

(A) GMeMs - (p) [M2L2T-3]
(B) 3RT/M - (q) [ML3T-2]
(C) F2/q2B2 - (r) [L2T-2]
(D) GMe/Re - (

A-q, B-r, C-r, D-r