**Answer:**

The dimension of a physical quantity refers to its fundamental units, such as length, mass, time, and so on. To determine the dimension of the quantity (nh/2qB), we need to analyze the dimensions of each term in the expression.

Let's break down the given expression into its constituent terms:

- n: positive integer (dimensionless)
- h: Planck constant (dimension of energy × time)
- q: charge (dimension of electric current × time)
- B: magnetic field (dimension of magnetic flux density)

**Analyzing the dimensions of each term:**

1. n: Since n is a positive integer, it does not have any dimension. It is dimensionless.

2. h: The Planck constant has the dimension of energy × time. In the International System of Units (SI), energy is measured in joules (J), and time is measured in seconds (s). Therefore, the dimension of h is [E][T].

3. q: The charge has the dimension of electric current × time. In SI, electric current is measured in amperes (A), and time is measured in seconds (s). Thus, the dimension of q is [I][T].

4. B: The magnetic field has the dimension of magnetic flux density. In SI, magnetic flux density is measured in teslas (T). Hence, the dimension of B is [B].

**Calculating the dimension of (nh/2qB):**

To determine the overall dimension of the quantity (nh/2qB), we need to multiply the dimensions of each term:

[nh/2qB] = [dimension of n] × [dimension of h] × [dimension of 1/2] × [dimension of q] × [dimension of B]

Since n is dimensionless, the first term does not contribute to the overall dimension. The dimension of 1/2 is also dimensionless.

Therefore, [nh/2qB] = [h] × [q] × [B]

The dimension of (nh/2qB) is given by the product of the dimensions of h, q, and B.

**Answer:**
The dimension of (nh/2qB) is represented by the product of the dimensions of h, q, and B. It does not correspond to any of the options provided (a. AREA, b. LENGTH, c. SPEED, d. ACCELERATION).

Area, h= ML2T-1, q= AT, B= MT-2A-1, n=0