**Solution:**

To determine the cracking moment of a reinforced concrete beam, we need to consider the properties of the concrete and steel used in the beam, as well as the dimensions of the cross section.

**Given:**
- Cross-sectional dimensions of the beam: 300 x 1000 mm
- Grade of concrete: M25
- Grade of steel reinforcement: Fe 500

**Step 1: Calculate the moment of inertia of the cross section**

The moment of inertia (I) of the cross section is a measure of its resistance to bending. For a rectangular cross section, the moment of inertia can be calculated using the formula:

I = (b * h^3) / 12

Where:
- b = width of the cross section (300 mm)
- h = height of the cross section (1000 mm)

Plugging in the values, we get:

I = (300 * 1000^3) / 12
I = 25,000,000,000 mm^4

**Step 2: Calculate the modular ratio**

The modular ratio (n) is the ratio of the modulus of elasticity of steel (Es) to the modulus of elasticity of concrete (Ec). For Fe 500 grade steel and M25 grade concrete, the modular ratio is typically taken as 10.

n = Es / Ec
n = 200,000 MPa / 20,000 MPa
n = 10

**Step 3: Calculate the cracking moment**

The cracking moment (Mc) is the moment at which the tensile stress in the extreme fiber of the concrete reaches its cracking strength (fct). The cracking moment can be calculated using the formula:

Mc = (n * fct * I) / d

Where:
- fct = cracking strength of concrete
- I = moment of inertia of the cross section
- d = effective depth of the beam

The cracking strength of concrete (fct) can be taken as 0.7 times the square root of the grade of concrete in MPa:

fct = 0.7 * √(fck)

Where:
- fck = characteristic compressive strength of concrete at 28 days

For M25 grade concrete, the characteristic compressive strength (fck) is 25 MPa. Therefore:

fct = 0.7 * √(25)
fct = 0.7 * 5
fct = 3.5 MPa

The effective depth of the beam (d) can be taken as the overall depth of the beam minus the cover to the reinforcing bars. Assuming a cover of 40 mm, the effective depth is:

d = 1000 - 40
d = 960 mm

Plugging in the values, we get:

Mc = (10 * 3.5 * 25,000,000,000) / 960
Mc = 91,666,666.67 Nmm
Mc = 91.67 kNm

Therefore, the cracking moment of the section is approximately 91.67 kNm.

**Conclusion:**

The cracking moment of the reinforced concrete beam with cross-sectional dimensions 300 x 1000 mm, M25 grade concrete, and Fe 500 grade steel is approximately 91.67 kNm.