**Influence lines for Shear Force**

To determine the maximum shear force caused by the given UDL, we need to construct the influence line diagram for shear force at the desired location on the beam.

**Step 1: Determine the support reactions**

Before constructing the influence line, we need to determine the support reactions for the beam. Since the beam is simply supported, the reaction at each support will be equal to half of the total load.

Total Load = UDL × Span = 50 kN/m × 25 m = 1250 kN
Reaction at each support = 1250 kN / 2 = 625 kN

**Step 2: Constructing the influence line diagram**

To construct the influence line diagram for shear force, we consider a unit load (1 kN) placed at different positions along the span of the beam. We then calculate the corresponding shear force at the desired location caused by the unit load. The resulting diagram is the influence line diagram.

In this case, the desired location is at a distance longer than the span. Therefore, we need to consider two sections on the beam:

1. Section 1 (to the left of the desired location): The unit load is placed at different positions on the left side of the desired location.
2. Section 2 (to the right of the desired location): The unit load is placed at different positions on the right side of the desired location.

**Step 2.1: Section 1 (to the left of the desired location)**

The influence line for shear force at the desired location caused by the unit load on the left side can be calculated using the following equation:

Shear Force = (Unit Load × Distance from the Load to the Desired Location) / Span

Using this equation, we can calculate the shear force at the desired location for each unit load position to the left of the desired location.

**Step 2.2: Section 2 (to the right of the desired location)**

Similarly, the influence line for shear force at the desired location caused by the unit load on the right side can be calculated using the same equation:

Shear Force = (Unit Load × Distance from the Desired Location to the Load) / Span

Using this equation, we can calculate the shear force at the desired location for each unit load position to the right of the desired location.

**Step 3: Determine the maximum shear force**

To determine the maximum shear force caused by the UDL, we need to consider the maximum values obtained from both sections of the influence line diagram.

In this case, the maximum shear force is 260 kN (option 3).

Therefore, the correct answer is option 3) 260 kN.