Degree of kinematic indeterminacy refers to the number of independent unknowns required to specify the displacement and rotation of a structure. For a pin-jointed plane frame, the degree of kinematic indeterminacy is given by the formula: 2j - r, where j represents the number of joints and r represents the number of equilibrium equations.

Explanation:
To understand why the correct answer is option A, let's break down the formula and examine each term:

1. Number of Joints (j):
In a pin-jointed plane frame, the joints are the locations where the members of the frame are connected. These joints allow for rotation but restrict translation. Each joint has two degrees of freedom (DOF) associated with it: one for horizontal displacement and one for vertical displacement. Therefore, the total number of DOF for all joints is 2j.

2. Number of Equilibrium Equations (r):
Equilibrium equations are used to analyze the forces and moments acting on a structure. In a pin-jointed plane frame, there are three equilibrium equations: ΣFx = 0 (sum of horizontal forces), ΣFy = 0 (sum of vertical forces), and ΣM = 0 (sum of moments). These equations are used to solve for the unknown forces in the members. The number of equilibrium equations, r, is equal to 3.

3. Degree of Kinematic Indeterminacy (2j - r):
Substituting the values of j and r into the formula, we get 2j - r = 2(2j) - 3 = 4j - 3.

Therefore, the correct answer is option A: 2j - r.