Consider a system represented by the block diagram shown below. Which of the following signal flow graphs represent(s) this system? Choose the correct option(s).





Step 1: Understand the block diagram. The system consists of two blocks \( G_1 \) and \( G_2 \), where the feedback path comes from the output \( Y(s) \) that goes to \( G_1 \), and the output from both \( G_1 \) and \( G_2 \) contribute to \( Y(s) \).
Step 2: Identify the corresponding signal flow graph. The system has a feedback loop, where the output \( Y(s) \) feeds back into \( G_1 \). This is correctly represented by option (B), where \( G_1 \) has feedback from the output \( Y(s) \). Thus, the correct answer is (B).
The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after 'Iteration n' is:

Consider the unity-negative-feedback system shown in Figure (i) below, where gain \( K \geq 0 \). The root locus of this system is shown in Figure (ii) below.
For what value(s) of \( K \) will the system in Figure (i) have a pole at \( -1 + j1 \)?

If rank(A) is at least 3, then what are the possible values of \( \alpha, \beta, \gamma \)?