Consider a system with the following: - \(\mathbb{P} = \{ P_1, P_2, P_3, P_4 \}\) consists of all active processes in an operating system. - \(\mathbb{R} = \{ R_1, R_2, R_3, R_4 \}\) consists of single instances of distinct types of resources in the system.
The resource allocation graph has the following assignment and claim edges: Assignment edges: \[ R_1 \to P_1, \quad R_2 \to P_2, \quad R_3 \to P_3, \quad R_4 \to P_4 \] (The assignment edge \( R_1 \to P_1 \) means resource \( R_1 \) is assigned to process \( P_1 \), and so on for others.)
Claim edges: \[ P_1 \to R_2, \quad P_2 \to R_3, \quad P_3 \to R_1, \quad P_2 \to R_4, \quad P_4 \to R_2 \] (The claim edge \( P_1 \to R_2 \) means process \( P_1 \) is waiting for resource \( R_2 \), and so on for others.)
Which of the following statement(s) is/are CORRECT?

In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point P and the line QR. What is the ratio of the area of the triangle PST to the area of the trapezium SQRT?
Note: The figure shown is representative

A square paper, shown in figure (I), is folded along the dotted lines as shown in figures (II) and (III). Then a few cuts are made as shown in figure (IV). Which one of the following patterns will be obtained when the paper is unfolded?
Consider the relationships among P, Q, R, S, and T:
• P is the brother of Q.
• S is the daughter of Q.
• T is the sister of S.
• R is the mother of Q.
The following statements are made based on the relationships given above.
(1) R is the grandmother of S.
(2) P is the uncle of S and T.
(3) R has only one son.
(4) Q has only one daughter.
Which one of the following options is correct?