To solve the problem, we need to identify the correct objective of Intramural tournaments, which are competitions held within a single institution among its own students.
1. Understanding Intramural Tournaments:
Intramural tournaments are organized within the same institution such as a school or college. They are designed to encourage participation, physical activity, and social bonding among students of the same campus.
2. Evaluating the Options:
- (A) To achieve high performance at the highest level of the tournament: This aligns more with extramural or elite competitions, not intramurals.
- (B) To develop the feeling of integration with other institutions: This applies to inter-school or extramural events.
- (C) To provide opportunities for choosing a career in sports: Intramurals are for recreational and participatory purposes, not career-oriented.
- (D) To promote health and recreation at the institution: This is the core purpose of intramural tournaments. They focus on fitness, enjoyment, and internal bonding among students.
Final Answer:
(D) To promote health and recreation at the institution.

A ladder of fixed length \( h \) is to be placed along the wall such that it is free to move along the height of the wall.
Based upon the above information, answer the following questions:
(iii) (b) If the foot of the ladder, whose length is 5 m, is being pulled towards the wall such that the rate of decrease of distance \( y \) is \( 2 \, \text{m/s} \), then at what rate is the height on the wall \( x \) increasing when the foot of the ladder is 3 m away from the wall?