Following are some questions posed by the teacher in the mathematics classroom:

A. What is the area of the rectangle whose one side is 5 cm and perimeter is 30 cm?

B. Find a set of numbers whose median is 4.

C. List all prime numbers between 0-8.

D. Tell me anything mathematical information you know about rectangles.

The correct option is: A & C are closed ended and B & D are open ended questions.

Understanding Closed-Ended vs. Open-Ended Questions in Mathematics:

1. Closed-Ended Questions: These questions have a unique, single correct answer or a fixed/finite set of specific responses. There is generally only one way or direct factual outcome required.

2. Open-Ended Questions: These questions allow for multiple correct responses, diverse interpretations, creative thinking, and varied methods of answering.

Analyzing Each Question:

Question A: "What is the area of the rectangle whose one side is 5 cm and perimeter is 30 cm?"

Perimeter = $2(l+b)=30$

If one side is $5\text{cm}$, the other side must be $10\text{cm}$.

The area is fixed at $5\times 10=50{\text{cm}}^2$. Since there is only one specific numeric answer, A is closed-ended.

Question B: "Find a set of numbers whose median is 4."

There are infinitely many sets of numbers with a median of 4 (e.g., {3, 4, 5}, {1, 2, 4, 6, 8}, {4, 4, 4}, etc.). Since students can provide many different correct sets, B is open-ended.

Question C: "List all prime numbers between 0-8."

The prime numbers strictly between 0 and 8 are fixed: 2, 3, 5, and 7. There is only one definite, fixed list of numbers that satisfies this condition. Thus, C is closed-ended.

Question D: "Tell me anything mathematical information you know about rectangles."

Students can give a wide variety of answers (e.g., "Opposite sides are equal", "All interior angles are 90 degrees", "Diagonals bisect each other", "Area is length times breadth", etc.). Since there are unlimited valid mathematical facts a student could share, D is open-ended.

Conclusion:

Questions A and C are closed-ended, while questions B and D are open-ended.