Natural Number

We need to determine which of the given collections is not a set.

Definition of a Set: A set is a well-defined collection of distinct objects. A collection is well-defined if there is no ambiguity about whether an element belongs to it or not.

Step 1: Analyze Each Option

Option 1: The collection of natural numbers between 2 and 20.

Natural numbers between 2 and 20 are: . Since the elements are clearly defined, this is a set.

Option 2: The collection of numbers which satisfy the equation .

Solving the equation:

The collection is , which is well-defined. Thus, this is a set.

Option 3: The collection of prime numbers between 1 and 100.

Prime numbers between 1 and 100 are clearly defined (e.g., ), so this is a set.

Option 4: The collection of all brilliant students in a class.

The term "brilliant students" is subjective and can vary based on different opinions or criteria. Since there is no clear definition, this collection is not a set.

Final Answer: The collection of all brilliant students in a class.

The last digit of follows a repeating cycle of 9 and 1:

• (last digit: 9)
• (last digit: 1)
• (last digit: 9)
• (last digit: 1)

From this, we see that the last digit of alternates between 9 and 1 for all .

Since the last digit never becomes 2, the answer is 2.