Question:

From the given sets, which is an infinite set:

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When dealing with sets, check if there is a limit to the number of elements (finite) or if the set extends indefinitely (infinite).

Updated On: Mar 7, 2026

\( \{ x: x \in \mathbb{N} \text{ and } (x - 1)(x - 2) = 0 \} \)
\( \{ x: x \in \mathbb{N} \text{ and } x \text{ is a prime number and less than 199} \} \)
\( \{ x: x \in \mathbb{N} \text{ and } x^5 - 1 = 0 \} \)
\( \{ x: x \in \mathbb{N} \text{ and } x \text{ is odd} \} \)

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The Correct Option is D

Solution and Explanation

Step 1: Analyze the sets.
- Set 1: \( (x - 1)(x - 2) = 0 \) has solutions \( x = 1 \) or \( x = 2 \), which is a finite set.

- Set 2: The prime numbers less than 199 are finite, so this is also a finite set.

- Set 3: \( x^5 - 1 = 0 \) implies \( x = 1 \), which is a finite set.

- Set 4: The set of odd numbers is infinite because there is no limit to how many odd numbers exist.

Step 2: Conclusion.
Thus, the infinite set is option 4, which consists of all odd numbers in \( \mathbb{N} \). Therefore, the correct answer is 4. \( \{ x: x \in \mathbb{N} \text{ and } x \text{ is odd} \} \).

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Top CUET PG Set Theory Questions

Match List-I with List-II.\[\begin{array}{|c|c|} \hline \textbf{List-I (Set operations)} & \textbf{List-II (Missing term)} \\ \hline \text{(A) If \(n(X)=17,\, n(Y)=23,\, n(X \cup Y)=38\), then \(n(X \cap Y)\) is} & \text{(I) 20} \\ \hline \text{(B) If \(n(X)=28,\, n(Y)=32,\, n(X \cap Y)=10\), then \(n(X \cup Y)\) is} & \text{(II) 10} \\ \hline \text{(C) If \(n(X)=10\), then \(n(X')\) is} & \text{(III) 50} \\ \hline \text{(D) If \(n(Y)=20\), then \(n\left(\tfrac{Y}{2}\right)\) is} & \text{(IV) 2} \\ \hline \end{array}\]
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Match List-I with List-II.

List-I	List-II
A. \(\sqrt{2} + \frac{1}{\sqrt{2}} + \sqrt{2} + \frac{1}{\sqrt{2}} + \cdots\)	I. \(\frac{19}{24}\)
B. \(\frac{1}{2} + \frac{1}{3} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{2^3} + \frac{1}{3^3} + \cdots\)	II. \(6\)
C. \(6^2 \times 6^3 \times 6^4 \times \cdots\)	III. \(82 + \sqrt{2}\)
D. \(8 + 4\sqrt{2} + \cdots\)	IV. \(4 + \frac{3\sqrt{2}}{2}\)

Choose the correct answer from the options given below:

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