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Questions › CUET-PG › CUET-PG 2025 › Q67
4 marks, −1Mathematics › Real analysis › Topology of the real line: open, closed and compact setsEasyabout 1 min

CUET-PG 2025 Question 67: Real analysis

Match List-I (Types of Interval for variable x) with List-II (Mathematical Representation, given a,b∈Ra,b \in \mathbb{R}a,b∈R with b>ab>ab>a): List-I: (A) Closed Interval; (B) Open Interval; (C) Unbounded Interval; (D) Half Open Interval. List-II: (I) [a,b)={x∈R:a≤x<b}[a,b) = \{x\in\mathbb{R}: a\le x<b\}[a,b)={x∈R:a≤x<b}; (II) [a,b]={x∈R:a≤x≤b}[a,b] = \{x\in\mathbb{R}: a\le x\le b\}[a,b]={x∈R:a≤x≤b}; (III) [a,∞)={x∈R:a≤x}[a,\infty) = \{x\in\mathbb{R}: a\le x\}[a,∞)={x∈R:a≤x}; (IV) (a,b)={x∈R:a<x<b}(a,b) = \{x\in\mathbb{R}: a<x<b\}(a,b)={x∈R:a<x<b}.

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Match List-I (Types of Interval for variable x) with List-II (Mathematical Representation, given a,b ∈ ℝ with b>a): List-I: (A) Closed Interval; (B) Open Interval; (C) Unbounded Interval; (D) Half Open Interval. List-II: (I) [a,b) = {x∈ℝ: a≤ x<b}; (II) [a,b] = {x∈ℝ: a≤ x≤ b}; (III) [a,∞) = {x∈ℝ: a≤ x}; (IV) (a,b) = {x∈ℝ: a<x<b}. (A) (A)-(I), (B)-(IV), (C)-(III), (D)-(II) (B) (A)-(II), (B)-(IV), (C)-(III), (D)-(I) (C) (A)-(II), (B)-(III), (C)-(IV), (D)-(I) (D) (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

Also written as: Match List-I (Types of Interval for variable x) with List-II (Mathematical Representation, given a,b in R with b>a): List-I: (A) Closed Interval; (B) Open Interval; (C) Unbounded Interval; (D) Half Open Interval. List-II: (I) [a,b) = {x in R: a<= x<b}; (II) [a,b] = {x in R: a<= x<= b}; (III) [a, inf) = {x in R: a<= x}; (IV) (a,b) = {x in R: a<x<b}.

Real analysis has come up 38 times in 5 exams since 2005.

What this question tests

This question is on Topology of the real line: open, closed and compact sets, part of Real analysis in Mathematics.

Which sets are open, closed or compact and how unions and intersections behave.

TestStop has 29 past-paper questions on this subtopic.

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