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Real Analysis Questions – Daily Mathematics MCQs

Practise carefully selected Real Analysis multiple-choice questions covering core undergraduate and competitive-exam concepts. Attempt each problem first, then reveal the detailed solution.

IIT JAMCUET-PGCSIR-NETUGC-NETGATE
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About These Real Analysis Questions

Use this question bank for focused practice. Each MCQ is presented in crawlable HTML and includes answer choices, an instant answer check and a detailed solution that you can reveal after attempting the problem.

SequencesSeriesSupremum & InfimumContinuityDifferentiabilityMetric SpacesCompactnessRiemann Integration

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Real Analysis Question Archive

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Real AnalysisSequencesModerateIIT JAM · CSIR-NET31 August 2026

Question RA-001

Let $(a_n)$ be a convergent sequence of real numbers. Which of the following statements is always true?

Detailed Solution

Since $(a_n)$ converges to some $L\in\mathbb R$, for $\varepsilon=1$ there exists $N$ such that $|a_n-L|<1$ for all $n\ge N$. Hence $|a_n|\le |L|+1$ for all $n\ge N$. The finitely many terms $a_1,\ldots,a_{N-1}$ are also bounded. Therefore $(a_n)$ is bounded. Thus the correct option is $\boxed{\mathrm{B}}$.
Concepts tested: Convergent sequencesBoundedness
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Real AnalysisSupremum & InfimumModerateCUET-PG · UGC-NET29 August 2026

Question RA-002

Let $S=(0,1)$. Which statement about its supremum and infimum is correct?

Detailed Solution

Every $x\in(0,1)$ satisfies $x<1$, so $1$ is an upper bound. Moreover, for every $\varepsilon>0$, there is $x\in(0,1)$ with $1-\varepsilonConcepts tested: SupremumInfimumOpen intervals
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Prepare Smarter with Real Analysis MCQs

For competitive mathematics examinations, knowing a definition is only the first step. These questions are designed to make you apply theorems, identify subtle distinctions and practise the kind of conceptual reasoning that is useful in IIT JAM, CUET-PG, CSIR-NET, UGC-NET and GATE preparation.

For deeper study, combine this practice bank with the mathematics lecture videos, notes and other resources available on Fractal Frontier Maths.

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