Limits & Continuity

87 NDA Mathematics previous year questions (PYQs) from 19 papers, 2017 to 2026, with answers and worked solutions.

About this chapter

Difficulty: 33 easy · 41 moderate · 13 hard.
Most-asked subtopics: Continuity and Differentiability — Piecewise, Modulus, Composed, Oscillatory (36), Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms (34), One-Sided Limits, Greatest Integer, and Absolute Value Limits (17).
Updated 14 September 2026.

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NDA · Sep 2026 · Q82Hard
#1Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Sep 2026 · Q87Moderate
#2Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Sep 2026 · Q88Hard
#3Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2017 · Q71Easy
#4Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2017 · Q79Easy
#5Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
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NDA · Apr 2017 · Q93Easy
#6Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
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NDA · Sep 2017 · Q75Easy
#7Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
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NDA · Apr 2018 · Q95Easy
#8Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2018 · Q96Moderate
#9Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Sep 2018 · Q79Moderate
#10Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Sep 2018 · Q100Moderate
#11Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2019 · Q75Moderate
#12Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Sep 2019 · Q73Easy
#13Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2020 · Q71Easy
#14Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2020 · Q73Moderate
#15Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2020 · Q75Moderate
#16Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2020 · Q93Moderate
#17Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2021 · Q76Hard
#18Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2021 · Q79Easy
#19Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2021 · Q92Moderate
#20Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Sep 2021 · Q74Easy
#21Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2022 · Q74Easy
#22Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2022 · Q75Moderate
#23Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Sep 2022 · Q84Moderate
#24Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Sep 2022 · Q85Moderate
#25Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Sep 2022 · Q87Easy
#26Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2023 · Q100Easy
#27Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2026 · Q72Easy
#28Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
NDA · Apr 2026 · Q73Easy
#29Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
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Set · 2 questions
Let $f(x)=\dfrac{a^{x-1}+b^{x-1}}{2}$ and $g(x)=x-1$ .
- NDA · Sep 2023 · Q53Hard
  #30Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
  Strategy Concept notes
- NDA · Sep 2023 · Q54Hard
  #31Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
  Strategy Concept notes
NDA · Sep 2024 · Q79Easy
#32Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
Strategy Concept notes
Set · 1 question
Let the function $f(x) = x^2 - 1$ .
- NDA · Apr 2025 · Q89Easy
  #33Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
  Strategy Concept notes
Set · 1 question
Let the function $f(x) = x^2 + 9$ .
- NDA · Apr 2025 · Q93Moderate
  #34Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
  Strategy Concept notes
NDA · Sep 2026 · Q84Moderate
#35One-Sided Limits, Greatest Integer, and Absolute Value Limits
Strategy Concept notes
NDA · Sep 2017 · Q79Hard
#36One-Sided Limits, Greatest Integer, and Absolute Value Limits
Strategy Concept notes
NDA · Sep 2021 · Q77Easy
#37One-Sided Limits, Greatest Integer, and Absolute Value Limits
Strategy Concept notes
NDA · Sep 2022 · Q86Moderate
#38One-Sided Limits, Greatest Integer, and Absolute Value Limits
Strategy Concept notes
Set · 2 questions
Consider the following for the next two (02) items that follow: Let $f(x)=\sin[\pi^{2}]x+\cos[-\pi^{2}]x$ where $[\cdot]$ is a greatest integer function.
- NDA · Apr 2023 · Q79Moderate
  #39One-Sided Limits, Greatest Integer, and Absolute Value Limits
  Strategy Concept notes
- NDA · Apr 2023 · Q80Moderate
  #40One-Sided Limits, Greatest Integer, and Absolute Value Limits
  Strategy Concept notes
NDA · Apr 2023 · Q99Easy
#41One-Sided Limits, Greatest Integer, and Absolute Value Limits
Strategy Concept notes
Set · 2 questions
For the following two (02) items: Let $f(x)=\begin{cases}\dfrac{1-\cos2x}{x^2}, & x<0\\ 9, & x=0\\ \dfrac{\sqrt{x}}{\sqrt{(16+\sqrt{x})}-4}, & x>0\end{cases}$
- NDA · Sep 2025 · Q71Moderate
  #42One-Sided Limits, Greatest Integer, and Absolute Value Limits
  Strategy Concept notes
- NDA · Sep 2025 · Q72Moderate
  #43One-Sided Limits, Greatest Integer, and Absolute Value Limits
  Strategy Concept notes
Set · 1 question
For the following three (03) items: Consider the function $f(x)=x|x|$ .
- NDA · Sep 2025 · Q73Easy
  #44One-Sided Limits, Greatest Integer, and Absolute Value Limits
  Strategy Concept notes
Set · 2 questions
Let $f(x)=|x|$ and $g(x)=[x]-1$ . Let $h(x)=\frac{f(g(x))}{g(f(x))}$ .
- NDA · Sep 2023 · Q57Hard
  #45One-Sided Limits, Greatest Integer, and Absolute Value Limits
  Strategy Concept notes
- NDA · Sep 2023 · Q58Hard
  #46One-Sided Limits, Greatest Integer, and Absolute Value Limits
  Strategy Concept notes
Set · 1 question
Consider the following for the next two (02) items that follow: Let $f(x)=\begin{cases}ax(x+1)+b, & x<1\\ x-1, & 1\leq x\leq 2\end{cases}$
- NDA · Sep 2023 · Q64Moderate
  #47One-Sided Limits, Greatest Integer, and Absolute Value Limits
  Strategy Concept notes
NDA · Apr 2024 · Q88Hard
#48One-Sided Limits, Greatest Integer, and Absolute Value Limits
Strategy Concept notes
NDA · Sep 2024 · Q74Easy
#49One-Sided Limits, Greatest Integer, and Absolute Value Limits
Strategy Concept notes
Set · 1 question
Let the function $f(x) = \sin[x]$ , where $[\cdot]$ is the greatest integer function and $g(x) = |x|$ .
- NDA · Apr 2025 · Q83Moderate
  #50One-Sided Limits, Greatest Integer, and Absolute Value Limits
  Strategy Concept notes

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