Continuity and Differentiability

JEE Advanced · Mathematics · 31 past questions

1. Q1 2026 Paper 1

   Let $\mathbb{R}$ denote the set of all real numbers. Let $f:\mathbb{R}\to\mathbb{R}$ be an arbitrary function…

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2. Q2 2026 Paper 1

   Consider the function $f : \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \to (-\infty, \infty)$ defined by…

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3. Q3 2026 Paper 2

   Let $\mathbb{R}$ denote the set of all real numbers. Consider the polynomial function…

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4. Q4 2026 Paper 2

   For a real number $\alpha$, let $[\alpha]$ denote the greatest integer less than or equal to $\alpha$. For a…

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5. Q5 2025 Paper 1

   Let $\mathbb{R}$ denote the set of all real numbers. Define the function $f:\mathbb{R}\to\mathbb{R}$ by…

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6. Q6 2024 Paper 2

   Let $f:\mathbb{R}\to\mathbb{R}$ be a function defined by…

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7. Q7 2023 Paper 2

   Let $f : (0,1) \to \mathbb{R}$ be the function defined as…

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8. Q8 2023 Paper 2

   Let $S$ be the set of all twice differentiable functions $f$ from $\mathbb{R}$ to $\mathbb{R}$ such that…

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9. Q9 2020 Paper 1

   Let the function $f:\mathbb{R}\to\mathbb{R}$ be defined by $f(x)=x^3-x^2+(x-1)\sin x$ and let…

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10. Q10 2020 Paper 1

    For a polynomial $g(x)$ with real coefficients, let $m_g$ denote the number of distinct real roots of $g(x)$.…

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11. Q11 2020 Paper 2

    Let the functions $f:(-1,1) \to \mathbb{R}$ and $g:(-1,1) \to (-1,1)$ be defined by…

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12. Q12 2019 Paper 2

    Let $f: \mathbb{R} \to \mathbb{R}$ be a function. We say that $f$ has…

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13. Q13 2018 Paper 1

    For every twice differentiable function $f: \mathbb{R} \to [-2, 2]$ with $(f(0))^2 + (f'(0))^2 = 85$, which…

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14. Q14 2018 Paper 2

    Let $f_1:\mathbb{R}\to\mathbb{R}$, $f_2:\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\to\mathbb{R}$…

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15. Q15 2017 Paper 1

    Let $[x]$ be the greatest integer less than or equals to $x$. Then, at which of the following point(s) the…

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16. Q16 2017 Paper 1

    Let $f:\mathbb{R}\to(0,1)$ be a continuous function. Then, which of the following function(s) has(have) the…

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17. Q17 2017 Paper 2

    If $f:\mathbb{R}\to\mathbb{R}$ is a twice differentiable function such that $f''(x)>0$ for all…

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18. Q18 2016 Paper 1

    Let $f:\mathbb{R}\to\mathbb{R}$, $g:\mathbb{R}\to\mathbb{R}$ and $h:\mathbb{R}\to\mathbb{R}$ be…

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19. Q19 2016 Paper 2

    Let $a,b\in\mathbb{R}$ and $f:\mathbb{R}\to\mathbb{R}$ be defined by $f(x)=a\cos(|x^3-x|)+b|x|\sin(|x^3+x|)$.…

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20. Q20 2016 Paper 2

    Let $f:\mathbb{R}\to(0,\infty)$ and $g:\mathbb{R}\to\mathbb{R}$ be twice differentiable functions such that…

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21. Q21 2015 Paper 1

    Let $g:\mathbb{R}\to\mathbb{R}$ be a differentiable function with $g(0)=0$, $g'(0)=0$ and $g'(1)\neq 0$. Let…

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22. Q22 2014 Paper 1

    Let $f:\mathbb{R}\to\mathbb{R}$ and $g:\mathbb{R}\to\mathbb{R}$ be respectively given by $f(x)=|x|+1$ and…

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23. Q23 2012 Paper 1

    Let $f(x)=\begin{cases} x^2\left|\cos\dfrac{\pi}{x}\right|, & x\neq 0\\ 0, & x=0\end{cases}$…

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24. Q24 2012 Paper 2

    For every integer $n$, let $a_n$ and $b_n$ be real numbers. Let function $f:\mathbb{R}\to\mathbb{R}$ be given…

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25. Q25 2011 Paper 1

    Let $f(\theta) = \sin\left(\tan^{-1}\left(\frac{\sin\theta}{\sqrt{\cos 2\theta}}\right)\right)$, where…

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26. Q26 2011 Paper 2

    If…

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27. Q27 2009 Paper 2

    For the function $f(x) = x\cos\frac{1}{x},\ x \ge 1$…

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28. Q28 2008 Paper 1

    Let $g(x) = \dfrac{(x-1)^n}{\log\cos^m(x-1)}$; $0 < x < 2$, $m$ and $n$ are integers, $m \neq 0$, $n > 0$…

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29. Q29 2008 Paper 1

    Paragraph for Question Nos. 18 to 20…

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30. Q30 2008 Paper 2

    Paragraph for Question Nos. 14 to 16…

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31. Q31 2008 Paper 2

    Paragraph for Question Nos. 14 to 16…

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