Relations and Functions

JEE Advanced · Mathematics · 31 past questions

1. Q1 2026 Paper 2

   Let $\mathbb{N}$ denote the set of all positive integers. Consider the sets…

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2. Q2 2025 Paper 1

   Let $\mathbb{N}$ denote the set of all natural numbers, and $\mathbb{Z}$ denote the set of all integers.…

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3. Q3 2025 Paper 1

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

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4. Q4 2025 Paper 1

   Let $\mathbb{R}$ denote the set of all real numbers. For a real number $x$, let $[x]$ denote the greatest…

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5. Q5 2025 Paper 2

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

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6. Q6 2024 Paper 1

   Let $f:\mathbb{R}\to\mathbb{R}$ and $g:\mathbb{R}\to\mathbb{R}$ be functions defined by…

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7. Q7 2024 Paper 2

   Let $f:\mathbb{R}\to\mathbb{R}$ be a function such that $f(x+y)=f(x)+f(y)$ for all $x,y\in\mathbb{R}$, and…

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8. Q8 2024 Paper 2

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

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9. Q9 2024 Paper 2

   PARAGRAPH “I”…

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10. Q10 2023 Paper 1

    Let $S = (0,1)\cup(1,2)\cup(3,4)$ and $T=\{0,1,2,3\}$. Then which of the following statements is(are) true?

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11. Q11 2022 Paper 2

    Let…

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12. Q12 2020 Paper 1

    If the function $f:\mathbb{R}\longrightarrow\mathbb{R}$ is defined by $f(x)=|x|(x-\sin x)$, then which of the…

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13. Q13 2020 Paper 2

    Let $f: \mathbb{R} \to \mathbb{R}$ and $g: \mathbb{R} \to \mathbb{R}$ be functions satisfying…

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14. Q14 2020 Paper 2

    Let the function $f:[0,1]\to\mathbb{R}$ be defined by…

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15. Q15 2018 Paper 2

    Let $X$ be a set with exactly 5 elements and $Y$ be a set with exactly 7 elements. If $\alpha$ is the number…

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16. Q16 2018 Paper 2

    Let $f:\mathbb{R}\to\mathbb{R}$ be a differentiable function with $f(0)=1$ and satisfying the equation…

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17. Q17 2018 Paper 2

    Let $E_1=\left\{x\in\mathbb{R}: x\neq 1 \text{ and } \frac{x}{x-1}>0\right\}$ and…

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18. Q18 2016 Paper 2

    Let $f:\left[-\dfrac12,2\right]\to\mathbb{R}$ and $g:\left[-\dfrac12,2\right]\to\mathbb{R}$ be functions…

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19. Q19 2015 Paper 1

    Let $f(x)=\sin\left(\frac{\pi}{6}\sin\left(\frac{\pi}{2}\sin x\right)\right)$ for all $x\in\mathbb{R}$ and…

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20. Q20 2014 Paper 1

    Let $f:\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\to\mathbb{R}$ be given by…

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21. Q21 2014 Paper 2

    Let $f_1:\mathbb{R}\to\mathbb{R}$, $f_2:[0,\infty)\to\mathbb{R}$, $f_3:\mathbb{R}\to\mathbb{R}$ and…

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22. Q22 2012 Paper 1

    The function $f:[0,3]\to[1,29]$, defined by $f(x)=2x^3-15x^2+36x+1$, is

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23. Q23 2012 Paper 2

    Let $f:(-1,1)\to\mathbb{R}$ be such that $f(\cos4\theta)=\dfrac{2}{2-\sec^2\theta}$ for…

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24. Q24 2011 Paper 1

    Let $f:\mathbb{R}\to\mathbb{R}$ be a function such that…

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25. Q25 2011 Paper 2

    Let $f(x)=x^2$ and $g(x)=\sin x$ for all $x\in\mathbb{R}$. Then the set of all $x$ satisfying…

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26. Q26 2011 Paper 2

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

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27. Q27 2010 Paper 2

    Let $f$ be a real-valued function defined on the interval $(-1, 1)$ such that…

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28. Q28 2009 Paper 2

    If the function $f(x)=x^3+e^{x/2}$ and $g(x)=f^{-1}(x)$, then the value of $g'(1)$ is

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29. Q29 2008 Paper 2

    Let the function $g:(-\infty,\infty)\to\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$ be given by…

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30. Q30 2007 Paper 2

    $\dfrac{d^2x}{dy^2}$ equals

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31. Q31 2007 Paper 2

    Let $f(x) = \dfrac{x^2-6x+5}{x^2-5x+6}$.…

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