Limits and Derivatives

JEE Advanced · Mathematics · 18 past questions

1. Q1 2025 Paper 1

   Let $\alpha$ and $\beta$ be the real numbers such that…

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2. Q2 2025 Paper 2

   Let $x_0$ be the real number such that $e^{x_0} + x_0 = 0$. For a given real number $\alpha$, define…

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3. Q3 2024 Paper 2

   Let $k\in\mathbb{R}$. If $\lim_{x\to0^+}\left(\sin(\sin kx)+\cos x+x\right)^{\frac{2}{x}}=e^6$, then the…

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4. Q4 2024 Paper 2

   Let $S$ be the set of all $(\alpha,\beta)\in\mathbb{R}\times\mathbb{R}$ such that…

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5. Q5 2023 Paper 1

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

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6. Q6 2022 Paper 1

   Let $\alpha$ be a positive real number. Let $f:\mathbb{R}\to\mathbb{R}$ and $g:(\alpha,\infty)\to\mathbb{R}$…

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7. Q7 2022 Paper 2

   If…

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8. Q8 2020 Paper 1

   Let $e$ denote the base of the natural logarithm. The value of the real number $a$ for which the right hand…

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9. Q9 2020 Paper 2

   The value of the limit…

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10. Q10 2017 Paper 2

    Let $f(x) = \frac{1-x(1+|1-x|)}{|1-x|}\cos\left(\frac{1}{1-x}\right)$ for $x \neq 1$. Then

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11. Q11 2016 Paper 1

    Let $\alpha, \beta \in \mathbb{R}$ be such that…

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12. Q12 2015 Paper 2

    Let $m$ and $n$ be two positive integers greater than 1. If…

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13. Q13 2014 Paper 1

    The largest value of the nonnegative integer $a$ for which…

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14. Q14 2012 Paper 1

    If $\lim_{x\to\infty}\left(\dfrac{x^2+x+1}{x+1}-ax-b\right)=4$, then

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15. Q15 2012 Paper 2

    Let $\alpha(a)$ and $\beta(a)$ be the roots of the equation…

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16. Q16 2011 Paper 2

    If…

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17. Q17 2009 Paper 1

    Let…

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18. Q18 2008 Paper 1

    Let $f$ and $g$ be real valued functions defined on interval $(-1, 1)$ such that $g''(x)$ is continuous…

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