Limits and Derivatives

JEE Main · Mathematics · 5 past questions

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1. Q1 2026 2 Apr Shift 1

   If $\lim_{x\to 2}\dfrac{\sin\left(x^3-5x^2+ax+b\right)}{\left(\sqrt{x-1}-1\right)\log_e(x-1)} = m$, then…

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2. Q2 2026 5 Apr Shift 1

   The product of all possible values of $\alpha$, for which…

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3. Q3 2026 5 Apr Shift 2

   Let $f(x) = \lim_{y \to 0} \frac{(1 - \cos(xy))\tan(xy)}{y^3}$. Then the number of solutions of the equation…

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4. Q4 2026 6 Apr Shift 1

   The value of $\lim_{x\to0}\left(\frac{x^2\sin^2x}{x^2-\sin^2x}\right)$ is…

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5. Q5 2026 6 Apr Shift 2

   Let $\lim_{x \to 2} \frac{(\tan(x-2))(rx^2+(p-2)x-2p)}{(x-2)^2} = 5$ for some $r, p \in \mathbb{R}$. If the…

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