JEE MAIN Limit Previous Year Questions (PYQs) – Page 1 of 10
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$\displaystyle \lim_{x\to 0}\frac{\sin(\pi \cos^{2}x)}{x^{2}}$ is equal to :
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$\lim_{x \to 1} \left( \dfrac{\int_{0}^{(x-1)^{2}} t \cos(t^{2}) \, dt}{(x-1)\sin(x-1)} \right)$
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Let $\beta=\lim_{x\to 0}\dfrac{\alpha x-(e^{3x}-1)}{\alpha x(e^{3x}-1)}$ for some $\alpha\in\mathbb{R}$.
Then the value of $\alpha+\beta$ is:
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$\lim_{x\to 0}\dfrac{x+2\sin x}{\sqrt{x^{2}+2\sin x+1}-\sqrt{\sin^{2}x-x+1}}$ is:
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Let f : R $\to$ R be a function such that f(2) = 4 and f'(2) = 1. Then, the value of $\mathop {\lim }\limits_{x \to 2} {{{x^2}f(2) - 4f(x)} \over {x - 2}}$ is equal to :
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$\displaystyle \lim_{x\to\infty}\frac{(2x^{2}-3x+5),(3x-1)^{x/2}}{(3x^{2}+5x+4),\sqrt{(3x+2)^{x}}}$ is equal to:
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$\displaystyle \lim_{x\to 0}\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$ is equal to :
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Let $f$ be a differentiable function on $\mathbb{R}$ such that $f(2)=1,\ f'(2)=4$.
Let $\displaystyle \lim_{x\to 0}\big(f(2+x)\big)^{\frac{3}{x}}=e^{\alpha}$.
Then the number of times the curve $y=4x^3-4x^2-4(\alpha-7)x-\alpha$ meets the $x$-axis is:
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Let $[x]$ denote the greatest integer less than or equal to $x$. Then
$\displaystyle \lim_{x\to 0}\frac{\tan(\pi\sin^{2}x)+\left(|x|-\sin(x[x])\right)^{2}}{x^{2}}$ :
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$\displaystyle \lim_{x\to 0^{+}}\frac{\tan\big(5x^{1/5}\big),\ln(1+3x^{2})}{\big(\tan^{-1}(3\sqrt{2})\big),\big(e^{x\sqrt{3}}-1\big)}$ is equal to
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Solution
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