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2021 JEE PYQ

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2021
Let $f(x)$ be a polynomial of degree 3 such that $f(k)=-\frac{2}{k}$ for $k=2,3,4,5$. Then the value of $52-10 f(10)$ is equal to :
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Let the points of intersections of the lines x – y + 1 = 0, x – 2y + 3 = 0 and 2x –...
JEE Main Mathematics Easy
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Q JEE MAIN 2021
If for the complex numbers $z$ satisfying $|z-2-2 i| \leq 1$, the maximum value of $|3 i z+6|$ is attained at $a+i b$, then $\mathrm{a}+\mathrm{b}$...
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Let $f(x)=x^6+2 x^4+x^3+2 x+3, x \in R$. Then the natural number $n$ for which $\lim _{x \rightarrow 1} \frac{x^n f(1)-f(x)}{x-1}=44$ is $\_\_\_\_$ .
JEE Main Mathematics Medium
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Q JEE MAIN 2021
Let X be a random variable with distribution.

If the mean of $X$ is 2.3...
JEE Main Mathematics Hard
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Q JEE MAIN 2021
Let $\theta$ be the acute angle between the tangents to the ellipse $\frac{x^2}{9}+\frac{y^2}{1}=1$ and the circle $x^2+y^2=3$ at their point of intersection in the first...
JEE Main Mathematics Easy
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Q JEE MAIN_2021
Given below are two statements: Statement I: $\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-},\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$ and $\left[\mathrm{Co}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}$ are $d^2 \mathrm{sp}^3$ hybridised. Statement Il: $\left[\mathrm{MnCl}_6\right]^{3-}$ and $\left[\mathrm{FeF}_6\right]^{3-}$ are paramagnetic and have 4...
JEE Main Chemistry Medium
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Q JEE MAIN 2021
The function $f(x)$, that satisfies the condition $f(x)=x+\int_0^{\pi / 2} \sin x \cdot \cos y f(y) d y$, is :
JEE Main Mathematics Medium
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Q JEE MAIN_2021_
Given below are two statements Statement I : Hyperconjugation is a permanent effect. Statement II : Hyperconjugation in ethyl cation $\left(\mathrm{CH}_3-\stackrel{+}{\mathrm{C}} \mathrm{H}_2\right)$ involves the overlapping...
JEE Main Chemistry Medium
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Q JEE MAIN 2021
Let $\mathrm{a}_1, \mathrm{a}_2 \ldots \ldots, \mathrm{a}_{21}$ be an AP such that $\sum_{\mathrm{n}=1}^{20} \frac{1}{\mathrm{a}_{\mathrm{n}} \mathrm{a}_{\mathrm{n}+1}}=\frac{4}{9}$. If the sum of this AP is 189 , then a6a16...
JEE Main Mathematics Easy
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