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2020 JEE PYQ

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2020
Let $u=\frac{2 z+i}{z-k i}, z=x+i y$ and $k>0$. If the curve represented by $\operatorname{Re}(\mathrm{u})+\operatorname{Im}(\mathrm{u})=1$ intersects the y axis at the point $P$ and $Q$ where...
JEE Main Mathematics Hard
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Q JEE MAIN 2020
Let $f$ be a twice differentiable function on $(1,6)$. If $f(2)=8, f^{\prime}(2)=5, f^{\prime}(x) \geq 1$ and $f^{\prime \prime}(x) \geq 4$, for all $x \in (1,6)$,...
JEE Main Mathematics Hard
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Q JEE MAIN 2020
Let $a-2 b+c=1$.
$f(x)=\left|\begin{array}{lll}x+a & x+2 & x+1 \\ x+b & x+3 & x+2\end{array}\right|$, then
JEE Main Mathematics Easy
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Q JEE MAIN 2020
Let $y=y(x)$ be the solution of the differential equation, $x y^{\prime}-y=x^2(x \cos x+\sin x), x>0$. If $y(\pi)=\pi$, then $y^{\prime \prime}\left(\frac{\pi}{2}\right)+y\left(\frac{\pi}{2}\right)$ is equal to :
JEE Main Mathematics Medium
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Q JEE MAIN 2020
If one end of a focal chord AB of the parabola $\mathrm{y}^2= 8 x$ is at $A\left(\frac{1}{2},-2\right)$, then the equation of the tangent to it...
JEE Main Mathematics Easy
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Q JEE MAIN 2020
Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$ be a given ellipse, length of whose latus rectum is 10 . If its eccentricity is the maximum value of the function, $\phi(t)=\frac{5}{12}+t-t^2$,...
JEE Main Mathematics Medium
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Q JEE MAIN 2020
Let $f(x)=\int \frac{\sqrt{x}}{(1+x)^2} d x(x \geq 0)$. Then $f(3)-f(1)$ is equal to:
JEE Main Mathematics Hard
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Q JEE MAIN 2020
The length of the minor axis (along $y$-axis) of an ellipse in the standard form is $\frac{4}{\sqrt{3}}$. If this ellipse touches the line, $x+6 y=8$;...
JEE Main Mathematics Easy
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Q JEE MAIN 2020
If $1+\left(1-2^2 \cdot 1\right)+\left(1-4^2 \cdot 3\right)+\left(1-6^2 \cdot 5\right)+\ldots \ldots+ \left(1-20^2 \cdot 19\right)=\alpha-220 \beta$, then an ordered pair $(\alpha, \beta)$ is equal to:
JEE Main Mathematics Hard
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Q JEE MAIN 2020
Let $x_0$ be the point of local maxima of $f(x)=\vec{a} \cdot(\vec{b} \times \vec{c})$, where $\vec{a}=x \hat{i}-2 \hat{j}+3 \hat{k}, \vec{b}=-2 \hat{i}+x \hat{j}+\hat{k}$ and $...
JEE Main Mathematics Hard
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