JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 1st September Evening ShiftQuestion 5516

Let $f:\mathbb R\to\mathbb R$ be a continuous function. Then $\displaystyle\lim_{x\to\pi/4}\frac{\frac\pi4\int_2^{\sec^2x}f(x)\,dx}{x^2-\frac{\pi^2}{16}}$ is equal to:

Limits & Continuity

$f(2)$$2f\left(\sqrt2\right)$$2f(2)$$4f(2)$

JEE Main 2025 (Online) 28th January Morning ShiftQuestion 5517

Let the equation of the circle, which touches $x$-axis at the point $(a,0)$, $a>0$ and cuts off an intercept of length $b$ on $y$-axis be $x^{2}+y^{2}-\alpha x+\beta y+\gamma=0$. If the circle lies below $x$-axis, then the ordered pair $(2a,b^{2})$ is equal to

Circle

$(\alpha,\ \beta^{2}+4\gamma)$$(\alpha,\ \beta^{2}-4\gamma)$$(\gamma,\ \beta^{2}-4\alpha)$$(\gamma,\ \beta^{2}+4\alpha)$

JEE Main 2025 (Online) 28th January Morning ShiftQuestion 5518

Let $O$ be the origin, the point $A$ be $z_1=\sqrt{3}+2\sqrt{2}\,i$, the point $B(z_2)$ be such that $\sqrt{3}\,|z_2|=|z_1|$ and $\arg(z_2)=\arg(z_1)+\frac{\pi}{6}$. Then

Complex Numbers

area of triangle $ABO$ is $\frac{11}{4}$area of triangle $ABO$ is $\frac{11}{\sqrt{3}}$$ABO$ is a scalene triangle$ABO$ is an obtuse angled isosceles triangle

JEE Main 2025 (Online) 28th January Morning ShiftQuestion 5519

Let for some function $y=f(x)$, $\int_{0}^{x}tf(t)\,dt=x^{2}f(x)$, $x>0$ and $f(2)=3$. Then $f(6)$ is equal to

Differential Equation

$1$$6$$2$$3$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5520

The sum of all the local minimum values of the twice differentiable function $f:\mathbf{R}\to\mathbf{R}$ defined by $f(x)=x^3-3x^2-\dfrac{3f''(2)}{2}x+f''(1)$ is :

Differentiation and its Application

$-22$$5$$-27$$0$

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