JEE Maths PYQ Practice, chapter-wise

JEE Main 2025 (Online) 28th January Morning ShiftQuestion 7486

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 7487

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 7488

Consider a triangle having vertices $A(-2,3)$, $B(1,9)$ and $C(3,8)$. If a line $L$ passing through the circum-centre of triangle $ABC$, bisects line $BC$, and intersects $y$-axis at point $\left(0,\dfrac{\alpha}{2}\right)$, then the value of real number $\alpha$ is $\_\_\_\_\_\_\_\_$ .

Points and Straight Lines

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JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7489

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$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7490

Let $P$ be a variable point on the parabola $y=4x^2+1$. Then, the locus of the mid-point of the point $P$ and the foot of the perpendicular drawn from the point $P$ to the line $y=x$ is :

Parabola

$(3x-y)^2+(x-3y)+2=0$$2(3x-y)^2+(x-3y)+2=0$$(3x-y)^2+2(x-3y)+2=0$$2(x-3y)^2+(3x-y)+2=0$

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