JEE Maths PYQ Practice, chapter-wise

JEE Main 2020 (Online) 7th January Evening ShiftQuestion 5501

Let $f(x)$ be a polynomial of degree $5$ such that $x=\pm1$ are its critical points. If $\lim_{x\to0}\left(2+\frac{f(x)}{x^3}\right)=4$, then which one of the following is not true?

Differentiation and its Application

$f$ is an odd function$x=1$ is a point of maxima and $x=-1$ is a point of minima of $f$$f(1)-4f(-1)=4$$x=1$ is a point of minima and $x=-1$ is a point of maxima of $f$

JEE Main 2023 (Online) 24th January Morning ShiftQuestion 5502

Let $PQR$ be a triangle. The points $A$, $B$ and $C$ are on the sides $QR$, $RP$ and $PQ$ respectively such that $\frac{QA}{AR}=\frac{RB}{BP}=\frac{PC}{CQ}=\frac12$. Then $\frac{\text{Area}(\triangle PQR)}{\text{Area}(\triangle ABC)}$ is equal to

Points and Straight Lines

$4$$3$$2$$\frac52$

JEE Main 2025 (Online) 29th January Evening ShiftQuestion 5503

Let the line $x+y=1$ meet the axes of $x$ and $y$ at $A$ and $B$, respectively. A right angled triangle $AMN$ is inscribed in the triangle $OAB$, where $O$ is the origin and the points $M$ and $N$ lie on the lines $OB$ and $AB$, respectively. If the area of the triangle $AMN$ is $\frac49$ of the area of the triangle $OAB$ and $AN:NB=\lambda:1$, then the sum of all possible value(s) of $\lambda$ is :

Points and Straight Lines

$2$$\frac52$$\frac12$$\frac{13}{6}$

JEE Main 2020 (Online) 7th January Morning ShiftQuestion 5504

A vector $\vec a=\alpha\hat i+2\hat j+\beta\hat k$ $(\alpha,\beta\in\mathbb R)$ lies in the plane of the vectors, $\vec b=\hat i+\hat j$ and $\vec c=\hat i-\hat j+4\hat k$. If $\vec a$ bisects the angle between $\vec b$ and $\vec c$, then

Vector Algebra

$\vec a\cdot\hat i+3=0$$\vec a\cdot\hat i+1=0$$\vec a\cdot\hat k+2=0$$\vec a\cdot\hat k+4=0$

JEE Main 2019 (Online) 9th January Morning ShiftQuestion 5505

The value of $\int_0^\pi|\cos x|^3\,dx$ is

Definite Integration

$\frac23$$0$$\frac43$$-\frac43$

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