JEE Maths PYQ Practice, chapter-wise

JEE Main 2026 (Online) 2nd April Evening ShiftQuestion 1

Let $\alpha,\beta$ be the roots of the equation $x^{2}-3x+r=0$, and $\frac{\alpha}{2},2\beta$ be the roots of the equation $x^{2}+3x+r=0$. If the roots of the equation $x^{2}+6x=m$ are $2\alpha+\beta+2r$ and $\alpha-2\beta-\frac{r}{2}$, then $m$ is equal to :

Quadratic Equation · Relation Between Roots and Coefficients

$-135$$-567$$135$$567$

JEE Main 2021 (Online) 24th February Evening ShiftQuestion 2

Let $a,b,c$ be in arithmetic progression. Let the centroid of the triangle with vertices $(a,c)$, $(2,b)$ and $(a,b)$ be $\left(\frac{10}{3},\frac{7}{3}\right)$. If $\alpha,\beta$ are the roots of the equation $ax^{2}+bx+1=0$, then the value of $\alpha^{2}+\beta^{2}-\alpha\beta$ is :

Quadratic Equation · Relation Between Roots and Coefficients

$-\frac{69}{256}$$-\frac{71}{256}$$\frac{69}{256}$$\frac{71}{256}$

JEE Main 2021 (Online) 25th February Morning ShiftQuestion 3

The integer '$k$', for which the inequality $x^{2}-2(3k-1)x+8k^{2}-7>0$ is valid for every $x$ in $\mathbf{R}$, is :

Quadratic Equation · Sign, Range and Inequalities of Quadratic Expressions

$2$$3$$4$$0$

JEE Main 2021 (Online) 24th February Morning ShiftQuestion 4

Let $p$ and $q$ be two positive numbers such that $p+q=2$ and $p^{4}+q^{4}=272$. Then $p$ and $q$ are roots of the equation :

Quadratic Equation · Relation Between Roots and Coefficients

$x^{2}-2x+136=0$$x^{2}-2x+16=0$$x^{2}-2x+8=0$$x^{2}-2x+2=0$

JEE Main 2026 (Online) 5th April Evening ShiftQuestion 5

Let $\alpha,\beta$ be the roots of the equation $x^{2}-x+p=0$ and $\gamma,\delta$ be the roots of the equation $x^{2}-4x+q=0$; $p,q\in\mathbf{Z}$. If $\alpha,\beta,\gamma,\delta$ are in G.P., then $|p+q|$ equals :

Quadratic Equation · Relation Between Roots and Coefficients

$16$$32$$34$$38$