JEE Maths PYQ Practice, chapter-wise

JEE Main 2023 (Online) 8th April Morning ShiftQuestion 1

If the points with position vectors $\alpha\hat{i}+10\hat{j}+13\hat{k}$, $6\hat{i}+11\hat{j}+11\hat{k}$, $\frac{9}{2}\hat{i}+\beta\hat{j}-8\hat{k}$ are collinear, then $(19\alpha-6\beta)^{2}$ is equal to

Vector Algebra

$16$$25$$36$$49$

JEE Main 2021 (Online) 22nd July Evening ShiftQuestion 2

Let a vector $\vec{a}$ be coplanar with vectors $\vec{b}=2\hat{i}+\hat{j}+\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}+\hat{k}$. If $\vec{a}$ is perpendicular to $\vec{d}=3\hat{i}+2\hat{j}+6\hat{k}$, and $|\vec{a}|=\sqrt{10}$. Then a possible value of $\left[\vec{a}\ \vec{b}\ \vec{c}\right]+\left[\vec{a}\ \vec{b}\ \vec{d}\right]+\left[\vec{a}\ \vec{c}\ \vec{d}\right]$ is equal to :

Vector Algebra

$-40$$-42$$-38$$-29$

JEE Main 2021 (Online) 26th February Morning ShiftQuestion 3

If $\vec{a}$ and $\vec{b}$ are perpendicular, then $\vec{a}\times\left(\vec{a}\times\left(\vec{a}\times\left(\vec{a}\times\vec{b}\right)\right)\right)$ is equal to :

Vector Algebra

$\vec{0}$$\frac{1}{2}|\vec{a}|^{4}\vec{b}$$|\vec{a}|^{4}\vec{b}$$\vec{a}\times\vec{b}$

JEE Main 2026 (Online) 8th April Evening ShiftQuestion 4

Let $\vec{a}=4\hat{i}-\hat{j}+3\hat{k}$, $\vec{b}=10\hat{i}+2\hat{j}-\hat{k}$ and a vector $\vec{c}$ be such that $2(\vec{a}\times\vec{b})+3(\vec{b}\times\vec{c})=\vec{0}$. If $\vec{a}\cdot\vec{c}=15$, then $\vec{c}\cdot(\hat{i}+\hat{j}-3\hat{k})$ is equal to :

Vector Algebra

$-6$$-5$$-4$$-3$

JEE Main 2023 (Online) 11th April Morning ShiftQuestion 5

For any vector $\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}$, with $10|a_i|<1$, $i=1,2,3$, consider the following statements : (A) : $\max\{|a_1|,|a_2|,|a_3|\}\le|\vec{a}|$ (B) : $|\vec{a}|\le3\max\{|a_1|,|a_2|,|a_3|\}$

Vector Algebra

Only (A) is trueOnly (B) is trueBoth (A) and (B) are trueNeither (A) nor (B) is true