JEE Mathematics / Practice

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JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7496

For $p>0$, a vector $\vec{v}_2=2\hat{i}+(p+1)\hat{j}$ is obtained by rotating the vector $\vec{v}_1=\sqrt{3}p\,\hat{i}+\hat{j}$ by an angle $\theta$ about origin in counter clockwise direction. If $\tan\theta=\dfrac{\alpha\sqrt{3}-2}{4\sqrt{3}+3}$, then the value of $\alpha$ is equal to $\_\_\_\_\_\_\_\_$ .

Vector Algebra

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JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7497

The lines $x=ay-1=z-2$ and $x=3y-2=bz-2$, $(ab eq0)$ are coplanar, if :

3D Geometry

$b=1,\ a\in\mathbf{R}-\{0\}$$a=1,\ b\in\mathbf{R}-\{0\}$$a=2,\ b=2$$a=2,\ b=3$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7498

Let a function $g:[0,4]\to\mathbf{R}$ be defined as $g(x)=\begin{cases}\max\limits_{0\le t\le x}\{t^3-6t^2+9t-3\}, & 0\le x\le 3\\ 4-x, & 3<x\le 4\end{cases}$, then the number of points in the interval $(0,4)$ where $g(x)$ is NOT differentiable, is $\_\_\_\_\_\_\_\_$ .

Differentiation and its Application

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JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7499

If sum of the first 21 terms of the series $\log_{9^{1/2}}x+\log_{9^{1/3}}x+\log_{9^{1/4}}x+\cdots$, where $x>0$ is $504$, then $x$ is equal to

Sequence and Series · Arithmetic Progression

$243$$9$$7$$81$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 7500

Let $A=\{a_{ij}\}$ be a $3\times3$ matrix, where $a_{ij}=\begin{cases}(-1)^{j-i} & \text{if } i<j,\\ 2 & \text{if } i=j,\\ (-1)^{i+j} & \text{if } i>j\end{cases}$ then $\det\left(3\,\mathrm{Adj}(2A^{-1})\right)$ is equal to $\_\_\_\_\_\_\_\_$ .

Matrices

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