JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5526

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 5527

The value of $k\in\mathbf{R}$, for which the following system of linear equations $3x-y+4z=3$, $x+2y-3z=-2$, $6x+5y+kz=-3$, has infinitely many solutions, is :

Determinant

$3$$-5$$5$$-3$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5528

In a triangle $ABC$, if $|\overrightarrow{BC}|=3$, $|\overrightarrow{CA}|=5$ and $|\overrightarrow{BA}|=7$, then the projection of the vector $\overrightarrow{BA}$ on $\overrightarrow{BC}$ is equal to :

Vector Algebra

$\dfrac{19}{2}$$\dfrac{13}{2}$$\dfrac{11}{2}$$\dfrac{15}{2}$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5529

Let $y=y(x)$ satisfy the equation $\dfrac{dy}{dx}-|A|=0$, for all $x>0$, where $A=\begin{bmatrix}y&\sin x&1\\0&-1&1\\2&0&\dfrac{1}{x}\end{bmatrix}$. If $y(\pi)=\pi+2$, then the value of $y\left(\dfrac{\pi}{2}\right)$ is :

Differential Equation

$\dfrac{\pi}{2}+\dfrac{4}{\pi}$$\dfrac{\pi}{2}-\dfrac{1}{\pi}$$\dfrac{3\pi}{2}-\dfrac{1}{\pi}$$\dfrac{\pi}{2}-\dfrac{4}{\pi}$

JEE Main 2021 (Online) 20th July Evening ShiftQuestion 5530

Let $r_1$ and $r_2$ be the radii of the largest and smallest circles, respectively, which pass through the point $(-4,1)$ and having their centres on the circumference of the circle $x^2+y^2+2x+4y-4=0$. If $\dfrac{r_1}{r_2}=a+b\sqrt{2}$, then $a+b$ is equal to :

Circle

$3$$11$$5$$7$

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