JEE MAIN 2023 Previous Year Questions (PYQs) – Page 20 of 34

The area of the region enclosed by the curve $f(x)=\max\{\sin x,\cos x\},\ -\pi \le x \le \pi$ and the $x$-axis is:

The number of functions $f:\{1,2,3,4\}\to \{\,a\in \mathbb{Z}\mid |a|\le 8\,\}$ satisfying $f(n)+\dfrac{1}{n}f(n+1)=1,\ \forall\, n\in\{1,2,3\}$ is:

Let $PQ$ be a focal chord of the parabola $y^{2}=36x$ of length $100$, making an acute angle with the positive $x$-axis. Let the ordinate of $P$ be positive and $M$ be the point on the line segment $PQ$ such that $PM:MQ=3:1$. Then which of the following points does NOT lie on the line passing through $M$ and perpendicular to the line $PQ$?

Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N-2,\ \sqrt{3N},\ N+2$ are in geometric progression be $\dfrac{k}{48}$. Then the value of $k$ is:

Let $\vec{a}=\hat{i}+4\hat{j}+2\hat{k}$, $\vec{b}=3\hat{i}-2\hat{j}+7\hat{k}$ and $\vec{c}=2\hat{i}-\hat{j}+4\hat{k}$. If a vector $\vec{d}$ satisfies $\vec{d}\times\vec{b}=\vec{c}\times\vec{b}$ and $\vec{d}\cdot\vec{a}=24$, then $|\vec{d}|^{2}$ is equal to:

For the system of linear equations

$2 x+4 y+2 a z=b$

$x+2 y+3 z=4$

$2 x-5 y+2 z=8$

which of the following is NOT correct?

If the function $f(x) = \left\{ {\matrix{ {(1 + |\cos x|)^{\lambda \over {|\cos x|}}} & , & {0 < x < {\pi \over 2}} \cr \mu & , & {x = {\pi \over 2}} \cr e^{{{\cot 6x} \over {{}\cot 4x}}} & , & {{\pi \over 2} < x < \pi } \cr } } \right.$

is continuous at $x = {\pi \over 2}$, then $9\lambda + 6{\log _e}\mu + {\mu ^6} - {e^{6\lambda }}$ is equal to

Let $y=y_1(x)$ and $y=y_2(x)$ be the solution curves of the differential equation $\dfrac{dy}{dx}=y+7$ with initial conditions $y_1(0)=0$ and $y_2(0)=1$ respectively. Then the curves $y=y_1(x)$ and $y=y_2(x)$ intersect at:

two points  

infinite number of points  

one point  

The shortest distance between the lines $x+1=2y=-12z$ and $x=y+2=6z-6$ is:

A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If $X$ denotes the number of tosses of the coin, then the mean of $X$ is:

$\dfrac{37}{16}$  

$\dfrac{21}{16}$  

 $\dfrac{15}{16}$