List of top Questions asked in JEE Main- 2023

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed.
Reason R: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.
In the light of the above statements, choose the most appropriate answer from the options given below:

A physical quantity P is given as
$ P = \frac{a^2b^2 }{ c\sqrt{d}} .$
The percentage error in the measurement of a,b, c and d are1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be

The ratio of de-Broglie wavelength of an $\alpha$ particle and a proton accelerated from rest by the same potential is $\frac {1}{\sqrt 𝑚}$ , the value of $m$ is-

The number of following statements which are incorrect line emission

The value of $\int\limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{(2+3 \sin x)}{\sin x(1+\cos x)} d x$ is equal to

Let $y=y(x)$ be the solution of the differential equation $\left(3 y^2-5 x^2\right) y d x+2 x\left(x^2-y^2\right) d y=0$ such that $y(1)=1$ Then $\left|(y(2))^3-12 y(2)\right|$ is equal to :

The set of all values of $a^2$ for which the line $x+y=0$ bisects two distinct chords drawn from a point $P \left(\frac{1+a}{2}, \frac{1-a}{2}\right)$ on the circle $2 x^2+2 y^2-(1+a) x-(1-a) y=0$, is equal to :

If $\vec{a}$, $\vec{b}$, $\vec{c}$ are three non-zero vectors and $\hat{n}$ is a unit vector perpendicular to $\vec{c}$ such that $\vec{a}$=$\alpha \vec{b}$-$\hat{n}$, $\alpha \neq 0$ and $\vec{b}$ .$ \vec{c}$=12, then |$\vec{c} \times(\vec{a} \times \vec{b})$| is equal to:

Match List I with List II

The minimum value of the function $f(x)=\int\limits_0^2 e^{|x-t|} d t$ is :

Correct statement is:

Let $\vec{\alpha}=4 \hat{i}+3 \hat{j}+5 \hat{k}$ and $\vec{\beta}=\hat{i}+2 \hat{j}-4 \hat{k}$ Let $\vec{\beta}_1$ be parallel to $\vec{\alpha}$ and $\vec{\beta}_2$ be perpendicular to $\vec{\alpha}$ If $\vec{\beta}=\vec{\beta}_1+\vec{\beta}_2$, then the value of $5 \vec{\beta}_2 \cdot(\hat{i}+\hat{j}+\hat{k})$ is

The value of the integral:$\int\limits_{\frac{3 \sqrt{2}}{4}}^{\frac{3 \sqrt{3}}{4}} \frac{48}{\sqrt{9-4 x^2}} d x$ is equal to

Let $p$ and $q$ be two statements Then $\sim(p \wedge(p \Rightarrow \sim q))$ is equivalent to

The number of molecules from the following which contain only two lone pair of electrons is _____ .
$H_2O, N_2, CO, XeF_4, NH_3, NO, CO_2, F_2$

The number of elements in the set $\{n ∈ Z : n^2-10n+19| < 6\}$ is __.

Let f: R→R be a function such that $f(x)=\frac{x^2+2x+1}{x^2+1}$. Then

If the local maximum value of the function f( x )=$(\frac{√3e}{2 sin x} )^{ sin^2x}$ ,$ x ∈ ( 0,\frac{π}{2} )$, is $\frac{k}{e}$, then $(\frac{k}{e})^8+\frac{k^8}{e^5}+k^8 $ is equal to

the points P and Q are respectively the circumcentre and the orthocentre of a ΔABC, then $ \overrightarrow{PA}+ \overrightarrow{PB}+ \overrightarrow{PC}$ is

If $\lim\limits_{x\rightarrow0}\frac{e^{ax}-\cos(bx)-\frac{cxe^{-ce}}{2}}{1-\cos(2x)}=17$ ,then 5a² + b² is equal to

Area bounded by larger part in I quadrant by x = 4y² , x = 2 and y = x is A then 3A equals

Let B and C be the two points on the line $y + x = 0$ such that B and C are symmetric with respect to the origin. Suppose A is a point on $y – 2x = 2$ such that $\Delta ABC$ is an equilateral triangle. Then, the area of the $\Delta ABC$ is

Let $x = 2$ be a root of the equation $x^2 + px + q = 0$ and $f(x)=\begin{cases}\frac{1-cos(x^2-4px+q^2+8q+16)}{(x-2p)^4} & x≠2p\\0 & x=2p\end{cases}$.
Then $lim_{x \rightarrow 2p}[f(x)]$, where [·] denotes greatest integer function, is

Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of its squares of first three terms is 33033, then the sum of these three terms is equal to

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is

List I (Current configuration)	List II(Magnetic field at point O)
A	i	\(B_0=\frac{\mu_0I}{4\pi r}[\pi+2]\)
B	ii	\(B_0=\frac{\mu_0}{4}\frac{I}{r}\)
C	iii	\(B_0=\frac{\mu_0I}{2\pi r}[\pi-1]\)
D	iv	\(B_0=\frac{\mu_0I}{4\pi r}[\pi+1]\)