List of top Questions asked in JEE Main- 2023

Statement (1): A truck and a car moving with equal kinetic energy are stopped by equal retarding force. Both will cover equal distance to stop.
Statement (2): A car moving towards east suddenly changes its direction towards north with same speed. Its acceleration is zero.
In the light of given statements, choose the most appropriate answer from the options given below.

In a cuboid of dimension $2L \times 2L \times L$, a charge q is placed at the center of the surface ‘S’ having area of 4 L². The flux through the opposite surface to ‘S’ is:

Given below are two statements :
Statement I : For transmitting a signal, size of antenna ( $f$ ) should be comparable to wavelength of signal (at least $l=\frac{\lambda}{4}$ in dimension)
Statement II : In amplitude modulation, amplitude of carrier wave remains constant (unchanged)
In the light of the above statements, choose the most appropriate answer from the options given below,

As per the given figure, a small ball $P$ slides down the quadrant of a circle and hits the other ball $Q$ of equal mass which is initially at rest Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball $Q$ after collision will be :$\left( g =10 \,m / s ^2\right)$

A 10 μC charge is divided into two equal parts and kept at 1 cm distance. Find repulsion between charges?

A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the center. If the angular velocity of the table is halved, it will just slip when placed at a distance of ----- from the centre:

Let $\alpha>0$ If $\int\limits_0^\alpha \frac{x}{\sqrt{x+\alpha}-\sqrt{x}} d x=\frac{16+20 \sqrt{2}}{15}$, then $\alpha$ is equal to :

Let the mean and variance of 12 observations be $ \frac{9}{2} $ and 4, respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is $ \frac{m}{n} $, where $ m $ and $ n $ are coprime, then $ m + n $ is equal to:

Let α and β be real numbers. Consider a $3 \times 3$ matrix A such that $A^2 = 3A + \alpha I$. If $A^4 = 21A + \beta I$, then

Let $\alpha$ be a root of the equation $(a-c) x^2+(b-a) x+(c-b)=0$where $a , b , c$ are distinct real numbers such that the matrix $\begin{bmatrix}\alpha^2 & \alpha & 1 \\ 1 & 1 & 1 \\ a & b & c\end{bmatrix}$is singular Then, the value of $\frac{(a-c)^2}{(b-a)(c-b)}+\frac{(b-a)^2}{(a-c)(c-b)}+\frac{(c-b)^2}{(a-c)(b-a)}$ is

The combined equation of the two lines $a x+b y+c=0$ and $a^{\prime} x+b^{\prime} y+c^{\prime}=0$ can be written as $(a x+b y+c)\left(a^{\prime} x+b^{\prime} y+c^{\prime}\right)=0$
The equation of the angle bisectors of the lines represented by the equation $2 x^2+x y-3 y^2=0$ is

The shortest distance between the lines $\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2}$ and $\frac{x-4}{1}=\frac{y-1}{2}=\frac{z+3}{0}$ is

For the system of linear equations
$x+y+z=6$
$\alpha x+\beta y+7 z=3$
$x+2 y+3 z=14$.
which of the following is NOT true ?

If $a_r$ is the coefficient of $x^{10-r}$ in the Binomial expansion of $(1+x)^{10}$, then $\displaystyle\sum_{r=1}^{10} r^3\left(\frac{a_r}{a_{r-1}}\right)^2$ is equal to

If four distinct points with position vectors $\overrightarrow a,\overrightarrow b,\overrightarrow c$ and $\overrightarrow d$ are coplanar, then $[\overrightarrow a \overrightarrow b \overrightarrow c]$ is equal to

For two groups of 15 sizes each, mean and variance of first group is 12, 14 respectively, and second group has mean 14 and variance of σ². If combined variance is 13 then find variance of second group?

The number of common tangents, to the circles $ x^2 + y^2 - 18x - 15y + 131 = 0 $ and $ x^2 + y^2 - 6x - 6y - 7 = 0 $, is