List of top Questions asked in JEE Main- 2023

The escape velocities of two planets \(A\) and \(B\) are in the ratio \(1: 2\) If the ratio of their radii respectively is\(1: 3\), then the ratio of acceleration due to gravity of planet \(A\) to the acceleration of gravity of planet B will be :

The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1\%,2\% and $3 \%$ respectively The maximum percentage error in the detection of the dissipated heat will be:
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.
Find the magnetic field at the point $P$ in figure. The curved portion is a semicircle connected to two long straight wires
curved portion is a semicircle

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 small ball P slides down the quadrant of a circle and hits the other ball Q of equal mass which is initially at rest

A 10 μC charge is divided into two equal parts and kept at 1 cm distance. Find repulsion between charges?
If the tangents at the points P and Q on the circle x2 + y2 – 2x + y = 5 meet at the point R  \(( \frac{9}{4},2 ) \)then the area of the triangle PQR is 
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:

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?

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

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 ?

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

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 \(\vec{a}\) = 2\(\widehat{i}\)+3\(\widehat{j}\)+4\(\widehat{k}\), \(\vec{b}\) = \(\widehat{i}\)-2\(\widehat{j}\)-2\(\widehat{k}\), \(\vec{c}\) = -\(\widehat{i}\)+4\(\widehat{j}\)+3\(\widehat{k}\) and \(\vec{d}\) is a vector perpendicular to \(\vec{b}\) and \(\vec{c}\),  \(\vec{a}\).\(\vec{d}\) = 18, then find |\(\vec{a}\)x\(\vec{d}\)|2
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
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
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
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 
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

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 :

Which of the following statements is correct about freons?
CH3CH2-Br \(\overrightarrow{Acetone}^{NaI}\) CH3-CH2-I+NaBr
Which of the following statement is correct ? 

Match items of Row I with those of Row II

Statement I : Dipole moment is a vector quantity and by convention it is depicted by a small arrow with tail on the negative centre and head pointing towards the positive centre
Statement II : The crossed arrow of the dipole moment symbolizes the direction of the shift of charges in the molecules.
In the light of the above statements, choose the most appropriate answer from the options given below:

The major products ' A ' and ' B ', respectively, are