List of top Questions asked in JEE Main- 2023

From the figure of column chromatography given below, identify incorrect statements

A. Compound 'c' is more polar than 'a' and 'b' 
B. Compound 'a' is least polar
C. Compound 'b' comes out of the column before 'c' and after 'a' 
D. Compound 'a' spends more time in the column 
Choose the correct answer from the options given below
Find out the major product from the following reaction.
major product from the following reaction jee main 2023
The strongest acid from the following is
Given below are two statements :
Statement-I: Morphine is a narcotic analgesis. It helps in relieving pain without producing sleep. 
Statement-II: Morphine and its derivatives are obtained from opium poppy. 
In the light of the above statements, choose the correct answer from the options given below.
For differentiable function f: R-{0}⟶ R, let 3f(x)+2f(\(\frac{1}{x}\))-\(\frac{1}{x}\)-10, then |f(3)+f(\(\frac{1}{4}\))| is equal to
The set of all a∈ R for which the equation x|x-1|+|x-2|+a=0 has exactly one real root is
Let B =\(\begin{bmatrix} 1 & 3 & α \\ 1 & 2& 3 \\ α & α & 4 \end{bmatrix}\) , α>2 be the adjoint of a matrix A and |A| = 2, then [α - 2α α] B\(\begin{bmatrix} α \\ -2α  \\ α \end{bmatrix}\)is equal to
For the system of linear equations  
2x+4y+2az=b
x+2y+3z=4 
2x-5y+2z=8 
which of the following is NOT correct ?  
Let s1, s2, s3,…..,s10 respectively be the sum to 12 terms of 10 A.P.s whose first terms are 1,2,3, …. ,10 and the common differences are 1, 3, 5, …. , 19 respectively. Then  \(10∑^{10}_{i=1} s_i\) is
\((S1) : lim_{n→∞}\frac{1}{ n ^2} ( 2 + 4 + 6 + . . . . + 2n) = 1\)
\((S2):  lim_n→∞\frac{1}{n^{16}}( 1^15 +2^15 +3^15 + . . . . + n^15 ) = \frac{1}{16} \)
Let a =\(\^i+4\^j​+2\^k,b=3\^i−2\^j​+7\^k \,\,\,\,and\,\,\.\ c=2\^i−\^j​+4\^k\). Find a vector d satisfies \(\overrightarrow{d}\times{\overrightarrow{b}}=\overrightarrow{c}\times{\overrightarrow{b}}\) and \(\overrightarrow{d}.\overrightarrow{a}=24\), then \(|\overrightarrow{d}|^2\) is equal to
\(max\\{0≤x≤π}\) \(\{x−2\,\, sin. x \,\,cos+\frac{1}{3} sin\,\, 3x \}=\)
Let the tangent and normal at the point \((3\sqrt{3},1)\) on the ellipse \(\frac{ x^2}{36}+\frac{y^2}{4} =1\) meet the y-axis at the points A and B respectively. Let the circle C be drawn taking AB as a diameter and the line x = \(2\sqrt{5}\) intersect C at the points P and Q. If the tangents at the points P and Q on the circle intersect at the point (α,β) , then α2 - β2 is equal to 
Let PQ be a focal chord of the parabola y2 = 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 \(\underline{NOT}\) lie on the line passing through M and perpendicular to the line PQ? 
The distance of the point ( -1,2,3) from the plane \(\overrightarrow{r}( \^i−2 \^j+3 \^k )=10\) parallel to the line of the shortest distance between the lines \(\overrightarrow{r}=(\^i=\^j)+λ(2\^i+\^k)\) and  \(\overrightarrow{r}=(2\^i=\^j)+μ(\^i+\^j+\^k)\)  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
The negation of the statement \(((A\land(B\lor C)) ⇒ (A\lor B)) ⇒ A\) is

A body of mass \( (5 \pm 0.5) \, \text{kg} \) is moving with a velocity of \( (20 \pm 0.4) \, \text{m/s} \). Its kinetic energy will be:

Two trains 'A' and 'B' of length \('l'\) and \('4l'\) are travelling into a tunnel of length 'L' in parallel tracks from opposite directions with velocities 108 km/h and 72 km/h, respectively. If train 'A' takes 35s less time than train 'B' to cross the tunnel then. length 'L' of tunnel is:
(Given L = 60 \(l\))

A disc is rolling without slipping on a surface. The radius of the disc is R. At t = 0, the top most point on the disc is A as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is

Rolling Disc
A bullet of 10 g leaves the barrel of gun with a velocity of 600 m/s. If the barrel of gun is 50 cm long and mass of gun is 3 kg, then value of impulse supplied to the gun will be :
A planet having mass \(9M_e\) and radius \(4R_e\), where \(M_e\) and \(R_e\) are mass and radius of earth respectively, has escape velocity in km/s given by: (Given escape velocity on earth \(V_e= 11.2 × 10^3 m/s\))
Liquid Density
The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross - section. Cross sectional areas at A is 1.5 cm², and B is is 25 mm², if the speed of liquid at B is 60 cm/s then \((P_A-P_B)\) is: 
(Given \(P_A\) and \(P_B\) are liquid pressures at A and B points.
density \(ρ = 1000 \space kg \space m^{-3}\)
A and B are on the axis of tube)
The rms speed of oxygen molecule in a vessel at particular temperature is \((1+\frac{5}{x})^{\frac{1}{2}} v\), where \(v\) is the average speed of the molecule. The value of x will be : (Take \(π = \frac{22}{7}\))
The ratio of powers of two motors is \(\frac{3\sqrt x}{\sqrt x+1}\), that are capable of raising 300 kg water in 5 minutes and 50 kg water in 2 minutes respectively from a well of 100 m deep. The value of x will be