List of top Questions asked in JEE Main- 2023

The correct order of $\mathrm{pK_a}$ values for the following compounds is:

A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is $p$. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colour is $q$. If $p : q = m : n$, where $m$ and $n$ are coprime, then $m + n$ is equal to :

$\lim_{n\to\infty} \frac{3}{n}\left\{4 + \left(2 + \frac{1}{n}\right)^2 + \left(2 + \frac{2}{n}\right)^2 + \dots + \left(3 - \frac{1}{n}\right)^2\right\}$ is equal to :

The parabolas : $ax^2 + 2bx + cy = 0$ and $dx^2 + 2ex + fy = 0$ intersect on the line $y = 1$. If $a, b, c, d, e, f$ are positive real numbers and $a, b, c$ are in G.P., then :

A flask contains hydrogen and oxygen in the ratio of $2:1$ by mass at temperature $27^\circ\mathrm{C}$. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is:

Let $q$ be the maximum integral value of $p$ in $[0,10]$ for which the roots of the equation $x^2 - px + \frac{5}{4}p = 0$ are rational. Then the area of the region $\left\{(x,y) : 0 \le y \le (x-q)^2,\ 0 \le x \le q\right\}$ is :

Let a unit vector $\widehat{OP}$ make angles $\alpha, \beta, \gamma$ with the positive directions of the co-ordinate axes OX, OY, OZ respectively, where $\beta \in \left(0, \frac{\pi}{2}\right)$. If $\widehat{OP}$ is perpendicular to the plane through points $(1,2,3), (2,3,4)$ and $(1,5,7)$, then which one of the following is true?

The compound which will have the lowest rate towards nucleophilic aromatic substitution on treatment with $\mathrm{OH^-}$ is

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Electromagnets are made of soft iron.
Reason R : Soft iron has high permeability and low retentivity.
In the light of above, statements, choose the most appropriate answer from the options given below.

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

Let $I(x) = \int \frac{x^2\left(x\sec^2 x + \tan x\right)}{(x\tan x + 1)^2}\,dx$. If $I(0) = 0$, then $I\left(\frac{\pi}{4}\right)$ is equal to :

Group-13 elements react with O₂ in amorphous form to form oxides of type M₂O₃ (M = element). Which among the following is the most basic oxide?

A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding wavelength for this transition is (given, h = 4 × 10⁻¹⁵ eVs) :

A single current-carrying loop of wire carrying current I flows in the anticlockwise direction (seen from the +z direction) and lies in the xy plane. The plot of $\hat{j}$ component of magnetic field ($B_y$) at a distance a (less than radius of the coil) and on the yz plane vs z coordinate looks like:

The energy levels of an atom is shown in figure:

Which one of these transitions will result in the emission of a photon of wavelength $1241\, nm$ ? Given $\left( h =6.62 \times 10^{-34} Js \right)$

Decreasing order of the hydrogen bonding in following forms of water is correctly represented by
A. Liquid water
B. Ice
C. Impure water
Choose the correct answer from the options given below:

On a temperature scale X, the boiling point of water is 65° X and the freezing point is 15° X. Assume that the X scale is linear. The equivalent temperature corresponding to 95° X on the Fahrenheit scale would be:

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

Let S = $\{z \in C-\{i,2i\}:\frac{z^2+8iz-15}{z^2-3iz-2}\in R\}$ if $\alpha-\frac{13}{11}i\in S, a \in R-{0}$, then $242\alpha^2$ is equal to ____.

A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should. (Select the best option)

Let awards in event A is 48 and awards in event B is 25 and awards in event C is 18 and also n(A ∪ B ∪ C) = 60, n(A ⋂ B ⋂ C) = 5, then how many got exactly two awards is?

Suppose $\displaystyle\sum_{r=0}^{2023} r^{22023} C_r=2023 \times \alpha \times 2^{2022}$ Then the value of $\alpha$ is

A fully loaded boeing aircraft has a mass of $5.4×10^5 $ kg. Its total wing area is $500 m^2$. It is in level flight with a speed of 1080 km/h. If the density of air 𝜌 is $1.2 kg m^{−3}$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be. ($𝑔=10 m/s^2$)

Let α,β be the roots of the quadratic equation x²+√6x+3=0. Then $\frac{α^23+β^23 + α ^14 + β ^14 }{α ^15 + β ^15 + α 160 + β ^{10}}$ is equal to

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height Choose the correct statement out of the following (Assume negligible air friction)