List of top Questions asked in JEE Main- 2023

Choose the correct option amongst the answer figures which complete the series.

$\lim_{x \to 0} (1 + 3x)^{\frac{x + 2}{x}}$ is equal to

The sum of the first eleven terms of the series is $\frac{1}{1 + 1^2 + 1^4} + \frac{2}{1 + 2^2 + 2^4} + \frac{3}{1 + 3^2 + 3^4} + \ldots$

Let $P(\alpha, \beta, \lambda)$ be the image of the point $\mathrm{Q}(1, 2, 0)$ in the line $\frac{x - 5}{3} = \frac{y - 12}{1} = \frac{z - 10}{2}$, then $(\mathrm{PQ})^2$ is equal to

From the given options below, choose the correct plan of the 3-D object, when viewed from the top.

The question figure shows the 3-D view of an object. Identify the correct view, looking in the direction of arrow.

Let $\alpha$ and $\beta$ be the roots of $x^2 - 3x + 9 = 0$. Then $\left(\frac{\beta^{30}}{(9\alpha)^{10}} + \frac{\alpha^{30}}{(9\beta)^{10}}\right)^2$ is equal to

If the system of equations
$Kx - \sqrt{2}y + \sqrt{5}z = \sqrt{7}$
$\sqrt{5}x + \sqrt{3}y - \sqrt{2}z = \sqrt{11}$
$30x + (3\sqrt{15} - 5\sqrt{6})y + (5\sqrt{15} - 3\sqrt{10})z = 5\sqrt{21} + 3\sqrt{55}$
has infinitely many solutions, then $\mathrm{K}^2$ is

For $z = 2 + 5i$, the modulus of $2z^3 + 21z^2 - 58z + 4$ is :

For $\alpha, \beta \in \mathbb{R}$, if the matrices $\mathrm{A} = \begin{pmatrix} \alpha & 0 \\ 0 & \beta \end{pmatrix}$, $\mathrm{B} = \begin{pmatrix} \alpha & 0 \\ 0 & \alpha \end{pmatrix}$ and $\mathrm{I} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$ satisfy the equation $(\mathrm{A} * \mathrm{B}) * 2\mathrm{I} = 20\mathrm{I}$, where $*$ is defined as $\mathrm{A} * \mathrm{B} = \mathrm{A}^2 + \mathrm{B}^2$, then $|\alpha\beta|$ is equal to :

Let $\mathrm{R}_1$ and $\mathrm{R}_2$ be two relations on $\mathbb{R}^2$ defined as
$(a, b)\ \mathrm{R}_1\ (c, d)$ if $ad - bc \geq 0$
$(a, b)\ \mathrm{R}_2\ (c, d)$ if $a + d \geq b + c$. Then :

Arrange the following compounds in increasing order of rate of aromatic electrophilic substitution reaction:

It is observed that characteristic $X$-ray spectra of elements show regularity When frequency to the power " $n$ " ie $v^n$ of $X$-rays emitted is plotted against atomic number " $Z$ ", following graph is obtained

The incorrect statement regarding the reaction given below is

Given below are two statements, one is labelled as Statement-1 and the other is labelled as Statement-2: Statement-1: Sulphides are converted into oxide first. Statement-2: Because oxides can be reduced easily. In the light of the above statements, choose the correct answer from the options given below

Match List I with List II

	List I-Examples		List II-Type
A	2-Chloro-1, 3-butadiene	I	Nylon 2-nylon 6
B	Nylon 2-nylon 6	II	Synthetic Rubber
C	Polyacrylonitrile	III	Polyester
D	Dacron	IV	Addition Polymer

Choose the correct answer from the options given below:

The octahedral diamagnetic low spin complex among the following is

A metal chloride contains 55.0% of chlorine by weight. 100 mL vapours of the metal chloride at STP weigh 0.57 g. The molecular formula of the metal chloride is (Given: Atomic mass of chlorine is 35.5u)

An $ \alpha $-particle, a proton, and an electron have the same kinetic energy. Which one of the following is correct in case of their De-Broglie wavelength:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R:
Assertion A: 3.1500 g of hydrated oxalic acid dissolved in water to make 250.0 mL solution will result in 0.1 M oxalic acid solution.
Reason R: Molar mass of hydrated oxalic acid is 126 g mol^–1.
In the light of the above statements, choose the correct answer from the options given below.

2-Methyl propyl bromide reacts with C₂H₅O^- and gives 'A' whereas on reaction with C₂H₅OH it gives 'B'. The mechanism followed in these reactions and the products 'A' and 'B' respectively are

Arrange the following gases in increasing order of van der Waals constant 'a'
A. Ar
B. CH4
C. H₂O
D. C6H6
Choose the correct option from the following.

The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion is

How many statements are correct:

If there is no relation between rate constant and temperature, then activation energy is negative.
If the activation energy is zero, rate constant is temperature independent.
If rate constant increases with increase of temperature, activation energy is positive.
If rate constant decreases with increase in temperature, activation energy is negative.

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): In expensive scientific instruments, silica gel is kept in watch-glasses or in semipermeable membrane bags.
Reason (R): Silica gel adsorbs moisture from air via adsorption, thus protects the instrument from water corrosion (rusting) and/or prevents malfunctioning.
In the light of the above statements, choose the correct answer from the options given below: