JEE Main 2024 (Online) 8th April Morning Shift

Identify the major products A and B respectively in the following set of reactions.

Identify the product (P) in the following reaction:

Which of the following are aromatic?

The number of optical isomers in following compound is : __________.

Given below are two statements :

In the light of the above statements, choose the most appropriate answer from the options given below:

The incorrect statement regarding the given structure is

Match List I with List II

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Number of molecules from the following which are exceptions to octet rule is _________.
$$\mathrm{CO}_2, \mathrm{NO}_2, \mathrm{H}_2 \mathrm{SO}_4, \mathrm{BF}_3, \mathrm{CH}_4, \mathrm{SiF}_4, \mathrm{ClO}_2, \mathrm{PCl}_5, \mathrm{BeF}_2...

For the given hypothetical reactions, the equilibrium constants are as follows :
$$\begin{aligned}
& \mathrm{X} \rightleftharpoons \mathrm{Y} ; \mathrm{K}_1=1.0 \\
& \mathrm{Y} \rightleftharpoons \mathrm{Z} ; \mathrm{K}_2=2.0 \\
& \mathrm{Z...

Consider the following reaction
\(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}\)
The time taken for A to become \(1 / 4^{\text {th }}\) of its initial concentration is twice the time taken to become \(1 / 2\) of the same. Also, when the cha...

If \(279 \mathrm{~g}\) of aniline is reacted with one equivalent of benzenediazonium chloride, the maximum amount of aniline yellow formed will be ________ g. (nearest integer)
(consider complete conversion).

Number of amine compounds from the following giving solids which are soluble in \(\mathrm{NaOH}\) upon reaction with Hinsberg's reagent is _________.

An octahedral complex with the formula \(\mathrm{CoCl}_3 \cdot \mathrm{nNH}_3\) upon reaction with excess of \(\mathrm{AgNO}_3\) solution gives 2 moles of \(\mathrm{AgCl}\). Consider the oxidation state of \(\mathrm{Co}\) in the complex is ...

Number of Complexes with even number of electrons in \(\mathrm{t_{2 g}}\) orbitals is -
$$\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+},\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+},\left[\mathrm{...

Match List I with List II

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...

Given below are two statements:
Statement I: \(\mathrm{N}\left(\mathrm{CH}_3\right)_3\) and \(\mathrm{P}\left(\mathrm{CH}_3\right)_3\) can act as ligands to form transition metal complexes.
Statement II: As N and P are from same group, the ...

The 'spin only' magnetic moment value of \(\mathrm{MO}_4{ }^{2-}\) is ________ BM. (Where M is a metal having least metallic radii. among \(\mathrm{Sc}, \mathrm{Ti}, \mathrm{V}, \mathrm{Cr}, \mathrm{Mn}\) and \(\mathrm{Zn}\) ).
(Given atomi...

Iron (III) catalyses the reaction between iodide and persulphate ions, in which
A. \(\mathrm{Fe}^{3+}\) oxidises the iodide ion
B. \(\mathrm{Fe}^{3+}\) oxidises the persulphate ion
C. \(\mathrm{Fe}^{2+}\) reduces the iodide ion
D. $$\mathrm...

Which among the following compounds will undergo fastest SN2 reaction.

In the given compound, the number of 2\(^\circ\) carbon atom/s is ________.

Major product B of the following reaction has ________ \(\pi\)-bond.

Give below are two statements: One is labelled as Assertion A and the other is labelled as Reason R:
Assertion A: The stability order of +1 oxidation state of \(\mathrm{Ga}\), In and \(\mathrm{Tl}\) is Ga < In < Tl.
Reason R: The inert pair...

Among the following halogens
\(\mathrm{F}_2, \mathrm{Cl}_2, \mathrm{Br}_2 \text { and } \mathrm{I}_2\)
Which can undergo disproportionation reactions?

Match List I with List II

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...

Thiosulphate reacts differently with iodine and bromine in the reactions given below:
$$\begin{aligned}
& 2 \mathrm{~S}_2 \mathrm{O}_3^{2-}+\mathrm{I}_2 \rightarrow \mathrm{S}_4 \mathrm{O}_6^{2-}+2 \mathrm{I}^{-} \\
& \mathrm{S}_2 \mathrm{O...

Match List I with List II

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A solution containing \(10 \mathrm{~g}\) of an electrolyte \(\mathrm{AB}_2\) in \(100 \mathrm{~g}\) of water boils at \(100.52^{\circ} \mathrm{C}\). The degree of ionization of the electrolyte \((\alpha)\) is _________ \(\times 10^{-1}\). (...

Combustion of glucose \((\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6)\) produces \(\mathrm{CO}_2\) and water. The amount of oxygen (in \(\mathrm{g}\)) required for the complete combustion of \(900 \mathrm{~g}\) of glucose is :
[Molar mass of ...

A hypothetical electromagnetic wave is show below.

The frequency of the wave is \(\mathrm{x} \times 10^{19} \mathrm{~Hz}\).
\(\mathrm{x}=\) _________ (nearest integer)

Consider the figure provided.
\(1 \mathrm{~mol}\) of an ideal gas is kept in a cylinder, fitted with a piston, at the position A, at \(18^{\circ} \mathrm{C}\). If the piston is moved to position \(\mathrm{B}\), keeping the temperature unch...

Let \(P(x, y, z)\) be a point in the first octant, whose projection in the \(x y\)-plane is the point \(Q\). Let \(O P=\gamma\); the angle between \(O Q\) and the positive \(x\)-axis be \(\theta\); and the angle between \(O P\) and the posi...

If the shortest distance between the lines
$$\begin{array}{ll}
L_1: \vec{r}=(2+\lambda) \hat{i}+(1-3 \lambda) \hat{j}+(3+4 \lambda) \hat{k}, & \lambda \in \mathbb{R} \\
L_2: \vec{r}=2(1+\mu) \hat{i}+3(1+\mu) \hat{j}+(5+\mu) \hat{k}, & \mu \...

The number of critical points of the function \(f(x)=(x-2)^{2 / 3}(2 x+1)\) is

Let \(f(x)=4 \cos ^3 x+3 \sqrt{3} \cos ^2 x-10\). The number of points of local maxima of \(f\) in interval \((0,2 \pi)\) is

For the function \(f(x)=(\cos x)-x+1, x \in \mathbb{R}\), between the following two statements
(S1) \(f(x)=0\) for only one value of \(x\) in \([0, \pi]\).
(S2) \(f(x)\) is decreasing in \(\left[0, \frac{\pi}{2}\right]\) and increasing in $...

Let the area of the region enclosed by the curve \(y=\min \{\sin x, \cos x\}\) and the \(x\) axis between \(x=-\pi\) to \(x=\pi\) be \(A\). Then \(A^2\) is equal to __________.

Let the circles \(C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2\) and \(C_2:(x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2\) touch each other externally at the point \((6,6)\). If the point \((6,6)\) divides the line segment joining the centres of the ci...

Let \(z\) be a complex number such that \(|z+2|=1\) and \(\operatorname{lm}\left(\frac{z+1}{z+2}\right)=\frac{1}{5}\). Then the value of \(|\operatorname{Re}(\overline{z+2})|\) is

If the set \(R=\{(a, b): a+5 b=42, a, b \in \mathbb{N}\}\) has \(m\) elements and \(\sum_\limits{n=1}^m\left(1-i^{n !}\right)=x+i y\), where \(i=\sqrt{-1}\), then the value of \(m+x+y\) is

The value of \(k \in \mathbb{N}\) for which the integral \(I_n=\int_0^1\left(1-x^k\right)^n d x, n \in \mathbb{N}\), satisfies \(147 I_{20}=148 I_{21}\) is

Let \(f(x)\) be a positive function such that the area bounded by \(y=f(x), y=0\) from \(x=0\) to \(x=a>0\) is \(e^{-a}+4 a^2+a-1\). Then the differential equation, whose general solution is \(y=c_1 f(x)+c_2\), where \(c_1\) and \(c_2\) are...

Let \(y=y(x)\) be the solution of the differential equation \((1+y^2) e^{\tan x} d x+\cos ^2 x(1+e^{2 \tan x}) d y=0, y(0)=1\). Then \(y\left(\frac{\pi}{4}\right)\) is equal to

If the range of \(f(\theta)=\frac{\sin ^4 \theta+3 \cos ^2 \theta}{\sin ^4 \theta+\cos ^2 \theta}, \theta \in \mathbb{R}\) is \([\alpha, \beta]\), then the sum of the infinite G.P., whose first term is 64 and the common ratio is $$\frac{\al...

Let \(H: \frac{-x^2}{a^2}+\frac{y^2}{b^2}=1\) be the hyperbola, whose eccentricity is \(\sqrt{3}\) and the length of the latus rectum is \(4 \sqrt{3}\). Suppose the point \((\alpha, 6), \alpha>0\) lies on \(H\). If \(\beta\) is the product ...

Let \(I(x)=\int \frac{6}{\sin ^2 x(1-\cot x)^2} d x\). If \(I(0)=3\), then \(I\left(\frac{\pi}{12}\right)\) is equal to

The value of \(\lim _\limits{x \rightarrow 0} 2\left(\frac{1-\cos x \sqrt{\cos 2 x} \sqrt[3]{\cos 3 x} \ldots \ldots . \sqrt[10]{\cos 10 x}}{x^2}\right)\) is __________.

Let $$A=\left[\begin{array}{lll}2 & a & 0 \\ 1 & 3 & 1 \\ 0 & 5 & b\end{array}\right]$$. If \(A^3=4 A^2-A-21 I\), where \(I\) is the identity matrix of order \(3 \times 3\), then \(2 a+3 b\) is equal to

Let $$A=\left[\begin{array}{cc}2 & -1 \\ 1 & 1\end{array}\right]$$. If the sum of the diagonal elements of \(A^{13}\) is \(3^n\), then \(n\) is equal to ________.

Let \([t]\) be the greatest integer less than or equal to \(t\). Let \(A\) be the set of all prime factors of 2310 and \(f: A \rightarrow \mathbb{Z}\) be the function \(f(x)=\left[\log _2\left(x^2+\left[\frac{x^3}{5}\right]\right)\right]\)....

The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3 , is equal to ________.