JEE Main 2024 (Online) 9th April Morning Shift

Identify major product "X" formed in the following reaction :

What is the structure of C?

Methods used for purification of organic compounds are based on :

Correct order of basic strength of Pyrrole , Pyridine and Piperidine is :

How many compounds among the following compounds show inductive, mesomeric as well as hyperconjugation effects?

For the given compounds, the correct order of increasing \(\mathrm{pK}_{\mathrm{a}}\) value :

Choose the correct answer from the options given below :

Relative stability of the contributing structures is :

The \(\mathrm{F}^{-}\) ions make the enamel on teeth much harder by converting hydroxyapatite (the enamel on the surface of teeth) into much harder fluoroapatite having the formula.

Total number of essential amino acid among the given list of amino acids is ________.
Arginine, Phenylalanine, Aspartic acid, Cysteine, Histidine, Valine, Proline

In which one of the following pairs the central atoms exhibit \(\mathrm{sp}^2\) hybridization ?

The total number of species from the following in which one unpaired electron is present, is _______.
$$\mathrm{N}_2, \mathrm{O}_2, \mathrm{C}_2^{-}, \mathrm{O}_2^{-}, \mathrm{O}_2^{2-}, \mathrm{H}_2^{+}, \mathrm{CN}^{-}, \mathrm{He}_2^{+}$...

Given below are two statements :
Statement I : The rate law for the reaction \(A+B \rightarrow C\) is rate \((r)=k[A]^2[B]\). When the concentration of both \(\mathrm{A}\) and \(\mathrm{B}\) is doubled, the reaction rate is increased "\(x\)...

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The total number of geometrical isomers shown by \([\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2]^{+}\) complex ion is thr...

Number of ambidentate ligands among the following is _________.
\(\mathrm{NO}_2^{-}, \mathrm{SCN}^{-}, \mathrm{C}_2 \mathrm{O}_4^{2-}, \mathrm{NH}_3, \mathrm{CN}^{-}, \mathrm{SO}_4^{2-}, \mathrm{H}_2 \mathrm{O} \text {. }\)

Number of colourless lanthanoid ions among the following is __________. \(\mathrm{Eu}^{3+}, \mathrm{Lu}^{3+}, \mathrm{Nd}^{3+}, \mathrm{La}^{3+}, \mathrm{Sm}^{3+}\)

The electronic configuration of \(\mathrm{Cu}(\mathrm{II})\) is \(3 \mathrm{~d}^9\) whereas that of \(\mathrm{Cu}(\mathrm{I})\) is \(3 \mathrm{~d}^{10}\). Which of the following is correct?

The standard reduction potentials at \(298 \mathrm{~K}\) for the following half cells are given below :
$$\mathrm{Cr}_2 \mathrm{O}_7^{2-}+14 \mathrm{H}^{+}+6 \mathrm{e}^{-} \rightarrow 2 \mathrm{Cr}^{3+}+7 \mathrm{H}_2 \mathrm{O}, \quad \ma...

The molar conductivity for electrolytes \(A\) and \(B\) are plotted against \(C^{3 / 2}\) as shown below. Electrolytes \(A\) and \(B\) respectively are:

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : \(\mathrm{S}_{\mathrm{N}} 2\) reaction of \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathrm{Br}\) occurs more readily...

In the following sequence of reaction, the major products B and C respectively are :

Identify the product A and product B in the following set of reactions.

On reaction of Lead Sulphide with dilute nitric acid which of the following is not formed?

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Both rhombic and monoclinic sulphur exist as \(\mathrm{S}_8\) while oxygen exists as \(\mathrm{O}_2\).
Reason (R) : O...

Given below are two statements :
Statement (I) : The oxidation state of an element in a particular compound is the charge acquired by its atom on the basis of electron gain enthalpy consideration from other atoms in the molecule.
Statement ...

Identify the incorrect statements regarding primary standard of titrimetric analysis.
(A) It should be purely available in dry form.
(B) It should not undergo chemical change in air.
(C) It should be hygroscopic and should react with anothe...

\(0.05 \mathrm{M} \mathrm{~CuSO}_4\) when treated with \(0.01 \mathrm{M} \mathrm{~K}_2 \mathrm{Cr}_2 \mathrm{O}_7\) gives green colour solution of \(\mathrm{Cu}_2 \mathrm{Cr}_2 \mathrm{O}_7\). The two solutions are separated as shown below ...

Molarity \((\mathrm{M})\) of an aqueous solution containing \(x \mathrm{~g}\) of anhyd. \(\mathrm{CuSO}_4\) in \(500 \mathrm{~mL}\) solution at \(32^{\circ} \mathrm{C}\) is \(2 \times 10^{-1} \mathrm{M}\). Its molality will be _________ $$...

Compare the energies of following sets of quantum numbers for multielectron system.
(A) \(\mathrm{n}=4,1=1\)
(B) \(\mathrm{n}=4,1=2\)
(C) \(\mathrm{n}=3, \mathrm{l}=1\)
(D) \(\mathrm{n}=3,1=2\)
(E) \(\mathrm{n}=4,1=0\)
Choose the correct an...

The heat of solution of anhydrous \(\mathrm{CuSO}_4\) and \(\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}\) are \(-70 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(+12 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively.
The heat of hydration of $$\...

When equal volume of \(1 \mathrm{~M} \mathrm{~HCl}\) and \(1 \mathrm{~M} \mathrm{~H}_2 \mathrm{SO}_4\) are separately neutralised by excess volume of \(1 \mathrm{M}\) \(\mathrm{NaOH}\) solution. \(x\) and \(y \mathrm{~kJ}\) of heat is liber...

Let the line \(\mathrm{L}\) intersect the lines \(x-2=-y=z-1,2(x+1)=2(y-1)=z+1\) and be parallel to the line \(\frac{x-2}{3}=\frac{y-1}{1}=\frac{z-2}{2}\). Then which of the following points lies on \(\mathrm{L}\) ?

The shortest distance between the lines \(\frac{x-3}{4}=\frac{y+7}{-11}=\frac{z-1}{5}\) and \(\frac{x-5}{3}=\frac{y-9}{-6}=\frac{z+2}{1}\) is:

Let the set of all positive values of \(\lambda\), for which the point of local minimum of the function \((1+x(\lambda^2-x^2))\) satisfies \(\frac{x^2+x+2}{x^2+5 x+6}<0\), be \((\alpha, \beta)\). Then \(\alpha^2+\beta^2\) is equal to ______...

The parabola \(y^2=4 x\) divides the area of the circle \(x^2+y^2=5\) in two parts. The area of the smaller part is equal to :

The coefficient of \(x^{70}\) in \(x^2(1+x)^{98}+x^3(1+x)^{97}+x^4(1+x)^{96}+\ldots+x^{54}(1+x)^{46}\) is \({ }^{99} \mathrm{C}_{\mathrm{p}}-{ }^{46} \mathrm{C}_{\mathrm{q}}\). Then a possible value of \(\mathrm{p}+\mathrm{q}\) is :

The remainder when \(428^{2024}\) is divided by 21 is __________.

Let a circle passing through \((2,0)\) have its centre at the point \((\mathrm{h}, \mathrm{k})\). Let \((x_{\mathrm{c}}, y_{\mathrm{c}})\) be the point of intersection of the lines \(3 x+5 y=1\) and \((2+\mathrm{c}) x+5 \mathrm{c}^2 y=1\). ...

Let the centre of a circle, passing through the points \((0,0),(1,0)\) and touching the circle \(x^2+y^2=9\), be \((h, k)\). Then for all possible values of the coordinates of the centre \((h, k), 4\left(h^2+k^2\right)\) is equal to _______...

The sum of the square of the modulus of the elements in the set \(\{z=\mathrm{a}+\mathrm{ib}: \mathrm{a}, \mathrm{b} \in \mathbf{Z}, z \in \mathbf{C},|z-1| \leq 1,|z-5| \leq|z-5 \mathrm{i}|\}\) is __________.

Let \(\lim _\limits{n \rightarrow \infty}\left(\frac{n}{\sqrt{n^4+1}}-\frac{2 n}{\left(n^2+1\right) \sqrt{n^4+1}}+\frac{n}{\sqrt{n^4+16}}-\frac{8 n}{\left(n^2+4\right) \sqrt{n^4+16}}\right.\) $$\left.+\ldots+\frac{n}{\sqrt{n^4+n^4}}-\frac{2...

The solution of the differential equation \((x^2+y^2) \mathrm{d} x-5 x y \mathrm{~d} y=0, y(1)=0\), is :

The solution curve, of the differential equation \(2 y \frac{\mathrm{d} y}{\mathrm{~d} x}+3=5 \frac{\mathrm{d} y}{\mathrm{~d} x}\), passing through the point \((0,1)\) is a conic, whose vertex lies on the line :

Let \(f(x)=a x^3+b x^2+c x+41\) be such that \(f(1)=40, f^{\prime}(1)=2\) and \(f^{\prime \prime}(1)=4\). Then \(a^2+b^2+c^2\) is equal to:

Let \(f(x)=x^2+9, g(x)=\frac{x}{x-9}\) and \(\mathrm{a}=f \circ g(10), \mathrm{b}=g \circ f(3)\). If \(\mathrm{e}\) and \(l\) denote the eccentricity and the length of the latus rectum of the ellipse $$\frac{x^2}{\mathrm{a}}+\frac{y^2}{\mat...

If the domain of the function \(f(x)=\sin ^{-1}\left(\frac{x-1}{2 x+3}\right)\) is \(\mathbf{R}-(\alpha, \beta)\), then \(12 \alpha \beta\) is equal to :

If a function \(f\) satisfies \(f(\mathrm{~m}+\mathrm{n})=f(\mathrm{~m})+f(\mathrm{n})\) for all \(\mathrm{m}, \mathrm{n} \in \mathbf{N}\) and \(f(1)=1\), then the largest natural number \(\lambda\) such that $$\sum_\limits{\mathrm{k}=1}^{2...

Let \(\int \frac{2-\tan x}{3+\tan x} \mathrm{~d} x=\frac{1}{2}\left(\alpha x+\log _e|\beta \sin x+\gamma \cos x|\right)+C\), where \(C\) is the constant of integration. Then \(\alpha+\frac{\gamma}{\beta}\) is equal to :

Let \(f:(0, \pi) \rightarrow \mathbf{R}\) be a function given by $$f(x)=\left\{\begin{array}{cc}\left(\frac{8}{7}\right)^{\frac{\tan 8 x}{\tan 7 x}}, & 0< x<\frac{\pi}{2} \\ \mathrm{a}-8, & x=\frac{\pi}{2} \\ (1+\mid \cot x)^{\frac{\mathrm{...

Let \(\lambda, \mu \in \mathbf{R}\). If the system of equations
$$\begin{aligned} & 3 x+5 y+\lambda z=3 \\ & 7 x+11 y-9 z=2 \\ & 97 x+155 y-189 z=\mu \end{aligned}$$
has infinitely many solutions, then \(\mu+2 \lambda\) is equal to :

Let \(A\) be a non-singular matrix of order 3. If \(\operatorname{det}(3 \operatorname{adj}(2 \operatorname{adj}((\operatorname{det} A) A)))=3^{-13} \cdot 2^{-10}\) and $$\operatorname{det}(3\operatorname{adj}(2 \mathrm{A}))=2^{\mathrm{m}} ...