JEE Main 2024 (Online) 30th January Morning Shift

This reduction reaction is known as:

Structure of 4-Methylpent-2-enal is :

Which of the following molecule/species is most stable?

Sugar which does not give reddish brown precipitate with Fehling's reagent, is :

Aluminium chloride in acidified aqueous solution forms an ion having geometry

Match List I with List II.

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : There is a considerable increase in covalent radius from \(\mathrm{N}\) to \(\mathrm{P}\). However from As to Bi only...

The total number of molecular orbitals formed from \(2 \mathrm{s}\) and \(2 \mathrm{p}\) atomic orbitals of a diatomic molecule is __________.

The rate of First order reaction is \(0.04 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\) at 10 minutes and \(0.03 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\) at 20 minutes after initiation. Half life of the reaction is _______ min...

Following is a confirmatory test for aromatic primary amines. Identify reagent (A) and (B).

The compound formed by the reaction of ethanal with semicarbazide contains _________ number of nitrogen atoms.

Choose the correct statements from the following :
(A) Ethane-1, 2-diamine is a chelating ligand.
(B) Metallic aluminium is produced by electrolysis of aluminium oxide in presence of cryolite.
(C) Cyanide ion is used as ligand for leaching ...

Diamagnetic Lanthanoid ions are :

Example of vinylic halide is :

The final product A, formed in the following multistep reaction sequence is :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : \(\mathrm{CH}_2=\mathrm{CH}-\mathrm{CH}_2-\mathrm{Cl}\) is an example of allyl halide.
Reason (R) : Allyl halides are...

Compound A formed in the following reaction reacts with B gives the product C. Find out A and B.

In the given reactions, identify the reagent A and reagent B.

The \(\mathrm{pH}\) at which \(\mathrm{Mg}(\mathrm{OH})_2\left[\mathrm{~K}_{\mathrm{sp}}=1 \times 10^{-11}\right]\) begins to precipitate from a solution containing \(0.10 \mathrm{~M} \mathrm{~Mg}^{2+}\) ions is __________.

The Lassiagne's extract is boiled with dil \(\mathrm{HNO}_3\) before testing for halogens because,

Match List I with List II.

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If IUPAC name of an element is "Unununnium" then the element belongs to nth group of Periodic table. The value of n is ________.

On a thin layer chromatographic plate, an organic compound moved by \(3.5 \mathrm{~cm}\), while the solvent moved by \(5 \mathrm{~cm}\). The retardation factor of the organic compound is ________ \(\times 10^{-1}\).

\(2 \mathrm{MnO}_4^{-}+\mathrm{bI}^{-}+\mathrm{cH}_2 \mathrm{O} \rightarrow x \mathrm{I}_2+y \mathrm{MnO}_2+z \overline{\mathrm{O}} \mathrm{H}\)
If the above equation is balanced with integer coefficients, the value of \(z\) is ________.

Given below are two statements :
Statement (I) : The gas liberated on warming a salt with dil \(\mathrm{H}_2 \mathrm{SO}_4\), turns a piece of paper dipped in lead acetate into black, it is a confirmatory test for sulphide ion.
Statement (I...

What happens to freezing point of benzene when small quantity of napthalene is added to benzene?

The mass of sodium acetate \(\left(\mathrm{CH}_3 \mathrm{COONa}\right)\) required to prepare \(250 \mathrm{~mL}\) of \(0.35 \mathrm{~M}\) aqueous solution is ________ g. (Molar mass of \(\mathrm{CH}_3 \mathrm{COONa}\) is $$82.02 \mathrm{~g}...

\(0.05 \mathrm{~cm}\) thick coating of silver is deposited on a plate of \(0.05 \mathrm{~m}^2\) area. The number of silver atoms deposited on plate are ________ \(\times 10^{23}\). (At mass $$\mathrm{Ag}=108, \mathrm{~d}=7.9 \mathrm{~g} \ma...

Given below are two statements :
Statement (I) : The orbitals having same energy are called as degenerate orbitals.
Statement (II) : In hydrogen atom, 3p and 3d orbitals are not degenerate orbitals.
In the light of the above statements, cho...

An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path \(\mathrm{A} \rightarrow \mathrm{B} \rightarrow \mathrm{C} \rightarrow \mathrm{A}\) as shown in the diagram abov...

Let \((\alpha, \beta, \gamma)\) be the foot of perpendicular from the point \((1,2,3)\) on the line \(\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}\). Then \(19(\alpha+\beta+\gamma)\) is equal to :

Let \(A(2,3,5)\) and \(C(-3,4,-2)\) be opposite vertices of a parallelogram \(A B C D\). If the diagonal \(\overrightarrow{\mathrm{BD}}=\hat{i}+2 \hat{j}+3 \hat{k}\), then the area of the parallelogram is equal to :

If \(\mathrm{d}_1\) is the shortest distance between the lines \(x+1=2 y=-12 z, x=y+2=6 z-6\) and \(\mathrm{d}_2\) is the shortest distance between the lines $$\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5}, \frac{x-1}{2}=\frac{y-2}{1}=\frac{z-...

The maximum area of a triangle whose one vertex is at \((0,0)\) and the other two vertices lie on the curve \(y=-2 x^2+54\) at points \((x, y)\) and \((-x, y)\), where \(y>0\), is :

The area (in square units) of the region bounded by the parabola \(y^2=4(x-2)\) and the line \(y=2 x-8\), is :

\(\text { Number of integral terms in the expansion of }\left\{7^{\left(\frac{1}{2}\right)}+11^{\left(\frac{1}{6}\right)}\right\}^{824} \text { is equal to _________. }\)

If the circles \((x+1)^2+(y+2)^2=r^2\) and \(x^2+y^2-4 x-4 y+4=0\) intersect at exactly two distinct points, then

If \(z=x+i y, x y \neq 0\), satisfies the equation \(z^2+i \bar{z}=0\), then \(\left|z^2\right|\) is equal to :

The value of \(\lim _\limits{n \rightarrow \infty} \sum_\limits{k=1}^n \frac{n^3}{\left(n^2+k^2\right)\left(n^2+3 k^2\right)}\) is :

Let \(f:\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \rightarrow \mathbf{R}\) be a differentiable function such that \(f(0)=\frac{1}{2}\). If the $$\lim _\limits{x \rightarrow 0} \frac{x \int_0^x f(\mathrm{t}) \mathrm{dt}}{\mathrm{e}^{x^2}-1}...

The value of \(9 \int_\limits0^9\left[\sqrt{\frac{10 x}{x+1}}\right] \mathrm{d} x\), where \([t]\) denotes the greatest integer less than or equal to \(t\), is

Let \(y=y(x)\) be the solution of the differential equation \(\sec x \mathrm{~d} y+\{2(1-x) \tan x+x(2-x)\} \mathrm{d} x=0\) such that \(y(0)=2\). Then \(y(2)\) is equal to:

Let \(y=y(x)\) be the solution of the differential equation \(\left(1-x^2\right) \mathrm{d} y=\left[x y+\left(x^3+2\right) \sqrt{3\left(1-x^2\right)}\right] \mathrm{d} x, -1< x<1, y(0)=0\). If $$y\left(\frac{1}{2}\right)=\frac{\mathrm{m}}{\...

Let \(g: \mathbf{R} \rightarrow \mathbf{R}\) be a non constant twice differentiable function such that \(\mathrm{g}^{\prime}\left(\frac{1}{2}\right)=\mathrm{g}^{\prime}\left(\frac{3}{2}\right)\). If a real valued function \(f\) is defined a...

If $$f(x)=\left|\begin{array}{ccc} 2 \cos ^4 x & 2 \sin ^4 x & 3+\sin ^2 2 x \\ 3+2 \cos ^4 x & 2 \sin ^4 x & \sin ^2 2 x \\ 2 \cos ^4 x & 3+2 \sin ^4 x & \sin ^2 2 x \end{array}\right|,$$ then \(\frac{1}{5} f^{\prime}(0)=\) is equal to :

If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is :

If the domain of the function \(f(x)=\cos ^{-1}\left(\frac{2-|x|}{4}\right)+\left\{\log _e(3-x)\right\}^{-1}\) is \([-\alpha, \beta)-\{\gamma\}\), then \(\alpha+\beta+\gamma\) is equal to :

Let \(\mathrm{A}=\{1,2,3, \ldots, 7\}\) and let \(\mathrm{P}(\mathrm{A})\) denote the power set of \(\mathrm{A}\). If the number of functions \(f: \mathrm{A} \rightarrow \mathrm{P}(\mathrm{A})\) such that $$\mathrm{a} \in f(\mathrm{a}), \fo...

Let the latus rectum of the hyperbola \(\frac{x^2}{9}-\frac{y^2}{b^2}=1\) subtend an angle of \(\frac{\pi}{3}\) at the centre of the hyperbola. If \(\mathrm{b}^2\) is equal to \(\frac{l}{\mathrm{~m}}(1+\sqrt{\mathrm{n}})\), where \(l\) and ...

If the function
$$f(x)= \begin{cases}\frac{1}{|x|}, & |x| \geqslant 2 \\ \mathrm{a} x^2+2 \mathrm{~b}, & |x|<2\end{cases}$$
is differentiable on \(\mathbf{R}\), then \(48(a+b)\) is equal to __________.