JEE Main 2024 (Online) 5th April Evening Shift

Consider the above reaction sequence and identify the major product P.

Which one of the following reactions is NOT possible?

In the Claisen-Schmidt reaction to prepare \(351 \mathrm{~g}\) of dibenzalacetone using \(87 \mathrm{~g}\) of acetone, the amount of benzaldehyde required is _________ g. (Nearest integer)

Consider the given chemical reaction :

Product "A" is :

The product C in the following sequence of reactions has ________ \(\pi\) bonds.

Identify A and B in the given chemical reaction sequence :

Match List - I with List - II.

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The correct nomenclature for the following compound is :

Using the given figure, the ratio of \(\mathrm{R}_f\) values of sample \(\mathrm{A}\) and sample \(\mathrm{C}\) is \(x \times 10^{-2}\). Value of \(x\) is __________.

Coagulation of egg, on heating is because of :

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) : \(\mathrm{NH}_3\) and \(\mathrm{NF}_3\) molecule have pyramidal shape with a lone pair of electrons on nitrogen atom....

Number of compounds from the following with zero dipole moment is _________.
$$\mathrm{HF}, \mathrm{H}_2, \mathrm{H}_2 \mathrm{~S}, \mathrm{CO}_2, \mathrm{NH}_3, \mathrm{BF}_3, \mathrm{CH}_4, \mathrm{CHCl}_3, \mathrm{SiF}_4, \mathrm{H}_2 \m...

Given below are two statements :
Statement I : On passing \(\mathrm{HCl}_{(\mathrm{g})}\) through a saturated solution of \(\mathrm{BaCl}_2\), at room temperature white turbidity appears.
Statement II : When \(\mathrm{HCl}\) gas is passed t...

Consider the following single step reaction in gas phase at constant temperature.
\(2 \mathrm{~A}_{(\mathrm{g})}+\mathrm{B}_{(\mathrm{g})} \rightarrow \mathrm{C}_{(\mathrm{g})}\)
The initial rate of the reaction is recorded as $$\mathrm{r}_...

\(\mathrm{X} \mathrm{~g}\) of ethanamine was subjected to reaction with \(\mathrm{NaNO}_2 / \mathrm{HCl}\) followed by hydrolysis to liberate \(\mathrm{N}_2\) and \(\mathrm{HCl}\). The \(\mathrm{HCl}\) generated was completely neutralised b...

The number of complexes from the following with no electrons in the \(t_2\) orbital is ______. $$\mathrm{TiCl}_4,\left[\mathrm{MnO}_4\right]^{-},\left[\mathrm{FeO}_4\right]^{2-},\left[\mathrm{FeCl}_4\right]^{-},\left[\mathrm{CoCl}_4\right]^...

The metal atom present in the complex MABXL (where A, B, X and L are unidentate ligands and \(\mathrm{M}\) is metal) involves \(\mathrm{sp}^3\) hybridization. The number of geometrical isomers exhibited by the complex is :

While preparing crystals of Mohr's salt, dil \(\mathrm{H}_2 \mathrm{SO}_4\) is added to a mixture of ferrous sulphate and ammonium sulphate, before dissolving this mixture in water, dil \(\mathrm{H_2SO_4}\) is added here to :

The number of ions from the following that have the ability to liberate hydrogen from a dilute acid is _________.
\(\mathrm{Ti}^{2+}, \mathrm{Cr}^{2+} \text { and } \mathrm{V}^{2+}\)

The fusion of chromite ore with sodium carbonate in the presence of air leads to the formation of products \(\mathrm{A}\) and \(\mathrm{B}\) along with the evolution of \(\mathrm{CO}_2\). The sum of spin-only magnetic moment values of A and...

The quantity of silver deposited when one coulomb charge is passed through \(\mathrm{AgNO}_3\) solution :

For the electro chemical cell
\(\mathrm{M}\left|\mathrm{M}^{2+}\right||\mathrm{X}| \mathrm{X}^{2-}\)
If \(\mathrm{E}_{\left(\mathrm{M}^{2+} / \mathrm{M}\right)}^0=0.46 \mathrm{~V}\) and $$\mathrm{E}_{\left(\mathrm{x} / \mathrm{x}^{2-}\right...

Identify the major product in the following reaction.

The correct statements from the following are :
(A) The decreasing order of atomic radii of group 13 elements is \(\mathrm{Tl}>\mathrm{In}>\mathrm{Ga}>\mathrm{Al}>\mathrm{B}\).
(B) Down the group 13 electronegativity decreases from top to b...

Given below are two statements :
Statement I : The metallic radius of \(\mathrm{Na}\) is \(1.86 \mathrm{~A}^{\circ}\) and the ionic radius of \(\mathrm{Na}^{+}\) is lesser than \(1.86 \mathrm{~A}^{\circ}\)
Statement II : Ions are always sma...

Considering acetic acid dissociates in water, its dissociation constant is \(6.25 \times 10^{-5}\). If \(5 \mathrm{~mL}\) of acetic acid is dissolved in 1 litre water, the solution will freeze at \(-x \times 10^{-2}{ }^{\circ} \mathrm{C}\),...

The number of moles of methane required to produce \(11 \mathrm{~g} \mathrm{~CO}_2(\mathrm{g})\) after complete combustion is : (Given molar mass of methane in \(\mathrm{g} \mathrm{~mol}^{-1}: 16\) )

In an atom, total number of electrons having quantum numbers \(\mathrm{n}=4,\left|\mathrm{~m}_l\right|=1\) and \(\mathrm{m}_{\mathrm{s}}=-\frac{1}{2}\) is _________.

Combustion of 1 mole of benzene is expressed at
\(\mathrm{C}_6 \mathrm{H}_6(\mathrm{l})+\frac{15}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow 6 \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \text {. }\)
The standard enthalpy...

Let \((\alpha, \beta, \gamma)\) be the image of the point \((8,5,7)\) in the line \(\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{5}\). Then \(\alpha+\beta+\gamma\) is equal to :

Let the point \((-1, \alpha, \beta)\) lie on the line of the shortest distance between the lines \(\frac{x+2}{-3}=\frac{y-2}{4}=\frac{z-5}{2}\) and \(\frac{x+2}{-1}=\frac{y+6}{2}=\frac{z-1}{0}\). Then \((\alpha-\beta)^2\) is equal to ______...

Let the maximum and minimum values of \(\left(\sqrt{8 x-x^2-12}-4\right)^2+(x-7)^2, x \in \mathbf{R}\) be \(\mathrm{M}\) and \(\mathrm{m}\), respectively. Then \(\mathrm{M}^2-\mathrm{m}^2\) is equal to _________.

The area enclosed between the curves \(y=x|x|\) and \(y=x-|x|\) is :

If the constant term in the expansion of \(\left(\frac{\sqrt[5]{3}}{x}+\frac{2 x}{\sqrt[3]{5}}\right)^{12}, x \neq 0\), is \(\alpha \times 2^8 \times \sqrt[5]{3}\), then \(25 \alpha\) is equal to :

Let the circle \(C_1: x^2+y^2-2(x+y)+1=0\) and \(\mathrm{C_2}\) be a circle having centre at \((-1,0)\) and radius 2 . If the line of the common chord of \(\mathrm{C}_1\) and \(\mathrm{C}_2\) intersects the \(\mathrm{y}\)-axis at the point ...

Let ABCD and AEFG be squares of side 4 and 2 units, respectively. The point E is on the line segment AB and the point F is on the diagonal AC. Then the radius r of the circle passing through the point F and touching the line segments BC and...

Let \(S_1=\{z \in \mathbf{C}:|z| \leq 5\}, S_2=\left\{z \in \mathbf{C}: \operatorname{Im}\left(\frac{z+1-\sqrt{3} i}{1-\sqrt{3} i}\right) \geq 0\right\}\) and \(S_3=\{z \in \mathbf{C}: \operatorname{Re}(z) \geq 0\}\). Then the area of the r...

Let \(\beta(\mathrm{m}, \mathrm{n})=\int_\limits0^1 x^{\mathrm{m}-1}(1-x)^{\mathrm{n}-1} \mathrm{~d} x, \mathrm{~m}, \mathrm{n}>0\). If $$\int_\limits0^1\left(1-x^{10}\right)^{20} \mathrm{~d} x=\mathrm{a} \times \beta(\mathrm{b}, \mathrm{c}...

If \(f(t)=\int_\limits0^\pi \frac{2 x \mathrm{~d} x}{1-\cos ^2 \mathrm{t} \sin ^2 x}, 0<\mathrm{t}<\pi\), then the value of \(\int_\limits0^{\frac{\pi}{2}} \frac{\pi^2 \mathrm{dt}}{f(\mathrm{t})}\) equals __________.

The differential equation of the family of circles passing through the origin and having centre at the line \(y=x\) is :

Let \(y=y(x)\) be the solution of the differential equation
\(\frac{\mathrm{d} y}{\mathrm{~d} x}+\frac{2 x}{\left(1+x^2\right)^2} y=x \mathrm{e}^{\frac{1}{\left(1+x^2\right)}} ; y(0)=0.\)
Then the area enclosed by the curve $$f(x)=y(x) \mat...

If \(y(\theta)=\frac{2 \cos \theta+\cos 2 \theta}{\cos 3 \theta+4 \cos 2 \theta+5 \cos \theta+2}\), then at \(\theta=\frac{\pi}{2}, y^{\prime \prime}+y^{\prime}+y\) is equal to :

Let \(f, g: \mathbf{R} \rightarrow \mathbf{R}\) be defined as :
$$f(x)=|x-1| \text { and } g(x)= \begin{cases}\mathrm{e}^x, & x \geq 0 \\ x+1, & x \leq 0 .\end{cases}$$
Then the function \(f(g(x))\) is

Let ,\(f:[-1,2] \rightarrow \mathbf{R}\) be given by \(f(x)=2 x^2+x+\left[x^2\right]-[x]\), where \([t]\) denotes the greatest integer less than or equal to \(t\). The number of points, where \(f\) is not continuous, is :

Let \(\mathrm{a}>0\) be a root of the equation \(2 x^2+x-2=0\). If \(\lim _\limits{x \rightarrow \frac{1}{a}} \frac{16\left(1-\cos \left(2+x-2 x^2\right)\right)}{(1-a x)^2}=\alpha+\beta \sqrt{17}\), where \(\alpha, \beta \in Z\), then $$\al...

The values of \(m, n\), for which the system of equations
$$\begin{aligned} & x+y+z=4, \\ & 2 x+5 y+5 z=17, \\ & x+2 y+\mathrm{m} z=\mathrm{n} \end{aligned}$$
has infinitely many solutions, satisfy the equation :

Let \(\alpha \beta \neq 0\) and $$A=\left[\begin{array}{rrr}\beta & \alpha & 3 \\ \alpha & \alpha & \beta \\ -\beta & \alpha & 2 \alpha\end{array}\right]$$. If $$B=\left[\begin{array}{rrr}3 \alpha & -9 & 3 \alpha \\ -\alpha & 7 & -2 \alpha ...

Let a line perpendicular to the line \(2 x-y=10\) touch the parabola \(y^2=4(x-9)\) at the point P. The distance of the point P from the centre of the circle \(x^2+y^2-14 x-8 y+56=0\) is __________.

Let the set \(S=\{2,4,8,16, \ldots, 512\}\) be partitioned into 3 sets \(A, B, C\) with equal number of elements such that \(\mathrm{A} \cup \mathrm{B} \cup \mathrm{C}=\mathrm{S}\) and $$\mathrm{A} \cap \mathrm{B}=\mathrm{B} \cap \mathrm{C}...