JEE Main 2024 (Online) 29th January Morning Shift

The major product(P) in the following reaction is

From the compounds given below, number of compounds which give positive Fehling's test is _________.
Benzaldehyde, Acetaldehyde, Acetone, Acetophenone, Methanal, 4nitrobenzaldehyde, cyclohexane carbaldehyde.

The interaction between \(\pi\) bond and lone pair of electrons present on an adjacent atom is responsible for

Type of amino acids obtained by hydrolysis of proteins is :

Number of compounds among the following which contain sulphur as heteroatom is ___________.
Furan, Thiophene, Pyridine, Pyrrole, Cysteine, Tyrosine

The difference in energy between the actual structure and the lowest energy resonance structure for the given compound is

The number of species from the following which are paramagnetic and with bond order equal to one is _________.
$$\mathrm{H}_2, \mathrm{He}_2^{+}, \mathrm{O}_2^{+}, \mathrm{N}_2^{2-}, \mathrm{O}_2^{2-}, \mathrm{F}_2, \mathrm{Ne}_2^{+}, \math...

Number of compounds with one lone pair of electrons on central atom amongst following is _________.
\(\mathrm{O}_3, \mathrm{H}_2 \mathrm{O}, \mathrm{SF}_4, \mathrm{ClF}_3, \mathrm{NH}_3, \mathrm{BrF}_5, \mathrm{XeF}_4\)

For the reaction \(\mathrm{N}_2 \mathrm{O}_{4(\mathrm{~g})} \rightleftarrows 2 \mathrm{NO}_{2(\mathrm{~g})}, \mathrm{K}_{\mathrm{p}}=0.492 \mathrm{~atm}\) at \(300 \mathrm{~K} . \mathrm{K}_{\mathrm{c}}\) for the reaction at same temperature...

For a reaction taking place in three steps at same temperature, overall rate constant \(\mathrm{K}=\frac{\mathrm{K}_1 \mathrm{~K}_2}{\mathrm{~K}_3}\). If \(\mathrm{Ea}_1, \mathrm{Ea}_2\) and \(\mathrm{Ea}_3\) are 40, 50 and $$60 \mathrm{~kJ...

the arenium ion which is not involved in the bromination of Aniline is __________.

Match List I with List II

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In which one of the following metal carbonyls, \(\mathrm{CO}\) forms a bridge between metal atoms?

\(\mathrm{KMnO}_4\) decomposes on heating at \(513 \mathrm{~K}\) to form \(\mathrm{O}_2\) along with

The mass of zinc produced by the electrolysis of zine sulphate solution with a steady current of \(0.015 \mathrm{~A}\) for 15 minutes is _________ \(\times 10^{-4} \mathrm{~g}\).
(Atomic mass of zinc \(=65.4 \mathrm{~amu}\))

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R :
Assertion A : Aryl halides cannot be prepared by replacement of hydroxyl group of phenol by halogen atom.
Reason R : Phenols react with ...

Identify product A and product B :

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

Consider the given reaction. The total number of oxygen atom/s present per molecule of the product \((\mathrm{P})\) is _________.

Identify the incorrect pair from the following :

Given below are two statements : one is labelled as Assertion \(\mathbf{A}\) and the other is labelled as Reason \(\mathbf{R}\) :
Assertion A : The first ionisation enthalpy decreases across a period.
Reason \(\mathbf{R}\) : The increasing ...

Given below are two statements :
Statement I : The electronegativity of group 14 elements from \(\mathrm{Si}\) to \(\mathrm{Pb}\), gradually decreases.
Statement II : Group 14 contains non-metallic, metallic, as well as metalloid elements.
...

In chromyl chloride test for confirmation of \(\mathrm{Cl}^{-}\) ion, a yellow solution is obtained. Acidification of the solution and addition of amyl alcohol and \(10 \% \mathrm{~H}_2 \mathrm{O}_2\) turns organic layer blue indicating for...

Appearance of blood red colour, on treatment of the sodium fusion extract of an organic compound with \(\mathrm{FeSO}_4\) in presence of concentrated \(\mathrm{H}_2 \mathrm{SO}_4\) indicates the presence of element/s

Chlorine undergoes disproportionation in alkaline medium as shown below :
$$\mathrm{aCl}_{2(\mathrm{~g})}+\mathrm{b} \mathrm{OH}_{(\mathrm{aq})}^{-} \rightarrow \mathrm{c} \mathrm{ClO}_{(\mathrm{aq)}}^{-}+\mathrm{d} \mathrm{Cl}_{(\mathrm{aq...

In alkaline medium, \(\mathrm{MnO}_4^{-}\) oxidises \(\mathrm{I}^{-}\) to

The osmotic pressure of a dilute solution is \(7 \times 10^5 \mathrm{~Pa}\) at \(273 \mathrm{~K}\). Osmotic pressure of the same solution at \(283 \mathrm{~K}\) is _________ \(\times 10^4 \mathrm{Nm}^{-2}\).

A solution of \(\mathrm{H}_2 \mathrm{SO}_4\) is \(31.4 \% \mathrm{H}_2 \mathrm{SO}_4\) by mass and has a density of \(1.25 \mathrm{~g} / \mathrm{mL}\). The molarity of the \(\mathrm{H}_2 \mathrm{SO}_4\) solution is _________ \(\mathrm{M}\) ...

The correct set of four quantum numbers for the valence electron of rubidium atom \((\mathrm{Z}=37)\) is :

Which of the following is not correct?

Let \(O\) be the origin and the position vectors of \(A\) and \(B\) be \(2 \hat{i}+2 \hat{j}+\hat{k}\) and \(2 \hat{i}+4 \hat{j}+4 \hat{k}\) respectively. If the internal bisector of \(\angle \mathrm{AOB}\) meets the line \(\mathrm{AB}\) at...

Let \(P Q R\) be a triangle with \(R(-1,4,2)\). Suppose \(M(2,1,2)\) is the mid point of \(\mathrm{PQ}\). The distance of the centroid of \(\triangle \mathrm{PQR}\) from the point of intersection of the lines $$\frac{x-2}{0}=\frac{y}{2}=\fr...

A line with direction ratios \(2,1,2\) meets the lines \(x=y+2=z\) and \(x+2=2 y=2 z\) respectively at the points \(\mathrm{P}\) and \(\mathrm{Q}\). If the length of the perpendicular from the point \((1,2,12)\) to the line \(\mathrm{PQ}\) ...

Consider the function \(f:\left[\frac{1}{2}, 1\right] \rightarrow \mathbb{R}\) defined by \(f(x)=4 \sqrt{2} x^3-3 \sqrt{2} x-1\). Consider the statements
(I) The curve \(y=f(x)\) intersects the \(x\)-axis exactly at one point.
(II) The curv...

Let \(f(x)=2^x-x^2, x \in \mathbb{R}\). If \(m\) and \(n\) are respectively the number of points at which the curves \(y=f(x)\) and \(y=f^{\prime}(x)\) intersect the \(x\)-axis, then the value of \(\mathrm{m}+\mathrm{n}\) is ___________.

The area (in sq. units) of the part of the circle \(x^2+y^2=169\) which is below the line \(5 x-y=13\) is \(\frac{\pi \alpha}{2 \beta}-\frac{65}{2}+\frac{\alpha}{\beta} \sin ^{-1}\left(\frac{12}{13}\right)\), where \(\alpha, \beta\) are cop...

If the points of intersection of two distinct conics \(x^2+y^2=4 b\) and \(\frac{x^2}{16}+\frac{y^2}{b^2}=1\) lie on the curve \(y^2=3 x^2\), then \(3 \sqrt{3}\) times the area of the rectangle formed by the intersection points is _________...

\(\text { If } \frac{{ }^{11} C_1}{2}+\frac{{ }^{11} C_2}{3}+\ldots+\frac{{ }^{11} C_9}{10}=\frac{n}{m} \text { with } \operatorname{gcd}(n, m)=1 \text {, then } n+m \text { is equal to }\) _______.

Equations of two diameters of a circle are \(2 x-3 y=5\) and \(3 x-4 y=7\). The line joining the points \(\left(-\frac{22}{7},-4\right)\) and \(\left(-\frac{1}{7}, 3\right)\) intersects the circle at only one point \(P(\alpha, \beta)\). The...

If \(z=\frac{1}{2}-2 i\) is such that \(|z+1|=\alpha z+\beta(1+i), i=\sqrt{-1}\) and \(\alpha, \beta \in \mathbb{R}\), then \(\alpha+\beta\) is equal to

Let \(\alpha, \beta\) be the roots of the equation \(x^2-x+2=0\) with \(\operatorname{Im}(\alpha)>\operatorname{Im}(\beta)\). Then \(\alpha^6+\alpha^4+\beta^4-5 \alpha^2\) is equal to ___________.

\(\mathop {\lim }\limits_{x \to {\pi \over 2}} \left( {{1 \over {{{\left( {x - {\pi \over 2}} \right)}^2}}}\int\limits_{{x^3}}^{{{\left( {{\pi \over 2}} \right)}^3}} {\cos \left( {{t^{{1 \over 3}}}} \right)dt} } \right)\) is equal to

If the value of the integral \(\int_\limits{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{x^2 \cos x}{1+\pi^x}+\frac{1+\sin ^2 x}{1+e^{\sin x^{2123}}}\right) d x=\frac{\pi}{4}(\pi+a)-2\), then the value of \(a\) is

A function \(y=f(x)\) satisfies \(f(x) \sin 2 x+\sin x-\left(1+\cos ^2 x\right) f^{\prime}(x)=0\) with condition \(f(0)=0\). Then, \(f\left(\frac{\pi}{2}\right)\) is equal to

If the solution curve \(y=y(x)\) of the differential equation \(\left(1+y^2\right)\left(1+\log _{\mathrm{e}} x\right) d x+x d y=0, x > 0\) passes through the point \((1,1)\) and $$y(e)=\frac{\alpha-\tan \left(\frac{3}{2}\right)}{\beta+\tan ...

Suppose \(f(x)=\frac{\left(2^x+2^{-x}\right) \tan x \sqrt{\tan ^{-1}\left(x^2-x+1\right)}}{\left(7 x^2+3 x+1\right)^3}\). Then the value of \(f^{\prime}(0)\) is equal to

If $$f(x)=\left\{\begin{array}{cc}2+2 x, & -1 \leq x < 0 \\ 1-\frac{x}{3}, & 0 \leq x \leq 3\end{array} ; g(x)=\left\{\begin{array}{cc}-x, & -3 \leq x \leq 0 \\ x, & 0 < x \leq 1\end{array}\right.\right.$$, then range of \((f o g)(x)\) is

For \(x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\), if \(y(x)=\int \frac{\operatorname{cosec} x+\sin x}{\operatorname{cosec} x \sec x+\tan x \sin ^2 x} d x\), and \(\lim _\limits{x \rightarrow\left(\frac{\pi}{2}\right)^{-}} y(x)=0\) th...

$$\text { Let } A=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha \end{array}\right] \text { and }|2 \mathrm{~A}|^3=2^{21} \text { where } \alpha, \beta \in Z \text {, Then a value of } \alpha \text { is }$$

Let \(\mathrm{A}\) be a square matrix such that \(\mathrm{AA}^{\mathrm{T}}=\mathrm{I}\). Then \(\frac{1}{2} A\left[\left(A+A^T\right)^2+\left(A-A^T\right)^2\right]\) is equal to