JEE Main 2024 (Online) 29th January Morning Shift

Paper was held on
Mon, Jan 29, 2024 3:30 AM

## Chemistry

Identify the incorrect pair from the following :

View Question Given below are two statements : one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\math

View Question The major product(P) in the following reaction is

View Question Identify product A and product B :

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

View Question Given below are two statements :
Statement I : The electronegativity of group 14 elements from $$\mathrm{Si}$$ to $$\mat

View Question Chlorine undergoes disproportionation in alkaline medium as shown below :
$$\mathrm{aCl}_{2(\mathrm{~g})}+\mathrm{b} \ma

View Question In chromyl chloride test for confirmation of $$\mathrm{Cl}^{-}$$ ion, a yellow solution is obtained. Acidification of th

View Question Type of amino acids obtained by hydrolysis of proteins is :

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

View Question The difference in energy between the actual structure and the lowest energy resonance structure for the given compound i

View Question Match List I with List II
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View Question The final product A formed in the following multistep reaction sequence is

View Question Which of the following is not correct?

View Question The interaction between $$\pi$$ bond and lone pair of electrons present on an adjacent atom is responsible for

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

View Question $$\mathrm{KMnO}_4$$ decomposes on heating at $$513 \mathrm{~K}$$ to form $$\mathrm{O}_2$$ along with

View Question Appearance of blood red colour, on treatment of the sodium fusion extract of an organic compound with $$\mathrm{FeSO}_4$

View Question Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R :
Assertion A : Ar

View Question In alkaline medium, $$\mathrm{MnO}_4^{-}$$ oxidises $$\mathrm{I}^{-}$$ to

View Question The mass of zinc produced by the electrolysis of zine sulphate solution with a steady current of $$0.015 \mathrm{~A}$$ f

View Question 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.

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

View Question For the reaction $$\mathrm{N}_2 \mathrm{O}_{4(\mathrm{~g})} \rightleftarrows 2 \mathrm{NO}_{2(\mathrm{~g})}, \mathrm{K}_

View Question The number of species from the following which are paramagnetic and with bond order equal to one is _________.
$$\mathrm

View Question For a reaction taking place in three steps at same temperature, overall rate constant $$\mathrm{K}=\frac{\mathrm{K}_1 \m

View Question From the compounds given below, number of compounds which give positive Fehling's test is _________.
Benzaldehyde, Aceta

View Question Number of compounds with one lone pair of electrons on central atom amongst following is _________.
$$\mathrm{O}_3, \mat

View Question Number of compounds among the following which contain sulphur as heteroatom is ___________.
Furan, Thiophene, Pyridine,

View Question The osmotic pressure of a dilute solution is $$7 \times 10^5 \mathrm{~Pa}$$ at $$273 \mathrm{~K}$$. Osmotic pressure of

View Question ## Mathematics

Suppose $$f(x)=\frac{\left(2^x+2^{-x}\right) \tan x \sqrt{\tan ^{-1}\left(x^2-x+1\right)}}{\left(7 x^2+3 x+1\right)^3}$$

View Question Let $$\vec{a}, \vec{b}$$ and $$\vec{c}$$ be three non-zero vectors such that $$\vec{b}$$ and $$\vec{c}$$ are non-colline

View Question Let $$\left(5, \frac{a}{4}\right)$$ be the circumcenter of a triangle with vertices $$\mathrm{A}(a,-2), \mathrm{B}(a, 6)

View Question If $$\alpha,-\frac{\pi}{2}

View Question If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio

View Question A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is

View Question In an A.P., the sixth term $$a_6=2$$. If the product $$a_1 a_4 a_5$$ is the greatest, then the common difference of the

View Question $$\text { Let } A=\left[\begin{array}{lll}
1 & 0 & 0 \\
0 & \alpha & \beta \\
0 & \beta & \alpha
\end{array}\right] \tex

View Question Let $$R$$ be a relation on $$Z \times Z$$ defined by $$(a, b) R(c, d)$$ if and only if $$a d-b c$$ is divisible by 5. Th

View Question If $$f(x)=\left\{\begin{array}{cc}2+2 x, & -1 \leq x

View Question 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

View Question In a $$\triangle A B C$$, suppose $$y=x$$ is the equation of the bisector of the angle $$B$$ and the equation of the sid

View Question For $$x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$, if $$y(x)=\int \frac{\operatorname{cosec} x+\sin x}{\operatorna

View Question Let $$\mathrm{A}$$ be a square matrix such that $$\mathrm{AA}^{\mathrm{T}}=\mathrm{I}$$. Then $$\frac{1}{2} A\left[\left

View Question If $$z=\frac{1}{2}-2 i$$ is such that $$|z+1|=\alpha z+\beta(1+i), i=\sqrt{-1}$$ and $$\alpha, \beta \in \mathbb{R}$$, t

View Question Consider the function $$f:\left[\frac{1}{2}, 1\right] \rightarrow \mathbb{R}$$ defined by $$f(x)=4 \sqrt{2} x^3-3 \sqrt{

View Question 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 o

View Question $$\mathop {\lim }\limits_{x \to {\pi \over 2}} \left( {{1 \over {{{\left( {x - {\pi \over 2}} \right)}^2}}}\int\limits

View Question 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)=

View Question 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

View Question 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 \a

View Question If the mean and variance of the data $$65,68,58,44,48,45,60, \alpha, \beta, 60$$ where $$\alpha> \beta$$, are 56 and 66.

View Question 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{2

View Question 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 $$\mat

View Question $$\text { If } \frac{{ }^{11} C_1}{2}+\frac{{ }^{11} C_2}{3}+\ldots+\frac{{ }^{11} C_9}{10}=\frac{n}{m} \text { with } \

View Question 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

View Question All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are writt

View Question Let $$\alpha, \beta$$ be the roots of the equation $$x^2-x+2=0$$ with $$\operatorname{Im}(\alpha)>\operatorname{Im}(\bet

View Question 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

View Question If the solution curve $$y=y(x)$$ of the differential equation $$\left(1+y^2\right)\left(1+\log _{\mathrm{e}} x\right) d

View Question ## Physics

The resistance $$R=\frac{V}{I}$$ where $$\mathrm{V}=(200 \pm 5) \mathrm{V}$$ and $$I=(20 \pm 0.2) \mathrm{A}$$, the perc

View Question The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is $$25 \%$$ of the ve

View Question A convex mirror of radius of curvature $$30 \mathrm{~cm}$$ forms an image that is half the size of the object. The objec

View Question The deflection in moving coil galvanometer falls from 25 divisions to 5 division when a shunt of $$24 \Omega$$ is applie

View Question A capacitor of capacitance $$100 \mu \mathrm{F}$$ is charged to a potential of $$12 \mathrm{~V}$$ and connected to a $$6

View Question At what distance above and below the surface of the earth a body will have same weight. (take radius of earth as $$R$$.)

View Question A galvanometer having coil resistance $$10 \Omega$$ shows a full scale deflection for a current of $$3 \mathrm{~mA}$$. F

View Question A thermodynamic system is taken from an original state $$\mathrm{A}$$ to an intermediate state $$B$$ by a linear process

View Question Two charges of $$5 Q$$ and $$-2 Q$$ are situated at the points $$(3 a, 0)$$ and $$(-5 a, 0)$$ respectively. The electric

View Question A biconvex lens of refractive index 1.5 has a focal length of $$20 \mathrm{~cm}$$ in air. Its focal length when immersed

View Question A block of mass $$100 \mathrm{~kg}$$ slides over a distance of $$10 \mathrm{~m}$$ on a horizontal surface. If the co-eff

View Question Given below are two statements:
Statement I : If a capillary tube is immersed first in cold water and then in hot water,

View Question If the radius of curvature of the path of two particles of same mass are in the ratio $$3: 4$$, then in order to have co

View Question Match List I with List II
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View Question Two vessels $$A$$ and $$B$$ are of the same size and are at same temperature. A contains $$1 \mathrm{~g}$$ of hydrogen a

View Question In the given circuit, the breakdown voltage of the Zener diode is $$3.0 \mathrm{~V}$$. What is the value of $$\mathrm{I}

View Question A body starts moving from rest with constant acceleration covers displacement $$S_1$$ in first $$(p-1)$$ seconds and $$\

View Question The electric current through a wire varies with time as $$I=I_0+\beta t$$, where $$I_0=20 \mathrm{~A}$$ and $$\beta=3 \m

View Question The potential energy function (in $$J$$ ) of a particle in a region of space is given as $$U=\left(2 x^2+3 y^3+2 z\right

View Question The explosive in a Hydrogen bomb is a mixture of $${ }_1 \mathrm{H}^2,{ }_1 \mathrm{H}^3$$ and $${ }_3 \mathrm{Li}^6$$ i

View Question In a double slit experiment shown in figure, when light of wavelength $$400 \mathrm{~nm}$$ is used, dark fringe is obser

View Question A cylinder is rolling down on an inclined plane of inclination $$60^{\circ}$$. It's acceleration during rolling down wil

View Question An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $$\mathrm{S}

View Question When a hydrogen atom going from $$n=2$$ to $$n=1$$ emits a photon, its recoil speed is $$\frac{x}{5} \mathrm{~m} / \math

View Question A square loop of side $$10 \mathrm{~cm}$$ and resistance $$0.7 \Omega$$ is placed vertically in east-west plane. A unifo

View Question The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of $$20 \mathrm{~cm}$$ fro

View Question A $$16 \Omega$$ wire is bend to form a square loop. A $$9 \mathrm{~V}$$ battery with internal resistance $$1 \Omega$$ is

View Question When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the ki

View Question A ball rolls off the top of a stairway with horizontal velocity $$u$$. The steps are $$0.1 \mathrm{~m}$$ high and $$0.1

View Question In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings a

View Question