JEE Main 2024 (Online) 29th January Evening Shift
Paper was held on Mon, Jan 29, 2024 9:30 AM
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Chemistry

On passing a gas, '$$\mathrm{X}$$', through Nessler's regent, a brown precipitate is obtained. The gas '$$\mathrm{X}$$'
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Which of the following acts as a strong reducing agent? (Atomic number: $$\mathrm{Ce}=58, \mathrm{Eu}=63, \mathrm{Gd}=64
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Given below are two statements: Statement I : Fluorine has most negative electron gain enthalpy in its group. Statement
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According to IUPAC system, the compound is named as
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The element having the highest first ionization enthalpy is
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Which of the following statements are correct about $$\mathrm{Zn}, \mathrm{Cd}$$ and $$\mathrm{Hg}$$ ? A. They exhibit h
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The ascending acidity order of the following H atoms is
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The correct IUPAC name of $$\mathrm{K}_2 \mathrm{MnO}_4$$ is
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Identify the reagents used for the following conversion
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Chromatographic technique/s based on the principle of differential adsorption is / are A. Column chromatography B. Thin
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Which of the following reaction is correct?
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Anomalous behavior of oxygen is due to its
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Which one of the following will show geometrical isomerism?
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A reagent which gives brilliant red precipitate with Nickel ions in basic medium is
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Phenol treated with chloroform in presence of sodium hydroxide, which further hydrolyzed in presence of an acid results
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The product A formed in the following reaction is
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Alkyl halide is converted into alkyl isocyanide by reaction with
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The total number of molecules with zero dipole moment among $$\mathrm{CH}_4, \mathrm{BF}_3, \mathrm{H}_2 \mathrm{O}, \ma
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Standard enthalpy of vapourisation for $$\mathrm{CCl}_4$$ is $$30.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$$. Heat required for
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If $$50 \mathrm{~mL}$$ of $$0.5 \mathrm{M}$$ oxalic acid is required to neutralise $$25 \mathrm{~mL}$$ of $$\mathrm{NaOH
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The following concentrations were observed at $$500 \mathrm{~K}$$ for the formation of $$\mathrm{NH}_3$$ from $$\mathrm{
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A constant current was passed through a solution of $$\mathrm{AuCl}_4^{-}$$ ion between gold electrodes. After a period
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The total number of anti bonding molecular orbitals, formed from $$2 s$$ and $$2 p$$ atomic orbitals in a diatomic molec
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The half-life of radioisotope bromine - 82 is 36 hours. The fraction which remains after one day is ________ $$\times 10
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The total number of 'Sigma' and 'Pi' bonds in 2-formylhex-4-enoic acid is _________.
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The oxidation number of iron in the compound formed during brown ring test for NO$$_3^-$$ iron is ________.
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Molality of 0.8 M H$$_2$$SO$$_4$$ solution (density 1.06 g cm$$^{-3}$$) is ________ $$\times10^{-3}$$ m.
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Mathematics

Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is e
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Let $$\mathrm{A}$$ be the point of intersection of the lines $$3 x+2 y=14,5 x-y=6$$ and $$\mathrm{B}$$ be the point of i
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If $$\int \frac{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x}{\sqrt{\sin ^3 x \cos ^3 x \sin (x-\theta)}} d x=A \sqrt{\co
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The distance of the point $$(2,3)$$ from the line $$2 x-3 y+28=0$$, measured parallel to the line $$\sqrt{3} x-y+1=0$$,
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Let a unit vector $$\hat{u}=x \hat{i}+y \hat{j}+z \hat{k}$$ make angles $$\frac{\pi}{2}, \frac{\pi}{3}$$ and $$\frac{2 \
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The function $$f(x)=\frac{x}{x^2-6 x-16}, x \in \mathbb{R}-\{-2,8\}$$
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If R is the smallest equivalence relation on the set $$\{1,2,3,4\}$$ such that $$\{(1,2),(1,3)\} \subset \mathrm{R}$$, t
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If the mean and variance of five observations are $$\frac{24}{5}$$ and $$\frac{194}{25}$$ respectively and the mean of t
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Let $$\mathrm{P}(3,2,3), \mathrm{Q}(4,6,2)$$ and $$\mathrm{R}(7,3,2)$$ be the vertices of $$\triangle \mathrm{PQR}$$. Th
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$$\text { Let } y=\log _e\left(\frac{1-x^2}{1+x^2}\right),-1
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If $$\log _e \mathrm{a}, \log _e \mathrm{~b}, \log _e \mathrm{c}$$ are in an A.P. and $$\log _e \mathrm{a}-\log _e 2 \ma
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If $$\sin \left(\frac{y}{x}\right)=\log _e|x|+\frac{\alpha}{2}$$ is the solution of the differential equation $$x \cos \
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An integer is chosen at random from the integers $$1,2,3, \ldots, 50$$. The probability that the chosen integer is a mul
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Let $$\overrightarrow{O A}=\vec{a}, \overrightarrow{O B}=12 \vec{a}+4 \vec{b} \text { and } \overrightarrow{O C}=\vec{b}
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The function $$f(x)=2 x+3(x)^{\frac{2}{3}}, x \in \mathbb{R}$$, has
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If each term of a geometric progression $$a_1, a_2, a_3, \ldots$$ with $$a_1=\frac{1}{8}$$ and $$a_2 \neq a_1$$, is the
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Let $$\mathrm{r}$$ and $$\theta$$ respectively be the modulus and amplitude of the complex number $$z=2-i\left(2 \tan \f
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The sum of the solutions $$x \in \mathbb{R}$$ of the equation $$\frac{3 \cos 2 x+\cos ^3 2 x}{\cos ^6 x-\sin ^6 x}=x^3-x
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Let $$x=\frac{m}{n}$$ ($$m, n$$ are co-prime natural numbers) be a solution of the equation $$\cos \left(2 \sin ^{-1} x\
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Let $$A=\left[\begin{array}{ccc}2 & 1 & 2 \\ 6 & 2 & 11 \\ 3 & 3 & 2\end{array}\right]$$ and $$P=\left[\begin{array}{lll
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Let O be the origin, and M and $$\mathrm{N}$$ be the points on the lines $$\frac{x-5}{4}=\frac{y-4}{1}=\frac{z-5}{3}$$ a
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Let the area of the region $$\left\{(x, y): 0 \leq x \leq 3,0 \leq y \leq \min \left\{x^2+2,2 x+2\right\}\right\}$$ be A
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Let the set $$C=\left\{(x, y) \mid x^2-2^y=2023, x, y \in \mathbb{N}\right\}$$. Then $$\sum_\limits{(x, y) \in C}(x+y)$$
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Let the slope of the line $$45 x+5 y+3=0$$ be $$27 r_1+\frac{9 r_2}{2}$$ for some $$r_1, r_2 \in \mathbb{R}$$. Then $$\l
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Let $$\alpha, \beta$$ be the roots of the equation $$x^2-\sqrt{6} x+3=0$$ such that $$\operatorname{Im}(\alpha)>\operato
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Let for any three distinct consecutive terms $$a, b, c$$ of an A.P, the lines $$a x+b y+c=0$$ be concurrent at the point
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Let $$P(\alpha, \beta)$$ be a point on the parabola $$y^2=4 x$$. If $$P$$ also lies on the chord of the parabola $$x^2=8
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Remainder when $$64^{32^{32}}$$ is divided by 9 is equal to ________.
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Let $$f(x)=\sqrt{\lim _\limits{r \rightarrow x}\left\{\frac{2 r^2\left[(f(r))^2-f(x) f(r)\right]}{r^2-x^2}-r^3 e^{\frac{
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If $$\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{3}} \sqrt{1-\sin 2 x} d x=\alpha+\beta \sqrt{2}+\gamma \sqrt{3}$$, where $$
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Physics

A small liquid drop of radius $$R$$ is divided into 27 identical liquid drops. If the surface tension is $$T$$, then the
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In the given circuit, the current in resistance R$$_3$$ is :
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A physical quantity $$Q$$ is found to depend on quantities $$a, b, c$$ by the relation $$Q=\frac{a^4 b^3}{c^2}$$. The pe
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A stone of mass $$900 \mathrm{~g}$$ is tied to a string and moved in a vertical circle of radius $$1 \mathrm{~m}$$ makin
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The truth table for this given circuit is :
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A bob of mass '$$m$$' is suspended by a light string of length '$$L$$'. It is imparted a minimum horizontal velocity at
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An electric field is given by $$(6 \hat{i}+5 \hat{j}+3 \hat{k}) \mathrm{N} / \mathrm{C}$$. The electric flux through a s
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A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to
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A wire of length $$L$$ and radius $$r$$ is clamped at one end. If its other end is pulled by a force $$F$$, its length i
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The temperature of a gas having $$2.0 \times 10^{25}$$ molecules per cubic meter at $$1.38 \mathrm{~atm}$$ (Given, $$\ma
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If the distance between object and its two times magnified virtual image produced by a curved mirror is $$15 \mathrm{~cm
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A plane electromagnetic wave of frequency $$35 \mathrm{~MHz}$$ travels in free space along the $$X$$-direction. At a par
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In an a.c. circuit, voltage and current are given by: $$V=100 \sin (100 t) V$$ and $$I=100 \sin \left(100 t+\frac{\pi}{3
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A particle is moving in a straight line. The variation of position '$$x$$' as a function of time '$$t$$' is given as $$x
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The bob of a pendulum was released from a horizontal position. The length of the pendulum is $$10 \mathrm{~m}$$. If it d
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$$N$$ moles of a polyatomic gas $$(f=6)$$ must be mixed with two moles of a monoatomic gas so that the mixture behaves a
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In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path difference b
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Given below are two statements: Statement I : Most of the mass of the atom and all its positive charge are concentrated
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Two sources of light emit with a power of $$200 \mathrm{~W}$$. The ratio of number of photons of visible light emitted b
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Two particles $$X$$ and $$Y$$ having equal charges are being accelerated through the same potential difference. Thereaft
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In the given circuit, the current flowing through the resistance $$20 \Omega$$ is $$0.3 \mathrm{~A}$$, while the ammeter
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In the given figure, the charge stored in $$6 \mu F$$ capacitor, when points $$A$$ and $$B$$ are joined by a connecting
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In a single slit diffraction pattern, a light of wavelength 6000$$\mathop A\limits^o$$ is used. The distance between the
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A body of mass $$5 \mathrm{~kg}$$ moving with a uniform speed $$3 \sqrt{2} \mathrm{~ms}^{-1}$$ in $$X-Y$$ plane along th
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Hydrogen atom is bombarded with electrons accelerated through a potential difference of $$\mathrm{V}$$, which causes exc
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A simple harmonic oscillator has an amplitude $$A$$ and time period $$6 \pi$$ second. Assuming the oscillation starts fr
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Two metallic wires $$P$$ and $$Q$$ have same volume and are made up of same material. If their area of cross sections ar
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A particle is moving in a circle of radius $$50 \mathrm{~cm}$$ in such a way that at any instant the normal and tangenti
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A charge of $$4.0 \mu \mathrm{C}$$ is moving with a velocity of $$4.0 \times 10^6 \mathrm{~ms}^{-1}$$ along the positive
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A horizontal straight wire $$5 \mathrm{~m}$$ long extending from east to west falling freely at right angle to horizonta
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