JEE Main 2023 (Online) 30th January Morning Shift

Paper was held on
Mon, Jan 30, 2023 3:30 AM

## Chemistry

Caprolactam when heated at high temperature in presence of water, gives

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To inhibit the growth of tumours, identify the compounds used from the following :
A. EDTA
B. Coordination Compounds of

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The major products 'A' and 'B', respectively, are

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In the wet tests for identification of various cations by precipitation, which transition element cation doesn't belong

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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)

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What is the correct order of acidity of the protons marked $$\mathrm{A}-\mathrm{D}$$ in the given compounds ?

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Formation of photochemical smog involves the following reaction in which $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ a

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Which of the following is correct order of ligand field strength?

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Which of the following compounds would give the following set of qualitative analysis ?
(i) Fehling's Test : Positive
(i

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In the extraction of copper, its sulphide ore is heated in a reverberatory furnace after mixing with silica to:

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During the qualitative analysis of $$\mathrm{SO}_{3}^{2-}$$ using dilute $$\mathrm{H}_{2} \mathrm{SO}_{4}, \mathrm{SO}_{

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For $$\mathrm{OF}_{2}$$ molecule consider the following :
A. Number of lone pairs on oxygen is 2 .
B. FOF angle is less

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Match List I with List II
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Amongst the following compounds, which one is an antacid?

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Benzyl isocyanide can be obtained by :
A.
B.
C.
D.
Choose the correct answer from the options given below :

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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)

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Match List I with List II
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Lithium aluminium hydride can be prepared from the reaction of :

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The alkaline earth metal sulphate(s) which are readily soluble in water is/are :
A. $$\mathrm{BeSO}_{4}$$
B. $$\mathrm{M

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A $$300 \mathrm{~mL}$$ bottle of soft drink has $$0.2 ~\mathrm{M}~ \mathrm{CO}_{2}$$ dissolved in it. Assuming $$\mathrm

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Some amount of dichloromethane $$\left(\mathrm{CH}_{2} \mathrm{Cl}_{2}\right)$$ is added to $$671.141 \mathrm{~mL}$$ of

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If compound A reacts with B following first order kinetics with rate constant $$2.011 \times 10^{-3} \mathrm{~s}^{-1}$$.

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$$600 \mathrm{~mL}$$ of $$0.01~\mathrm{M} ~\mathrm{HCl}$$ is mixed with $$400 \mathrm{~mL}$$ of $$0.01~\mathrm{M} ~\math

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When 2 litre of ideal gas expands isothermally into vacuum to a total volume of 6 litre, the change in internal energy i

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Consider the cell
$$\mathrm{Pt}_{(\mathrm{s})}\left|\mathrm{H}_{2}(\mathrm{~g}, 1 \mathrm{~atm})\right| \mathrm{H}^{+}(\

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A trisubstituted compound '$$\mathrm{A}$$', $$\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}_{2}$$ gives neutral $$\mathrm{F

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The number of electrons involved in the reduction of permanganate to manganese dioxide in acidic medium is _____________

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A solution containing $$2 \mathrm{~g}$$ of a non-volatile solute in $$20 \mathrm{~g}$$ of water boils at $$373.52 \mathr

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The energy of one mole of photons of radiation of frequency $$2 \times 10^{12} \mathrm{~Hz}$$ in $$\mathrm{J} ~\mathrm{m

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## Mathematics

Among the statements :
$$(\mathrm{S} 1)~((\mathrm{p} \vee \mathrm{q}) \Rightarrow \mathrm{r}) \Leftrightarrow(\mathrm{p}

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If $${a_n} = {{ - 2} \over {4{n^2} - 16n + 15}}$$, then $${a_1} + {a_2}\, + \,....\, + \,{a_{25}}$$ is equal to :

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A straight line cuts off the intercepts $$\mathrm{OA}=\mathrm{a}$$ and $$\mathrm{OB}=\mathrm{b}$$ on the positive direct

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Let the solution curve $$y=y(x)$$ of the differential equation $$
\frac{\mathrm{d} y}{\mathrm{~d} x}-\frac{3 x^{5} \tan

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The minimum number of elements that must be added to the relation $$ \mathrm{R}=\{(\mathrm{a}, \mathrm{b}),(\mathrm{b},

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Let the system of linear equations
$$x+y+kz=2$$
$$2x+3y-z=1$$
$$3x+4y+2z=k$$
have infinitely many solutions. Then the sy

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If [t] denotes the greatest integer $$\le \mathrm{t}$$, then the value of $${{3(e - 1)} \over e}\int\limits_1^2 {{x^2}{e

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If $$\mathrm{P}(\mathrm{h}, \mathrm{k})$$ be a point on the parabola $$x=4 y^{2}$$, which is nearest to the point $$\mat

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If $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c $$ are three non-zero vectors and $$\widehat n$$ is a unit

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If the coefficient of $$x^{15}$$ in the expansion of $$\left(\mathrm{a} x^{3}+\frac{1}{\mathrm{~b} x^{1 / 3}}\right)^{15

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The coefficient of $${x^{301}}$$ in $${(1 + x)^{500}} + x{(1 + x)^{499}} + {x^2}{(1 + x)^{498}}\, + \,...\, + \,{x^{500}

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Suppose $$f: \mathbb{R} \rightarrow(0, \infty)$$ be a differentiable function such that $$5 f(x+y)=f(x) \cdot f(y), \for

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If the solution of the equation $$\log _{\cos x} \cot x+4 \log _{\sin x} \tan x=1, x \in\left(0, \frac{\pi}{2}\right)$$,

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Let $$A=\left(\begin{array}{cc}\mathrm{m} & \mathrm{n} \\ \mathrm{p} & \mathrm{q}\end{array}\right), \mathrm{d}=|\mathrm

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If $$\tan 15^\circ + {1 \over {\tan 75^\circ }} + {1 \over {\tan 105^\circ }} + \tan 195^\circ = 2a$$, then the value

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The line $$l_1$$ passes through the point (2, 6, 2) and is perpendicular to the plane $$2x+y-2z=10$$. Then the shortest

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The number of points on the curve $$y=54 x^{5}-135 x^{4}-70 x^{3}+180 x^{2}+210 x$$ at which the normal lines are parall

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Let a unit vector $$\widehat{O P}$$ make angles $$\alpha, \beta, \gamma$$ with the positive directions of the co-ordinat

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If an unbiased die, marked with $$-2,-1,0,1,2,3$$ on its faces, is thrown five times, then the probability that the prod

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Let $$y=x+2,4y=3x+6$$ and $$3y=4x+1$$ be three tangent lines to the circle $$(x-h)^2+(y-k)^2=r^2$$. Then $$h+k$$ is equa

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$$\lim_\limits{x \rightarrow 0} \frac{48}{x^{4}} \int_\limits{0}^{x} \frac{t^{3}}{t^{6}+1} \mathrm{~d} t$$ is equal to _

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Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1, 2, 3 and 5, and are d

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Let $$\sum_\limits{n=0}^{\infty} \frac{\mathrm{n}^{3}((2 \mathrm{n}) !)+(2 \mathrm{n}-1)(\mathrm{n} !)}{(\mathrm{n} !)((

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If the equation of the plane passing through the point $$(1,1,2)$$ and perpendicular to the line $$x-3 y+ 2 z-1=0=4 x-y+

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Let $$z=1+i$$ and $$z_{1}=\frac{1+i \bar{z}}{\bar{z}(1-z)+\frac{1}{z}}$$. Then $$\frac{12}{\pi} \arg \left(z_{1}\right)$

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Let $$\alpha$$ be the area of the larger region bounded by the curve $$y^{2}=8 x$$ and the lines $$y=x$$ and $$x=2$$, wh

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Let $$S=\{1,2,3,4,5,6\}$$. Then the number of one-one functions $$f: \mathrm{S} \rightarrow \mathrm{P}(\mathrm{S})$$, wh

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If $$\lambda_{1}

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Let $$f^{1}(x)=\frac{3 x+2}{2 x+3}, x \in \mathbf{R}-\left\{\frac{-3}{2}\right\}$$ For $$\mathrm{n} \geq 2$$, define $$f

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The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted and a and b are resp

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## Physics

A massless square loop, of wire of resistance $$10 \Omega$$, supporting a mass of $$1 \mathrm{~g}$$, hangs vertically wi

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The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, $$5 \mat

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A small object at rest, absorbs a light pulse of power $$20 \mathrm{~mW}$$ and duration $$300 \mathrm{~ns}$$. Assuming s

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Choose the correct relationship between Poisson ratio $$(\sigma)$$, bulk modulus (K) and modulus of rigidity $$(\eta)$$

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The pressure $$(\mathrm{P})$$ and temperature ($$\mathrm{T})$$ relationship of an ideal gas obeys the equation
$$\mathr

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The output waveform of the given logical circuit for the following inputs A and B as shown below, is :

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As per the given figure, a small ball P slides down the quadrant of a circle and hits the other ball Q of equal mass whi

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The charge flowing in a conductor changes with time as $$\mathrm{Q}(\mathrm{t})=\alpha \mathrm{t}-\beta \mathrm{t}^{2}+\

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Heat is given to an ideal gas in an isothermal process.
A. Internal energy of the gas will decrease.
B. Internal energy

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Electric field in a certain region is given by $$\overrightarrow{\mathrm{E}}=\left(\frac{\mathrm{A}}{x^{2}} \hat{i}+\fra

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Two isolated metallic solid spheres of radii $$\mathrm{R}$$ and $$2 \mathrm{R}$$ are charged such that both have same ch

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A sinusoidal carrier voltage is amplitude modulated. The resultant amplitude modulated wave has maximum and minimum ampl

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Speed of an electron in Bohr's $$7^{\text {th }}$$ orbit for Hydrogen atom is $$3.6 \times 10^{6} \mathrm{~m} / \mathrm{

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The magnetic moments associated with two closely wound circular coils $$\mathrm{A}$$ and $$\mathrm{B}$$ of radius $$\mat

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The figure represents the momentum time ($$\mathrm{p}-\mathrm{t}$$) curve for a particle moving along an axis under the

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If the gravitational field in the space is given as $$\left(-\frac{K}{r^{2}}\right)$$. Taking the reference point to be

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Match Column-I with Column-II :
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A ball of mass $$200 \mathrm{~g}$$ rests on a vertical post of height $$20 \mathrm{~m}$$. A bullet of mass $$10 \mathrm{

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A person has been using spectacles of power $$-1.0$$ dioptre for distant vision and a separate reading glass of power $$

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In a series LR circuit with $$\mathrm{X_L=R}$$, power factor P1. If a capacitor of capacitance C with $$\mathrm{X_C=X_L}

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In the following circuit, the magnitude of current I1, is ___________ A.

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In an experiment for estimating the value of focal length of converging mirror, image of an object placed at $$40 \mathr

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The general displacement of a simple harmonic oscillator is $$x = A\sin \omega t$$. Let T be its time period. The slope

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In Young's double slit experiment, two slits $$S_{1}$$ and $$S_{2}$$ are '$$d$$' distance apart and the separation from

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A thin uniform rod of length $$2 \mathrm{~m}$$, cross sectional area '$$A$$' and density '$$\mathrm{d}$$' is rotated abo

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A horse rider covers half the distance with $$5 \mathrm{~m} / \mathrm{s}$$ speed. The remaining part of the distance was

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As per the given figure, if $$\frac{\mathrm{dI}}{\mathrm{dt}}=-1 \mathrm{~A} / s$$ then the value of $$\mathrm{V}_{\mat

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In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by $$0.5 \mathrm{~mm}$$ on a co

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A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of $$2

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A capacitor of capacitance $$900 \mu \mathrm{F}$$ is charged by a $$100 \mathrm{~V}$$ battery. The capacitor is disconne

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