JEE Main 2023 (Online) 31st January Morning Shift

Paper was held on
Tue, Jan 31, 2023 3:30 AM

## Chemistry

The methods NOT involved in concentration of ore are
A. Liquation
B. Leaching
C. Electrolysis
D. Hydraulic washing
E. Fr

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When $$\mathrm{Cu}^{2+}$$ ion is treated with $$\mathrm{KI}$$, a white precipitate, $$\mathrm{X}$$ appears in solution.

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Match items of column I and II
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Consider the following reaction
The correct statement for product B is. It is

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$$\mathrm{Nd^{2+}}$$ = __________

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The correct order of basicity of oxides of vanadium is

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The correct increasing order of the ionic radii is

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The correct order of melting points of dichlorobenzenes is

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Consider the above reaction and identify the product B.

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Identify X, Y and Z in the following reaction. (Equation not balanced)

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A protein '$$\mathrm{X}$$' with molecular weight of $$70,000 \mathrm{~u}$$, on hydrolysis gives amino acids. One of thes

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Choose the correct set of reagents for the following conversion.
trans $$\left(\mathrm{Ph}-\mathrm{CH}=\mathrm{CH}-\math

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Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from $$\mathrm{n=

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Adding surfactants in non polar solvent, the micelles structure will look like

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$$\mathrm{H}_{2} \mathrm{O}_{2}$$ acts as a reducing agent in

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Which one of the following statements is correct for electrolysis of brine solution?

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Cobalt chloride when dissolved in water forms pink colored complex $$\underline{\mathrm{X}}$$ which has
octahedral geome

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An organic compound 'A' with emperical formula $$\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}$$ gives sooty flame on burning

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Match List I with List II
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Which of the following artificial sweeteners has the highest sweetness value in comparison to cane sugar ?

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The total pressure of a mixture of non-reacting gases $$\mathrm{X}(0.6 \mathrm{~g})$$ and $$\mathrm{Y}(0.45 \mathrm{~g})

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Zinc reacts with hydrochloric acid to give hydrogen and zinc chloride. The volume of hydrogen gas produced at STP from t

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The logarithm of equilibrium constant for the reaction $$\mathrm{Pd}^{2+}+4 \mathrm{Cl}^{-} \rightleftharpoons \mathrm{P

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The enthalpy change for the conversion of $$\frac{1}{2} \mathrm{Cl}_{2}(\mathrm{~g})$$ to $$\mathrm{Cl}^{-}$$(aq) is ($$

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On complete combustion, $$0.492 \mathrm{~g}$$ of an organic compound gave $$0.792 \mathrm{~g}$$ of $$\mathrm{CO}_{2}$$.

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At $$27^{\circ} \mathrm{C}$$, a solution containing $$2.5 \mathrm{~g}$$ of solute in $$250.0 \mathrm{~mL}$$ of solution

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The oxidation state of phosphorus in hypophosphoric acid is + _____________.

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How many of the transformations given below would result in aromatic amines?

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A $$\to$$ B
The rate constants of the above reaction at 200 K and 300 K are 0.03 min$$^{-1}$$ and 0.05 min$$^{-1}$$ resp

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For reaction : $$\mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_{3}

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## Mathematics

The number of real roots of the equation $$\sqrt{x^{2}-4 x+3}+\sqrt{x^{2}-9}=\sqrt{4 x^{2}-14 x+6}$$, is :

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A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the b

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If $${\sin ^{ - 1}}{\alpha \over {17}} + {\cos ^{ - 1}}{4 \over 5} - {\tan ^{ - 1}}{{77} \over {36}} = 0,0

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Let a differentiable function $$f$$ satisfy $$f(x)+\int_\limits{3}^{x} \frac{f(t)}{t} d t=\sqrt{x+1}, x \geq 3$$. Then

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If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296 , respectively, then the sum of co

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For the system of linear equations
$$x+y+z=6$$
$$\alpha x+\beta y+7 z=3$$
$$x+2 y+3 z=14$$
which of the following is NOT

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Let $$\mathrm{R}$$ be a relation on $$\mathrm{N} \times \mathbb{N}$$ defined by $$(a, b) ~\mathrm{R}~(c, d)$$ if and onl

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If the domain of the function $$f(x)=\frac{[x]}{1+x^{2}}$$, where $$[x]$$ is greatest integer $$\leq x$$, is $$[2,6)$$,

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A wire of length $$20 \mathrm{~m}$$ is to be cut into two pieces. A piece of length $$l_{1}$$ is bent to make a square o

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Let a circle $$C_{1}$$ be obtained on rolling the circle $$x^{2}+y^{2}-4 x-6 y+11=0$$ upwards 4 units on the tangent $$\

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Let $$\alpha \in (0,1)$$ and $$\beta = {\log _e}(1 - \alpha )$$. Let $${P_n}(x) = x + {{{x^2}} \over 2} + {{{x^3}} \ov

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Let the shortest distance between the lines
$$L: \frac{x-5}{-2}=\frac{y-\lambda}{0}=\frac{z+\lambda}{1}, \lambda \geq 0

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Let $$\vec{a}=2 \hat{i}+\hat{j}+\hat{k}$$, and $$\vec{b}$$ and $$\vec{c}$$ be two nonzero vectors such that $$|\vec{a}+\

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Let $$A = \left( {\matrix{
1 & 0 & 0 \cr
0 & 4 & { - 1} \cr
0 & {12} & { - 3} \cr
} } \right)$$. Then t

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For all $$z \in C$$ on the curve $$C_{1}:|z|=4$$, let the locus of the point $$z+\frac{1}{z}$$ be the curve $$\mathrm{C}

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The value of $$\int_\limits{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{(2+3 \sin x)}{\sin x(1+\cos x)} d x$$ is equal to

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If the maximum distance of normal to the ellipse $$\frac{x^{2}}{4}+\frac{y^{2}}{b^{2}}=1, b

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Let $$y=f(x)=\sin ^{3}\left(\frac{\pi}{3}\left(\cos \left(\frac{\pi}{3 \sqrt{2}}\left(-4 x^{3}+5 x^{2}+1\right)^{\frac{3

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$$(\mathrm{S} 1)~(p \Rightarrow q) \vee(p \wedge(\sim q))$$ is a tautology
$$(\mathrm{S} 2)~((\sim p) \Rightarrow(\sim q

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Let $$\mathrm{y}=f(x)$$ represent a parabola with focus $$\left(-\frac{1}{2}, 0\right)$$ and directrix $$y=-\frac{1}{2}$

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The remainder on dividing $$5^{99}$$ by 11 is ____________.

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Let the line $$L: \frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-3}{1}$$ intersect the plane $$2 x+y+3 z=16$$ at the point
$$P$$.

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Let 5 digit numbers be constructed using the digits $$0,2,3,4,7,9$$ with repetition allowed, and are arranged in ascendi

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Let $$\alpha>0$$, be the smallest number such that the expansion of $$\left(x^{\frac{2}{3}}+\frac{2}{x^{3}}\right)^{30}$

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Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to _________

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Let $$a_{1}, a_{2}, \ldots, a_{n}$$ be in A.P. If $$a_{5}=2 a_{7}$$ and $$a_{11}=18$$, then
$$12\left(\frac{1}{\sqrt{a_

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Let $$\vec{a}$$ and $$\vec{b}$$ be two vectors such that $$|\vec{a}|=\sqrt{14},|\vec{b}|=\sqrt{6}$$ and $$|\vec{a} \time

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Let for $$x \in \mathbb{R}$$,
$$
f(x)=\frac{x+|x|}{2} \text { and } g(x)=\left\{\begin{array}{cc}
x, & x
Then area bound

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Let $$\theta$$ be the angle between the planes $$P_{1}: \vec{r} \cdot(\hat{i}+\hat{j}+2 \hat{k})=9$$ and $$P_{2}: \vec{r

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If the variance of the frequency distribution
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## Physics

The initial speed of a projectile fired from ground is $$\mathrm{u}$$. At the highest point during its motion, the speed

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A bar magnet with a magnetic moment $$5.0 \mathrm{Am}^{2}$$ is placed in parallel position relative to a magnetic field

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Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose t

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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 : The

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The effect of increase in temperature on the number of electrons in conduction band ($$\mathrm{n_e}$$) and resistance of

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Which of the following correctly represents the variation of electric potential $$(\mathrm{V})$$ of a charged spherical

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The amplitude of $$15 \sin (1000 \pi \mathrm{t})$$ is modulated by $$10 \sin (4 \pi \mathrm{t})$$ signal. The amplitude

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The drift velocity of electrons for a conductor connected in an electrical circuit is $$\mathrm{V}_{\mathrm{d}}$$. The c

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A rod with circular cross-section area $$2 \mathrm{~cm}^{2}$$ and length $$40 \mathrm{~cm}$$ is wound uniformly with 400

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At a certain depth "d " below surface of earth, value of acceleration due to gravity becomes four times that of its valu

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Two polaroide $$\mathrm{A}$$ and $$\mathrm{B}$$ are placed in such a way that the pass-axis of polaroids are perpendicul

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100 balls each of mass $$\mathrm{m}$$ moving with speed $$v$$ simultaneously strike a wall normally and reflected back w

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A free neutron decays into a proton but a free proton does not decay into neutron. This is because

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If $$\mathrm{R}, \mathrm{X}_{\mathrm{L}}$$, and $$\mathrm{X}_{\mathrm{C}}$$ represent resistance, inductive reactance an

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The maximum potential energy of a block executing simple harmonic motion is $$25 \mathrm{~J}$$. A is amplitude of oscill

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If 1000 droplets of water of surface tension $$0.07 \mathrm{~N} / \mathrm{m}$$, having same radius $$1 \mathrm{~mm}$$ ea

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As shown in figure, a $$70 \mathrm{~kg}$$ garden roller is pushed with a force of $$\vec{F}=200 \mathrm{~N}$$ at an angl

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The pressure of a gas changes linearly with volume from $$\mathrm{A}$$ to $$\mathrm{B}$$ as shown in figure. If no heat

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The correct relation between $$\gamma = {{{c_p}} \over {{c_v}}}$$ and temperature T is :

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If a source of electromagnetic radiation having power $$15 \mathrm{~kW}$$ produces $$10^{16}$$ photons per second, the r

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A lift of mass $$\mathrm{M}=500 \mathrm{~kg}$$ is descending with speed of $$2 \mathrm{~ms}^{-1}$$. Its supporting cable

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For hydrogen atom, $$\lambda_{1}$$ and $$\lambda_{2}$$ are the wavelengths corresponding to the transitions 1 and 2 resp

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In the figure given below, a block of mass $$M=490 \mathrm{~g}$$ placed on a frictionless table is connected with two sp

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The speed of a swimmer is $$4 \mathrm{~km} \mathrm{~h}^{-1}$$ in still water. If the swimmer makes his strokes normal to

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A solid sphere of mass $$1 \mathrm{~kg}$$ rolls without slipping on a plane surface. Its kinetic energy is $$7 \times 10

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Expression for an electric field is given by $$\overrightarrow{\mathrm{E}}=4000 x^{2} \hat{i} \frac{\mathrm{V}}{\mathrm{

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A thin rod having a length of $$1 \mathrm{~m}$$ and area of cross-section $$3 \times 10^{-6} \mathrm{~m}^{2}$$ is suspen

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In a medium the speed of light wave decreases to $$0.2$$ times to its speed in free space The ratio of relative permitti

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Two identical cells, when connected either in parallel or in series gives same current in an external resistance $$5 ~\O

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An inductor of $$0.5 ~\mathrm{mH}$$, a capacitor of $$20 ~\mu \mathrm{F}$$ and resistance of $$20 ~\Omega$$ are connecte

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