JEE Main 2023 · 31 Jan 2023 · Shift 1

Q1.A bar magnet with a magnetic moment $5.0{\mathrm{Am}}^2$ is placed in parallel position relative to a magnetic field of 0.4 T. The amount of required work done in turning the magnet form parallel to antiparallel position relative to the field direction is ______.

Q2.If a source of electromagnetic radiation having power 15 kW produces $10^{16}$ photons per second, the radiation belongs to a part of spectrum is.
(Take Planck constant $\mathrm{h}=6\times 10^{-34}$ Js)

Q3.The amplitude of $15\sin (1000\pi \mathrm{t})$ is modulated by $10\sin (4\pi \mathrm{t})$ signal. The amplitude modulated signal contains frequency(ies) of
(A) 500 Hz
(B) 2 Hz
(C) 250 Hz
(D) 498 Hz
(E) 502 Hz

Choose the correct answer from the options given below:

Q4.As shown in figure, a 70 kg garden roller is pushed with a force of $\overrightarrow{\mathrm{F}}=200\mathrm{N}$ at an angle of $30^{\circ }$ with horizontal. The normal reaction on the roller is (Given $\mathrm{g}=10\mathrm{m}{\mathrm{s}}^{-2}$)

Q5.The initial speed of a projectile fired from ground is $u$. At the highest point during its motion, the speed of projectile is $\frac{\sqrt{3}}{2}u$. The time of flight of the projectile is:

Q6.Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following {Assume negligible air friction}

Q7.A free neutron decays into a proton but a free proton does not decay into neutron. This is because

Q8.The effect of increase in temperature on the number of electrons in conduction band (${\mathrm{n}}_{\mathrm{e}}$) and resistance of a semiconductor will be as:

Q9.The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude of oscillation. At A/2, the kinetic energy of the block is

Q10.The pressure of a gas changes linearly with volume from A to B as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be

Q11.Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of radius (R) with radial distance $(\mathrm{r})$ from the centre?

Q12.Given below are two statements: One is labelled as
Assertion A and the other is labelled as Reason R
Assertion A: The beam of electrons shows wave nature and exhibit interference and diffraction.
Reason R : Davisson Germer Experimentally verified the wave nature of electrons.
In …

Q13.The drift velocity of electrons for a conductor connected in an electrical circuit is $V_d$. The conductor in now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same. The new drift velocity of ele …

Q14.At a certain depth "d" below surface of earth. value of acceleration due to gravity becomes four times that of its value at a height $3R$ above earth surface. Where R is Radius of earth (Take $R=6400$ km). The depth d is equal to

Q15.If 1000 droplets of water of surface tension $0.07$ N/m. having same radius 1 mm each, combine to from a single drop. In the process the released surface energy is-
(Take $\pi =\frac{22}{7}$)

Q16.A rod with circular cross-section area $2$ cm${}^2$ and length 40 cm is wound uniformly with 400 turns of an insulated wire. If a current of 0.4 A flows in the wire windings, the total magnetic flux produced inside windings is $4\pi \times 10^{-6}$ Wb. The relative permeability of …

Q17.The correct relation between $\gamma =\frac{C_p}{C_v}$ and temperature T is :

Q18.Two polaroide A and B are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid C is placed between A and B bisecting angle between them. If intensity of unpolarised light is $I_0$ then intensity of transmitted light after pas …

Q19.If $R$, $X_L$, and $X_C$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:

Q20.100 balls each of mass m moving with speed v simultaneously strike a wall normally and reflected back with same speed, in time $t$ s. The total force exerted by the balls on the wall is

Q21.A thin rod having a length of 1 m and area of cross-section $3\times 10^{-6}$ m${}^2$ is suspended vertically from one end. The rod is cooled from $210°C$ to $160°C$. After cooling, a mass M is attached at the lower end of the rod such that the length of rod again becomes 1 m. You …

Q22.The speed of a swimmer is $4$ km h${}^{-1}$ in still water. If the swimmer makes his strokes normal to the flow of river of width 1 km, he reaches a point 750 m down the stream on the opposite bank.

The speed of the river water is _____ km h${}^{-1}$.

Q23.In the figure given below, a block of mass $M=490$ g placed on a frictionless table is connected with two springs having same spring constant ($K=2$ N m${}^{-1}$). If the block is horizontally displaced through 'X' m then the number of complete oscillations it will make in $14\pi$ …

Q24.In a medium the speed of light wave decreases to 0.2 times to its speed in free space. The ratio of relative permittivity to the refractive index of the medium is $x:1$. The value of x is _____.
(Given speed of light in free space $=3\times 10^8$ m s${}^{-1}$ and for the given med …

Q25.A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is $7\times 10^{-3}\mathrm{J}$. The speed of the centre of mass of the sphere is $\_\_\_\_$ $\mathrm{cm}{\mathrm{s}}^{-1}$.

Q26.An inductor of 0.5 mH, a capacitor of $20\mu \mathrm{F}$ and resistance of $20\Omega$ are connected in series with a 220 V ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $\sqrt{\mathrm{x}}\mathrm{A}$. The value of x is -

Q27.Expression for an electric field is given by $\overrightarrow{\mathrm{E}}=4000{\mathrm{x}}^2\hat{\mathrm{i}}\frac{\mathrm{V}}{\mathrm{m}}$. The electric flux through the cube of side 20 cm when placed in electric field (as shown in the figure) is $\_\_\_\_$ V cm.

Q28.A lift of mass $\mathrm{M}=500\mathrm{kg}$ is descending with speed of $2{\mathrm{ms}}^{-1}$. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of $2{\mathrm{ms}}^{-2}$. The kinetic energy of the lift at the end of fall through to a dista …

Q29.For hydrogen atom, ${\lambda }_1$ and ${\lambda }_2$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of ${\lambda }_1$ and ${\lambda }_2$ is $\frac{x}{32}$. The value of $x$ is $\_\_\_\_$.

Q30.Two identical cells, when connected either in parallel or in series gives same current in an external resistance $5\Omega$. The internal resistance of each cell will be $\_\_\_\_$ $\Omega$.

Q1.${\mathrm{Nd}}^{2+}=$ ____

Q2.The methods NOT involved in concentration of ore are
(A) Liquation
(B) Leaching
(C) Electrolysis
(D) Hydraulic washing
(E) Froth floatation

Choose the correct answer from the options given below :

Q3.Consider the following reaction

Propanal+Methanal= …

Q4.The correct order of basicity of oxides of vanadium is

Q5.When ${\mathrm{Cu}}^{2+}$ ion is treated with KI , a white precipitate, X appears in solution. The solution is titrated with sodium thiosulphate, the compound Y is formed. X and Y respectively are

Q6.(see structure)

Q7.Cobalt chloride when dissolved in water forms pink colored complex X which has octahedral geometry. This solution on treating with cone HCl forms deep blue complex, Y which has a Z geometry. $\mathrm{X},\mathrm{Y}$ and Z , respectively, are

Q8.Identify $\mathrm{X},\mathrm{Y}$ and Z in the following reaction.
(Equation not balanced)
$\mathrm{ClO}+{\mathrm{NO}}_2\to \underline{\mathrm{X}}\stackrel{{\mathrm{H}}_2\mathrm{O}}{\to }\underline{\mathrm{Y}}+\underline{\mathrm{Z}}$

Q9.The correct order of melting point of dichlorobenzenes is

Q10.A protein ' X ' with molecular weight of $70,000\mathrm{u}$, on hydrolysis gives amino acids. One of these amino acid is

Q11.Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from $n=4$ to $n=2$ of ${\mathrm{He}}^{+}$spectrum

Q12.Match items of column I and II

Q13.The correct increasing order of the ionic radii is

Q14.${\mathrm{H}}_2{\mathrm{O}}_2$ acts as a reducing agent in

Q15.Which of the following artificial sweeteners has the highest sweetness value in comparison to cane sugar?

Q16.Choose the correct set of reagents for the following conversion
trans ($\mathrm{Ph}-\mathrm{CH}=\mathrm{CH}-{\mathrm{CH}}_3$) → cis ($\mathrm{Ph}-\mathrm{CH}=\mathrm{CH}-{\mathrm{CH}}_3$)

Q17.Adding surfactants in non polar solvent, the micelles structure will look like

Q18.An organic compound 'A' with empirical formula ${\mathrm{C}}_6{\mathrm{H}}_6\mathrm{O}$ gives sooty flame on burning. Its reaction with bromine solution in low polarity solvent results in high yield of B. B is

Q19.Which one of the following statements is correct for electrolysis of brine solution?

Q20.The logarithm of equilibrium constant for the reaction ${\mathrm{Pd}}^{2+}+4{\mathrm{Cl}}^{-}\rightleftharpoons {\mathrm{PdCl}}_4^{2-}$ is ______ (Nearest integer)

Given: $\frac{2.303RT}{F}=0.06\mathrm{V}$ …

Q21.$\mathrm{A}\to \mathrm{B}$

The rate constants of the above reaction at 200 K and 300 K are $0.03{\min }^{-1}$ and $0.05{\min }^{-1}$ respectively. The activation energy for the reaction is ______ J (Nearest integer)

(Given: $\ln 10=2.3$ …

Q22.The enthalpy change for the conversion of $\frac{1}{2}{\mathrm{Cl}}_2(\mathrm{g})$ to ${\mathrm{Cl}}^{-}(\mathrm{aq})$ is $(-)$ ______ $\mathrm{kJ}{\mathrm{mol}}^{-1}$ (Nearest integer)

Given: …

Q23.On complete combustion, 0.492 g of an organic compound gave 0.792 g of ${\mathrm{CO}}_2$.

The % of carbon in the organic compound is ______ (Nearest integer)

Q24.At $27^{\circ }\mathrm{C}$, a solution containing 2.5 g of solute in 250.0 mL of solution exerts an osmotic pressure of 400 Pa. The molar mass of the solute is ______ g ${\mathrm{mol}}^{-1}$ (Nearest integer)

(Given: $\mathrm{R}=0.083\mathrm{L}$ bar …

Q25.Zinc reacts with hydrochloric acid to give hydrogen and zinc chloride. The volume of hydrogen gas produced at STP from the reaction of 11.5 g of zinc with excess HCl is ______ L (Nearest integer)
(Given : Molar mass of Zn is $65.4\mathrm{g}{\mathrm{mol}}^{-1}$ and Molar volume …

Q26.How many of the transformation given below would result in aromatic amines?
(1)
(2)
(3)
(4)

Q27.For reaction : ${\mathrm{SO}}_2(\mathrm{g})+\frac{1}{2}{\mathrm{O}}_2(\mathrm{g})\rightleftharpoons {\mathrm{SO}}_3(\mathrm{g})$
${\mathrm{K}}_{\mathrm{P}}=2\times 10^{12}$ at $27^{\circ }\mathrm{C}$ and 1 atm pressure. The ${\mathrm{K}}_{\mathrm{c}}$ for the same reaction is _ …

Q28.The oxidation state of phosphorus in hypophosphoric acid is + ______.

Q29.The total pressure of a mixture of non-reacting gases $\mathrm{X}(0.6\mathrm{g})$ and $\mathrm{Y}(0.45\mathrm{g})$ in a vessel is 740 mm of Hg. The partial pressure of the gas X is ______ mm of Hg. (Nearest Integer)
(Given : molar mass $\mathrm{X}=20$ and …

Q1.If the maximum distance of normal to the ellipse $\frac{x^2}{4}+\frac{y^2}{b^2}=1,b<2$, from the origin is 1, then the eccentricity of the ellipse is:

Q2.For all $z\in \mathbb{C}$ on the curve $C_1:|z|=4$, let the locus of the point $z+\frac{1}{z}$ be the curve $C_2$. Then

Q3.A wire of length 20 m is to be cut into two pieces. A piece of length ${\ell }_1$ is bent to make a square of area $A_1$ and the other piece of length ${\ell }_2$ is made into a circle of area $A_2$. If $2A_1+3A_2$ is minimum then $(\pi {\ell }_1):{\ell }_2$ is e …

Q4.For the system of linear equations
$x+y+z=6$
$\alpha x+\beta y+7z=3$
$x+2y+3z=14$,
which of the following is NOT true?

Q5.Let the shortest distance between the lines $L:\frac{x-5}{-2}=\frac{y-\lambda }{0}=\frac{z+\lambda }{1},\lambda \ge 0$ and $L_1:x+1=y-1=4-z$ be $2\sqrt{6}$. If $(\alpha ,\beta ,\gamma )$ lies on L, then which of the following is NOT possible?

Q6.Let $y=f(x)$ represent a parabola with focus $\left(-\frac{1}{2},0\right)$ and directrix $y=-\frac{1}{2}$.

Then
$S=\left\{x\in \mathbb{R}:{\tan }^{-1}\left(\sqrt{f(x)}\right)+{\sin }^{-1}(\sqrt{f(x)+1})=\frac{\pi }{2}\right\}$:

Q7.Let $A=\left(\begin{array}{ccc}1& 0& 0\\ 0& 4& -1\\ 0& 12& -3\end{array}\right)$. Then the sum of the diagonal elements of the matrix $(A+I{)}^{11}$ is equal to:

Q8.Let R be a relation on $\mathbb{N}\times \mathbb{N}$ defined by $(a,b)R(c,d)$ if and only if $ad(b-c)=bc(a-d)$. Then R is

Q9.Let
$y=f(x)={\sin }^3\left(\frac{\pi }{3}\left(\cos \left(\frac{\pi }{3\sqrt{2}}{\left(-4x^3+5x^2+1\right)}^{\frac{3}{2}}\right)\right)\right)$.
Then, at $x=1$,

Q10.If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296, respectively, then the sum of common ratios of all such GPs is

Q11.The number of real roots of the equation $\sqrt{x^2-4x+3}+\sqrt{x^2-9}=\sqrt{4x^2-14x+6}$, is:

Q12.Let a differentiable function f satisfy $f(x)+{\int }_3^x\frac{f(t)}{t}dt=\sqrt{x+1},x\ge 3$. Then 12f(8) is equal to:

Q13.Let $\vec{a}=2\hat{i}+\hat{j}+\hat{k}$, and $\vec{b}$ and $\vec{c}$ be two nonzero vectors such that $|\vec{a}+\vec{b}+\vec{c}|=|\vec{a}+\vec{b}-\vec{c}|$ and $\overrightarrow{\mathrm{b}}.\overrightarrow{\mathrm{c}}=0$. Consider the following two statement:
(A) …

Q14.Let $\alpha \in (0,1)$ and $\beta ={\log }_{\mathrm{e}}(1-\alpha )$. Let $P_n(x)=x+\frac{x^2}{2}+\frac{x^3}{3}+\dots ..+\frac{x^n}{n},x\in (0,1)$.

Then the integral ${\int }_0^{\alpha }\frac{{\mathrm{t}}^{50}}{1-\mathrm{t}}\mathrm{dt}$ is equal to

Q15.If ${\sin }^{-1}\frac{\alpha }{17}+{\cos }^{-1}\frac{4}{5}-{\tan }^{-1}\frac{77}{36}=0,0<\alpha <13$, then ${\sin }^{-1}(\sin \alpha )+{\cos }^{-1}(\cos \alpha )$ is equal to

Q16.Let a circle ${\mathrm{C}}_1$ be obtained on rolling the circle $x^2+y^2-4x-6y+11=0$ upwards 4 units on the tangent T to it at the point $(3,2)$. Let ${\mathrm{C}}_2$ be the image of ${\mathrm{C}}_1$ in T . Let A and B be the centers of circles ${\mathrm{C}}_1$ …

Q17.(S1) $(\mathrm{p}\Rightarrow \mathrm{q})\vee (\mathrm{p}\wedge (\sim \mathrm{q}))$ is a tautology
(S2) $((\sim \mathrm{p})\Rightarrow (\sim \mathrm{q}))\wedge ((\sim \mathrm{p})\vee \mathrm{q})$ is a Contradiction. Then

Q18.The value of ${\int }_{\frac{\pi }{3}}^{\frac{\pi }{2}}\frac{(2+3\sin x)}{\sin x(1+\cos x)}dx$ is equal to

Q19.A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is

Q20.Let 5 digit numbers be constructed using the digits $0,2,3,4,7,9$ with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is

Q21.Let ${\mathrm{a}}_1,{\mathrm{a}}_2,\dots \dots ,{\mathrm{a}}_{\mathrm{n}}$ be in A.P. If ${\mathrm{a}}_5=2{\mathrm{a}}_7$ and ${\mathrm{a}}_{11}=18$, then …

Q22.Let $\theta$ be the angle between the planes $P_1=\vec{r}\cdot (\hat{i}+\hat{j}+2\hat{k})=9$ and $P_2=\vec{r}\cdot (2\hat{i}-\hat{j}+\hat{k})=15$. Let L be the line that meets ${\mathrm{P}}_2$ at the point ( $4,-2,5$ ) and makes an angle $\theta$ with the normal …

Q23.Let $\alpha >0$, be the smallest number such that the expansion of ${\left(x^{\frac{2}{3}}+\frac{2}{x^3}\right)}^{30}$ has a term $\beta x^{-\alpha },\beta \in \mathbb{N}$. Then $\alpha$ is equal to

Q24.Let $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$ be two vector such that $|\overrightarrow{\mathrm{a}}|=\sqrt{14}$, $|\overrightarrow{\mathrm{b}}|=\sqrt{6}$ and $|\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{b}}|=\sqrt{48}$. Then …

Q25.Let the line $L:\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-3}{1}$ intersect the plane $2x+y+3z=16$ at the point $P$. Let the point Q be the foot of perpendicular from the point $\mathrm{R}(1,-1,-3)$ on the line L. If $\alpha$ is the area of triangle PQR, then ${\alpha }^2$ is equal t …

Q26.The remainder on dividing $5^{99}$ by 11 is

Q27.If the variance of the frequency distribution

is 3, then $\alpha$ is equal to

Q28.Let for $\mathrm{x}\in \mathrm{R}$


Then area bounded by the curve $\mathrm{y}=(\mathrm{fog})(\mathrm{x})$ and the lines $\mathrm{y}=0,2\mathrm{y}-\mathrm{x}=15$ is equal to

Q29.Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11, is equal to