JEE Main 2023 · 06 Apr 2023 · Shift 1

Q1.For the plane electromagnetic wave given by $\mathrm{E}={\mathrm{E}}_0\sin (\omega \mathrm{t}-\mathrm{kx})$ and $\mathrm{B}={\mathrm{B}}_0\sin (\omega \mathrm{t}-\mathrm{kx})$, the ratio of average electric energy density to average magnetic energy density is

Q2.Name the logic gate equivalent to the diagram attached

Q3.A small ball of mass M and density $\rho$ is dropped in a viscous liquid of density ${\rho }_0$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball?

Q4.The number of air molecules per ${\mathrm{cm}}^3$ increased from $3\times 10^{19}$ to $12\times 10^{19}$. The ratio of collision frequency of air molecules before and after the increase in number respectively is

Q5.A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W. The rate at which internal energy of the system increases

Q6.A particle is moving with constant speed in a circular path. When the particle turns by an angle $90^{\circ }$, the ratio of instantaneous velocity to its average velocity is $\pi :x\sqrt{2}$. The value of $x$ will be

Q7.A small block of mass 100 g is tied to a spring of spring constant $7.5\mathrm{N}/\mathrm{m}$ and length 20 cm. The other end of spring is fixed at a particular point A. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity …

Q8.A monochromatic light wave with wavelength ${\lambda }_1$ and frequency $v_1$ in air enters another medium. If the angle of incidence and angle of refraction at the interface are $45^{\circ }$ and $30^{\circ }$ respectively, then the wavelength ${\lambda }_2$ and frequency $v_2$ …

Q9.Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : When a body is projected at an angle $45^{\circ }$, it's range is maximum.
Reason R : For maximum range, the value of $\sin 2\theta$ should be equal to one.
In th …

Q10.Two resistances are given as $R_1=(10\pm 0.5)\Omega$ and ${\mathrm{R}}_2=(15\pm 0.5)\Omega$. The percentage error in the measurement of equivalent resistance when they are connected in parallel is

Q11.A planet has double the mass of the earth. Its average density is equal to the that of the earth. An object weighing W on earth will weigh on that planet :

Q12.Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Earth has atmosphere whereas moon doesn't have any atmosphere.

Reason R: The escape velocity on moon is very small as compared to that on earth.

In the light of …

Q13.For a uniformly charged thin spherical shell, the electric potential (V) radially away from the center (O) of shell can be graphically represented as

Q14.The resistivity ($\rho$) of semiconductor varies with temperature. Which of the following curve represents the correct behaviour

Q15.The kinetic energy of an electron, $\alpha$-particle and a proton are given as $4K$, $2K$ and K respectively. The de-Broglie wavelength associated with electron ($\lambda e$) $\alpha$-particle ($\lambda \alpha$) and the proton ($\lambda p$) are as follows:

Q16.By what percentage will the transmission range of a TV tower be affected when the height of the tower is increased by $21\%$?

Q17.The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is

Q18.A mass m is attached to two springs as shown in figure. The spring constants of two springs are $K_1$ and $K_2$. For the frictionless surface, the time period of oscillation of mass $m$ is

Q19.The induced emf can be produced in a coil by
A. moving the coil with uniform speed inside magnetic field
B. moving the coil with non-uniform speed inside uniform magnetic field
C. rotating the coil inside the uniform magnetic field
D. changing the area of the coil inside the unif …

Q20.A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is

Q21.A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2.15 m within water when sunlight is incident at an angle of $30^{\circ }$ with the surface of water. If swimming pool is filled to a height of 1.5 m, then the height of the pole above the water s …

Q22.The length of a metallic wire is increased by $20\%$ and its area of cross section is reduced by $4\%$. The percentage change in resistance of the metallic wire is

Q23.A particle of mass 10 g moves in a straight line with retardation 2 x, where x is the displacement in SI units. Its loss of kinetic energy for above displacement is ${\left(\frac{10}{x}\right)}^{-n}$ J. The value of $n$ will be

Q24.Two identical circular wires of radius 20 cm and carrying current $\sqrt{2}$ A are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wire is $\times 10^{-8}$ T. (Take $\pi =3.14$)

Q25.A person driving car at a constant speed of $15\mathrm{m}/\mathrm{s}$ is approaching a vertical wall. The person notices a change of 40 Hz in the frequency of his car's horn upon reflection from the wall. The frequency of horn is $\_\_\_\_$ Hz.
(Given : Speed of sound : …

Q26.The radius of fifth orbit of the ${\mathrm{Li}}^{++}$ is $\_\_\_\_$ $\times 10^{-12}$ m. Take : radius of hydrogen atom $=0.51\mathring{A}$

Q27.A steel rod has a radius of 20 mm and a length of 2.0 m. A force of 62.8 kN stretches it along its length. Young's modulus of steel is $2.0\times 10^{11}\mathrm{N}/{\mathrm{m}}^2$. The longitudinal strain produced in the wire is $\_\_\_\_$ $\times 10^{-5}$

Q28.An ideal transformer with purely resistive load operates at 12 kV on the primary side. It supplies electrical energy to a number of nearby houses at 120 V. The average rate of energy consumption in the houses served by the transformer is 60 kW. The value of resistive load (Rs) re …

Q29.Two identical solid spheres each of mass 2 kg and radii 10 cm are fixed at the ends of a light rod. The separation between the centres of the spheres is 40 cm. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is …

Q30.A parallel plate capacitor with plate area A and plate separation d is filled with a dielectric material of dielectric constant $\mathrm{K}=4$. The thickness of the dielectric material is x, where $\mathrm{x}<\mathrm{d}$.

Let ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ be the capacita …

Q1.A compound is formed by two elements X and Y. The element Y forms cubic close packed arrangement and those of element X occupy one third of the tetrahedral voids. What is the formula of the compound?

Q2.The standard electrode potential of ${\mathrm{M}}^{+}/\mathrm{M}$ in aqueous solution does not depend on

Q3.Polymer used in orlon is:

Q4.The difference between electron gain enthalpies will be maximum between:

Q5.The possibility of photochemical smog formation is more at

Q6.The setting time of Cement is increased by adding

Q7.Given below are two statements: one is labelled as assertion and the other is labelled as reason.
Assertion: Loss of electron from hydrogen atom results in nucles of $\sim 1.5\times 10^{-3}$ pm size.
Reason: Proton $({\mathrm{H}}^{+})$ always exists in combined form

In the light …

Q8.Compound P is neutral. Q gives effervescence with ${\mathrm{NaHCO}}_3$ while R reacts with Hinsbergs reagent to give solid soluble in NaOH. Compound P is

Q9.The major products A and B from the following reactions are:

Q10.Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The spin only magnetic moment value for $[\mathrm{Fe}(\mathrm{CN}{)}_6{]}^{3-}$ is 1.74 BM, whereas for $[\mathrm{Fe}({\mathrm{H}}_2\mathrm{O}{)}_6{]}^{3+}$ is 5.92 BM. …

Q11.Which of the following options are correct for the reaction
$2[\mathrm{Au}(\mathrm{CN}{)}_2{]}_{(\mathrm{aq})}^{-}+\mathrm{Zn}(\mathrm{s})\to 2\mathrm{Au}(\mathrm{s})+[\mathrm{Zn}(\mathrm{CN}{)}_4{]}_{(\mathrm{aq})}^{2-}$
A. Redox reaction
B. Displacement reaction
C. Decomp …

Q12.Match List I with List II

List I (Oxide) | List II (Type of Bond)
A. N₂O₄ | I. 1 N=O bond
B. NO₂ | II. 1 N-O-N bond
C. N₂O₅ | III. 1 N-N bond
D. N₂O | IV. 1 N=N/N≡N bond

Choose the correct answer from the options given below:

Q13.Strong reducing and oxidizing agents among the following, respectively, are

Q14.The major product formed in the following reaction is

Q15.For a concentrated solution of a weak electrolyte (${\mathrm{K}}_{\mathrm{eq}}=$ equilibrium constant) ${\mathrm{A}}_2{\mathrm{B}}_3$ of concentration 'c', the degree of dissociation "$\alpha$' is

Q16.For the reaction:


The correct statement is:

Q17.The wavelength of an electron of kinetic energy $4.50\times 10^{-29}\mathrm{J}$ is...... $\times 10^{-5}\mathrm{m}$. (Nearest integer)

Given: mass of electron is $9\times 10^{-31}\mathrm{kg}$, $\mathrm{h}=6.6\times 10^{-34}\mathrm{J}\mathrm{s}$

Q18.Number of bromo derivatives obtained on treating ethane with excess of ${\mathrm{Br}}_2$, in diffused sunlight is...

Q19.Consider the graph of Gibbs free energy G vs Extent of reaction. The number of statement/s from the following which are true with respect to points (a), (b) and (c) is ______

A. Reaction is spontaneous at (a) and (b)
B. Reaction is at equilibrium at point (b) and nonspontaneous …

Q20.Mass of Urea (${\mathrm{NH}}_2{\mathrm{CONH}}_2$) required to be dissolved in 1000 g of water to reduce the vapour pressure of water by $25\%$ is......g. (Nearest integer)

Given: Molar mass of N, C, O and H are 14, 12, 16 and 1 g ${\mathrm{mol}}^{-1}$ respectively.

Q21.The value of $\log \mathrm{K}$ for the reaction $\mathrm{A}\leftrightharpoons \mathrm{B}$ at 298 K is ______ (Nearest integer)

Given: $\Delta {\mathrm{H}}^0=-54.07\mathrm{kJ}{\mathrm{mol}}^{-1}$
$\Delta {\mathrm{S}}^{\circ }=10{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$
(Take …

Q22.The number of species from the following which have square pyramidal structure is
${\mathrm{PF}}_5,{\mathrm{BrF}}_4^{-},{\mathrm{IF}}_5;{\mathrm{BrF}}_5,{\mathrm{XeOF}}_4,{\mathrm{ICl}}_4^{-}$

Q23.Number of ambidentate ligands in a representative metal complex $\left[\mathrm{M}(\mathrm{en})(\mathrm{SCN}{)}_4\right]$ is
[en = ethylenediamine]

Q24.For the adsorption of hydrogen on platinum, the activation energy is $30\mathrm{kJ}{\mathrm{mol}}^{-1}$ and for the adsorption of hydrogen on nickel, the activation energy is $41.4\mathrm{kJ}{\mathrm{mol}}^{-1}$. The logarithm of the ratio of the rates of chemisorption on equ …

Q25.If 5 moles of ${\mathrm{BaCl}}_2$ is mixed with 2 moles of ${\mathrm{Na}}_3{\mathrm{PO}}_4$, the maximum number of moles of ${\mathrm{Ba}}_3{\left({\mathrm{PO}}_4\right)}_2$ formed is ______
(Nearest integer)

Q26.In ammonium-phosphomolybdate, the oxidation state of Mo is ${}^{+}$ ______

Q27.Match List I with List II:
List-I (Enzymatic reaction): A. Sucrose → Glucose and Fructose B. Glucose → ethyl alcohol and CO₂ C. Starch → Maltose D. Proteins → Amino acids
List-II (Enzyme): I. Zymase II. Pepsin III. Invertase IV. Diastase
Choose the correct answer from th …

Q28.Match List I with List II:
List-I (Name of reaction): A. Hell-Volhard-Zelinsky reaction B. Iodoform reaction C. Etard reaction D. Gatterman-Koch reaction
List-II (Reagent used): I. NaOH + I₂ II. (i) CrO₂Cl₂, CS₂ (ii) H₂O III. (i) Br₂/red phosphorus (ii) H₂O IV. CO, HCl, a …

Q29.Match List I with List II:
List-I (Vitamin): A. Vitamin A B. Thiamine C. Ascorbic acid D. Riboflavin
List-II (Deficiency disease): I. Beri-Beri II. Cheilosis III. Xerophthalmia IV. Scurvy
Choose the correct answer from the options given below:

Q1.Let $5\mathrm{f}(\mathrm{x})+4\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)=\frac{1}{\mathrm{x}}+3,\mathrm{x}>0$. Then $18{\int }_1^2\mathrm{f}(\mathrm{x})\mathrm{dx}$ is equal to:

Q2.A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If the probability of at least 4 successes is $\frac{\mathrm{k}}{3^{11}}$,then k is equal to

Q3.If ${}^{2\mathrm{n}}{\mathrm{C}}_3:{}^{\mathrm{n}}{\mathrm{C}}_3=10:1$, then the ratio
$\left(n^2+3n\right):\left(n^2-3n+4\right)$ is

Q4.If the ratio of the fifth term from the begining to the fifth term from the end in the expansion of ${\left(\sqrt[4]{2}+\frac{1}{\sqrt[4]{3}}\right)}^{\mathrm{n}}$ is $\sqrt{6}:1$, then the third term from the beginning is:

Q5.Let $\vec{a}=2\hat{i}+3\hat{j}+4\hat{k},\vec{b}=\hat{i}-2\hat{j}-2\hat{k}$ and $\vec{c}=-\hat{i}+4\hat{j}+3\hat{k}$. If $\vec{d}$ is a vector perpendicular to both $\vec{b}$ and $\vec{c}$ and $\vec{a}\cdot \vec{d}=18$, Then $|\vec{a}\times \vec{d}{|}^2$ is …

Q6.The straight lines $l_1$ and $l_2$ pass through the origin and trisect the line segment of the line L : $9\mathrm{x}+5\mathrm{y}=45$ between the axes. If ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ are the slopes of the lines $l_1$ and $l_2$,then the point of in …

Q7.From the top A of a vertical wall AB of height 30 m , the angles of depression of the top P and bottom Q of a vertical tower PQ are $15^{\circ }$ and $60^{\circ }$ respectively. B and Q are on the same horizontal level. If C is a point on AB such that …

Q8.The sum of the first 20 terms of the series $5+11+19+29+41+\dots$ is

Q9.The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and ${\sigma }^2$ respectively. If the variance of all the 30 numbers in the two sets is 13 , then ${\sigma }^2$ is equal to

Q10.Let $A={\left[a_{ij}\right]}_{2\times 2}$ where $a_{ij}\ne 0$ for all $i,j$ and $A^2=I$. Let a be the sum of all diagonal elements of A and $\mathrm{b}=|\mathrm{A}|$, then $3{\mathrm{a}}^2+4{\mathrm{b}}^2$ is equal to

Q11.Let $\mathrm{I}(\mathrm{x})=\int \frac{{\mathrm{x}}^2({\mathrm{xsec}}^2\mathrm{x}+\tan \mathrm{x})}{(\mathrm{x}\tan \mathrm{x}+1{)}^2}\mathrm{dx}$. If $\mathrm{I}(0)=0$ the I
$\left(\frac{\pi }{4}\right)$ is equal to

Q12.If the equation of the plane passing through the line of intersection of the planes $2\mathrm{x}-\mathrm{y}+\mathrm{z}=3,4\mathrm{x}-3\mathrm{y}+5z+9=0$ and parallel to the line $\frac{\mathrm{x}+1}{-2}=\frac{\mathrm{y}+3}{4}=\frac{\mathrm{z}-2}{5}$ is …

Q13.Statement $(P\Rightarrow Q)\wedge (R\Rightarrow Q)$ is logically equivalent to

Q14.The sum of all the roots of the equation $\left|{\mathrm{x}}^2-8\mathrm{x}+15\right|-2\mathrm{x}+7=0$ is:

Q15.Let ${\mathrm{a}}_1,{\mathrm{a}}_2,{\mathrm{a}}_3\dots {\mathrm{a}}_{\mathrm{n}}$ be n positive consecutive terms of an arithmetic progression. If $\mathrm{d}>0$ is its common difference, then …

Q16.If the system of equations



has infinitely many solutions, then $2\mathrm{a}+3\mathrm{b}$ is equal to

Q17.If $2x^y+3y^x=20$, then $\frac{dy}{dx}$ at $(2,2)$ is equal to

Q18.One vertex of a rectangular parallelopiped is at the origin O and the lengths of its edges along x , y and z axes are 3, 4 and 5 units respectively. Let P be the vertex $(3,4,5)$. Then the shortest distance between the diagonal OP and an edge parallel to z axis, not passing thr …

Q19.Let the position vectors of the points $\mathrm{A},\mathrm{B},\mathrm{C}$ and $D$ be $5\hat{i}+5\hat{j}+2\lambda k,\hat{i}+2\hat{j}+3k,-2\hat{i}+\lambda \hat{j}+4k$ and $-\hat{\mathrm{i}}+5\hat{\mathrm{j}}+6\mathrm{k}$. Let the set …

Q20.Let $\mathrm{A}=\{\mathrm{x}\in \mathbb{R}:[\mathrm{x}+3]+[\mathrm{x}+4]\le 3\}$,
$B=\left\{x\in \mathbb{R}:3^x{\left({\sum }_{r=1}^{\infty }\frac{3}{10^r}\right)}^{x-3}<3^{-3x}\right\}$, where $[t]$
denotes greatest integer function. Then,

Q21.Let $\mathrm{a}\in \mathbb{Z}$ and $[\mathrm{t}]$ be the greatest integer $\le \mathrm{t}$. Then the number of points, where the function $\mathrm{f}(\mathrm{x})=[\mathrm{a}+13\sin \mathrm{x}],\mathrm{x}\in (0,\pi )$ is not differentiable, is ____

Q22.A circle passing through the point $\mathrm{P}(\alpha ,\beta )$ in the first quadrant touches the two coordinate axes at the points A and B . The point P is above the line AB . The point Q on the line segment AB is the foot of perpendicular from P on AB . If PQ is equal to 11 un …

Q23.The number of ways of giving 20 distinct oranges to 3 children such that each child gets atleast one orange is ____

Q24.If the area of the region
$S=\left\{(x,y):2y-y^2\le x^2\le 2y,x\ge y\right\}$ is equal to
$\frac{n+2}{n+1}-\frac{\pi }{n-1}$, then the natural number n is equal to

Q25.Let the point $(p,p+1)$ lie inside the region
$E=\left\{(x,y):3-x\le y\le \sqrt{9-x^2},0\le x\le 3\right\}$
If the set of all values of p is the interval $(a,b)$, then $b^2+b-a^2$ is equal to

Q26.Let $y=y(x)$ be a solution of the differential equation $(x\cos x)dy+(xy\sin x+y\cos x-1)dx=0$, $0<x<\frac{\pi }{2}$. If $\frac{\pi }{3}y\left(\frac{\pi }{3}\right)=\sqrt{3}$, then …

Q27.The coefficient of $x^{18}$ in the expansion of ${\left(x^4-\frac{1}{x^3}\right)}^{15}$ is

Q28.Let $A=\{1,2,3,4,\dots 10\}$ and $B=\{0,1,2,3,4\}$.

The number of elements in the relation $R=\{(a,b)\in A\times A:2(a-b{)}^2+3(a-b)\in B\}$ is

Q29.Let the image of the point $P(1,2,3)$ in the plane $2x-y+z=9$ be $Q$. If the coordinates of the point $R$ are $(6,10,7)$, then the square of the area of the triangle PQR is

Q30.Let the tangent to the curve $x^2+2x-4y+9=0$ at the point $P(1,3)$ on it meet the y-axis at A. Let the line passing through P and parallel to the line $x-3y=6$ meet the parabola $y^2=4x$ at B. If B lies on the line $2x-3y=8$, then $(AB{)}^2$ is equal to