JEE Main 2023 · 15 Apr 2023 · Shift 1

Q1.The electric field due to a short electric dipole at a large distance (r) from center of dipole on the equatorial plane varies with distance as :

Q2.In a linear simple harmonic motion (SHM)
(A) Restoring force is directly proportional to the displacement.
(B) The acceleration and displacement are opposite in direction.
(C) The velocity is maximum at mean position.
(D) The acceleration is minimum at extreme points.

Choose the …

Q3.Two identical particles each of mass 'm' go round a circle of radius $a$ under the action of their mutual gravitational attraction. The angular speed of each particle will be :

Q4.The height of transmitting antenna is 180 m and the height of the receiving antenna is 245 m. The maximum distance between them for satisfactory communication in line of sight will be :
(given $R=6400$ km)

Q5.The half-life of a radioactive nucleus is 5 years, The fraction of the original sample that would decay in 15 years is :

Q6.The de Broglie wavelength of an electron having kinetic energy E is $\lambda$. If the kinetic energy of electron becomes $\frac{E}{4}$, then its de-Broglie wavelength will be :

Q7.For designing a voltmeter of range 50 V and an ammeter of range 10 mA using a galvanometer which has a coil of resistance $54\Omega$ showing a full scale deflection for 1 mA as in figure.

(A) for voltmeter $R\approx 50k\Omega$
(B) for ammeter $r\approx 0.2\Omega$
(C) for am …

Q8.A flask contains Hydrogen and Argon in the ratio 2:1 by mass. The temperature of the mixture is $30^{\circ }C$. The ratio of average kinetic energy per molecule of the two gases (K argon/K hydrogen) is: (Given: Atomic Weight of $Ar=39.9$)

Q9.Given below are two statements:

Statement I: The equivalent resistance of resistors in a series combination is smaller than least resistance used in the combination.

Statement II: The resistivity of the material is independent of temperature.
In the light of the above statement …

Q10.A body is released from a height equal to the radius (R) of the earth. The velocity of the body when it strikes the surface of the earth will be :
(Given $g=$ acceleration due to gravity on the earth.)

Q11.A 12 V battery connected to a coil of resistance $6\Omega$ through a switch, drives a constant current in the circuit. The switch is opened in 1 ms. The emf induced across the coil is 20 V. The inductance of the coil is :

Q12.A wire of length 'L' and radius 'r' is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by '$\ell$'. Another wire of same material of length '2L' and radius '2r' is pulled by a force '2f'. Then the increase in its length will …

Q13.The position of a particle related to time is given by $x=\left(5t^2-4t+5\right)\mathrm{m}$. The magnitude of velocity of the particle at $t=2\mathrm{s}$ will be :

Q14.The position vector of a particle related to time $t$ is given by
$\overrightarrow{\mathrm{r}}=\left(10\mathrm{t}\hat{\mathrm{i}}+15{\mathrm{t}}^2\hat{\mathrm{j}}+7\hat{\mathrm{k}}\right)\mathrm{m}$
The direction of net force experienced by the particle is :

Q15.Match List I with List II of Electromagnetic waves with corresponding wavelength range :

List I
(A) Microwave
(B) Ultraviolet
(C) X-Ray
(D) Infra-red

List II
(I) 400 nm to 1 nm
(II) 1 nm to $10^{-3}\mathrm{nm}$
(III) 1 mm to 700 nm
(IV) 0.1 m to 1 mm

Choose the correct answe …

Q16.A vector in $\mathrm{x}-\mathrm{y}$ plane makes an angle of $30^{\circ }$ with y-axis. The magnitude of y-component of vector is $2\sqrt{3}$. The magnitude of x-component of the vector will be :

Q17.The speed of a wave produced in water is given by $v={\lambda }^a{g}^b{\rho }^c$. Where $\lambda ,g$ and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $\mathrm{a},\mathrm{b}$ and c respectively, are :

Q18.A thermodynamic system is taken through cyclic process. The total work done in the process is :

Q19.A single slit of width $a$ is illuminated by a monochromatic light of wavelength 600 nm. The value of 'a' for which first minimum appears at $\theta =30^{\circ }$ on the screen will be :

Q20.In the given circuit, the current (I) through the battery will be :

Q21.A 20 cm long metallic rod is rotated with 210 rpm about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field 0.2 T parallel to the axis exists everywhere. The emf develop …

Q22.A network of four resistances is connected to 9 V battery, as shown in figure. The magnitude of voltage difference between the points A and B is ______ V.

Q23.The fundamental frequency of vibration of a string stretched between two rigid support is 50 Hz. The mass of the string is 18 g and its linear mass density is $20\mathrm{g}/\mathrm{m}$. The speed of the transverse waves so produced in the string is ______ ${\mathrm{ms}}^{-1}$.

Q24.As per given figure A, B and C are the first, second and third excited energy level of hydrogen atom respectively. If the ratio of the two wavelengths (i.e. $\frac{{\lambda }_1}{{\lambda }_2}$) is $\frac{7}{4n}$, then the value of $n$ will be

Q25.A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively ($k_{\text{sph}}:k_{\text{cyl}}$) is $2:\sqrt{x}$, then value of $x$ is ______.

Q26.The refractive index of a transparent liquid filled in an equilateral hollow prism is $\sqrt{2}$. The angle of minimum deviation for the liquid will be ______°.

Q27.An electron in a hydrogen atom revolves around its nucleus with a speed of $6.76\times 10^6$ ms${}^{-1}$ in an orbit of radius $0.52$ Å. The magnetic field produced at the nucleus of the hydrogen atom is ______ T.

Q28.There is an air bubble of radius 1.0 mm in a liquid of surface tension $0.075$ Nm${}^{-1}$ and density 1000 kg m${}^{-3}$ at a depth of 10 cm below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is ______ Pa ($g=10$ ms …

Q29.A block of mass 10 kg is moving along x-axis under the action of force $F=5x$ N. The work done by the force in moving the block from $x=2$ m to 4 m will be ______ J.

Q30.In the given figure the total charge stored in the combination of capacitors is 100 μC. The value of 'x' is ______.

Q1.Match List I with List II:

List I-(Monomer)
(A) Tetrafluoroethylene
(B) Acrylonitrile
(C) Caprolactam
(D) Isoprene

List II-(Polymer)
(i) Orlon
(ii) Natural rubber
(iii) Teflon
(IV) Nylon-6

Choose the correct answer from the options given below:

Q2.The product formed in the following multistep reaction is:

Q3.The possibility of photochemical smog formation will be minimum at

Q4.Which one of the following is not an example of calcination?

Q5.Consider the following statements:
(A) ${\mathrm{NF}}_3$ molecule has a trigonal planar structure.
(B) Bond length of ${\mathrm{N}}_2$ is shorter than ${\mathrm{O}}_2$.
(C) Isoelectronic molecules or ions have identical bond order.
(D) Dipole moment of …

Q6.Consider the following sequence of reactions:

The product 'B' is

Q7.The number of $\mathrm{P}-\mathrm{O}-\mathrm{P}$ bonds in ${\mathrm{H}}_4{\mathrm{P}}_2{\mathrm{O}}_7$, ${\left({\mathrm{HPO}}_3\right)}_3$ and ${\mathrm{P}}_4{\mathrm{O}}_{10}$ are respectively.

Q8.Given below are two statements:

Statement I: According to Bohr's model of hydrogen atom, the angular momentum of an electron in a given stationary state is quantised.

Statement II : The concept of electron in Bohr's orbit, violates the Heisenberg uncertainty principle. In the l …

Q9.Decreasing order of reactivity towards electrophilic substitution for the following compounds is :

Q10.Which of the following statement(s) is/are correct?
(A) The pH of $1\times 10^{-8}\mathrm{M}\mathrm{HCl}$ solution is 8 .
(B) The conjugate base ${\mathrm{H}}_2{\mathrm{PO}}_4{}^{-}$ is ${\mathrm{HPO}}_4{}^{2-}$.
(C) ${\mathrm{K}}_{\mathrm{w}}$ increases with increase in temp …

Q11.Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R :

Assertion (A) : ${\mathrm{BeCl}}_2$ and ${\mathrm{MgCl}}_2$ produce characteristic flame.

Reason (R) : The excitation energy is high in ${\mathrm{BeCl}}_2$ and …

Q12.In the above conversion the correct sequence of reagents to be added is

Q13.major product 'A' formed in the above reaction is

Q14.Which is not true for arginine?

Q15.During water-gas shift reaction

Q16.For a good quality cement, the ratio of silica to alumina is found to be

Q17.Which of the following statement is correct for paper chromatography?

Q18.The major product formed in the Friedel-Craft acylation of chlorobenzene is .

Q19.The complex with highest magnitude of crystal field splitting energy ( ${\Delta }_{\mathrm{o}}$ ) is

Q20.Which of the following expressions is correct in case of a CsCl unit cell (edge length'a')?

Q21.The homoleptic and octahedral complex of ${\mathrm{Co}}^{2+}$ and ${\mathrm{H}}_2\mathrm{O}$ has ____ unpaired electron(s) in the ${\mathrm{t}}_{2\mathrm{g}}$ set of orbitals.

Q22.The volume (in mL ) of $0.1\mathrm{M}{\mathrm{AgNO}}_3$ required for complete precipitation of chloride ions present in 20 mL of 0.01 M solution of $\left[\mathrm{Cr}{\left({\mathrm{H}}_2\mathrm{O}\right)}_5\mathrm{Cl}\right]{\mathrm{Cl}}_2$ as silver chloride is ____

Q23.The total change in the oxidation state of manganese involved in the reaction of ${\mathrm{KMnO}}_4$ and potassium iodide in the acidic medium is ____

Q24.In Chromyl chloride, the oxidation state of chromium is ( + ) ____

Q25.The total number of isoelectronic species from the given set is ____
${\mathrm{O}}^{2-},{\mathrm{F}}^{-},\mathrm{Al},{\mathrm{Mg}}^{2+},{\mathrm{Na}}^{+},{\mathrm{O}}^{+},\mathrm{Mg},{\mathrm{Al}}^{3+},\mathrm{F}$

Q26.The vapour pressure of $30\%(\mathrm{w}/\mathrm{v})$ aqueous solution of glucose is ____ mm Hg at $25^{\circ }\mathrm{C}$.
[Given : The density of $30\%(\mathrm{w}/\mathrm{v})$, aqueous solution of glucose is $1.2\mathrm{g}{\mathrm{cm}}^{-3}$ and vapour pressure of pu …

Q27.20 mL of 0.5 M NaCl is required to coagulate 200 mL of ${\mathrm{As}}_2{\mathrm{S}}_3$ solution in 2 hours. The coagulating value of NaCl is ______

Q28.For a reversible reaction $\mathrm{A}\rightleftharpoons \mathrm{B}$, the $\Delta {\mathrm{H}}_{\text{forward}}$ reaction $=20\mathrm{kJ}{\mathrm{mol}}^{-1}$. The activation energy of the uncatalysed forward reaction is $300\mathrm{kJ}{\mathrm{mol}}^{-1}$. When the reac …

Q29.The number of correct statements from the following is ______
(A) Conductivity always decreases with decrease in concentration for both strong and weak electrolytes.
(B) The number of ions per unit volume that carry current in a solution increases on dilution.
(C) Molar conductiv …

Q30.30.4 kJ of heat is required to melt one mole of sodium chloride and the entropy change at the melting point is $28.4\mathrm{J}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$ at 1 atm. The melting point of sodium chloride is ______ K
(Nearest Integer)

Q1.The total number of three-digit numbers, divisible by 3, which can be formed using the digits $1,3,5,8$, if repetition of digits is allowed, is:

Q2.Let S be the set of all values of $\lambda$, for which the shortest distance between the lines $\frac{\mathrm{x}-\lambda }{0}=\frac{\mathrm{y}-3}{4}=\frac{\mathrm{z}+6}{1}$ and $\frac{\mathrm{x}+\lambda }{3}=\frac{\mathrm{y}}{-4}=\frac{\mathrm{z}-6}{0}$ is 13. Then …

Q3.The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instead of 40. Then the correct variance is:

Q4.Let ABCD be a quadrilateral. If E and F are the mid points of the diagonals AC and BD respectively and $(\overrightarrow{\mathrm{AB}}-\overrightarrow{\mathrm{BC}})+(\overrightarrow{\mathrm{AD}}-\overrightarrow{\mathrm{DC}})=\mathrm{k}\overrightarrow{\mathrm{FE}}$, then k …

Q5.Let $x=x(y)$ be the solution of the differential equation $2(\mathrm{y}+2){\log }_{\mathrm{e}}(\mathrm{y}+2)\mathrm{dx}+(\mathrm{x}+4-2{\log }_{\mathrm{e}}(\mathrm{y}+2))\mathrm{dy}=0$, $\mathrm{y}>-1$ with $\mathrm{x}\left({\mathrm{e}}^4-2\right)=1$. Then …

Q6.Let $[\mathrm{x}]$ denote the greatest integer function and $\mathrm{f}(\mathrm{x})=\max \{1+\mathrm{x}+[\mathrm{x}],2+\mathrm{x},\mathrm{x}+2[\mathrm{x}]\},0\le \mathrm{x}\le 2$. Let $m$ be the number of points in $[0,2]$, where $f$ is not continuous and $n$ b …

Q7.The number of real roots of the equation $\mathrm{x}|\mathrm{x}|-5|\mathrm{x}+2|+6=0$, is

Q8.Let ${\left(a+bx+c{x}^2\right)}^{10}={\sum }_{i=0}^{20}{p}_i{x}^i,a,b,c\in \mathbb{N}$. If $p_1=20$ and ${\mathrm{p}}_2=210$, then $2(\mathrm{a}+\mathrm{b}+\mathrm{c})$ is equal to

Q9.Let the determinant of a square matrix A of order m be $\mathrm{m}-\mathrm{n}$, where m and n satisfy $4\mathrm{m}+\mathrm{n}=22$ and $17\mathrm{m}+4\mathrm{n}=93$. If det $(\mathrm{n}\mathrm{adj}(\mathrm{adj}(\mathrm{mA})))=3^a{5}^b{6}^c$, then …

Q10.Let ${\mathrm{A}}_1$ and ${\mathrm{A}}_2$ be two arithmetic means and ${\mathrm{G}}_1,{\mathrm{G}}_2,{\mathrm{G}}_3$ be three geometric means of two distinct positive numbers. Then …

Q11.If the set $\left\{\mathrm{Re}\left(\frac{z-\bar{z}+z\bar{z}}{2-3z+5\bar{z}}\right):z\in \mathbb{C},\mathrm{Re}(z)=3\right\}$ is equal to the interval $(\alpha ,\beta ]$, then $24(\beta -\alpha )$ is equal to

Q12.The number of common tangents, to the circles $x^2+y^2-18x-15y+131=0$ and ${\mathrm{x}}^2+{\mathrm{y}}^2-6\mathrm{x}-6\mathrm{y}-7=0$, is:

Q13.Negation of $\mathrm{p}\wedge (\mathrm{q}\wedge \sim (\mathrm{p}\wedge \mathrm{q}))$ is

Q14.Let the system of linear equations
$-x+2y-9z=7$
$-x+3y+7z=9$
$-2x+y+5z=8$
$-3x+y+13z=\lambda$
has a unique solution $\mathrm{x}=\alpha ,\mathrm{y}=\beta ,\mathrm{z}=\gamma$. Then the distance of the point ( $\alpha ,\beta ,\gamma$ ) from the plane …

Q15.If $(\alpha ,\beta )$ is the orthocentre of the triangle ABC with vertices $\mathrm{A}(3,-7),\mathrm{B}(-1,2)$ and $\mathrm{C}(4,5)$, then $9\alpha -6\beta +60$ is equal to:

Q16.Let the foot of perpendicular of the point $\mathrm{P}(3,-2,-9)$ on the plane passing through the points $(-1,-2,-3),(9,3,4),(9,-2,1)$ be $\mathrm{Q}(\alpha ,\beta ,\gamma )$. Then the distance of Q from the origin is:

Q17.A bag contains 6 white and 4 black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is:

Q18.If
${\int }_0^1\frac{1}{\left(5+2\mathrm{x}-2{\mathrm{x}}^2\right)\left(1+{\mathrm{e}}^{(2-4\mathrm{x})}\right)}\mathrm{dx}=\frac{1}{\alpha }{\log }_{\mathrm{e}}\left(\frac{\alpha +1}{\beta }\right)$,
$\alpha ,\beta >0$, then ${\alpha }^4-{\beta }^4$ is equal to:

Q19.Let S be the set of all $(\lambda ,\mu )$ for which the vectors $\lambda \hat{i}-\hat{j}+\hat{k},\hat{i}+2\hat{j}+\mu \hat{k}$ and $3\hat{i}-4\hat{j}+5\hat{k}$, where $\lambda -\mu =5$, are coplanar, then …

Q20.If the domain of the function
$f(x)={\log }_e\left(4x^2+11x+6\right)+{\sin }^{-1}(4\mathrm{x}+3)+{\cos }^{-1}\left(\frac{10\mathrm{x}+6}{3}\right)$ is $(\alpha ,\beta ]$,
Then $36|\alpha +\beta |$ is equal to :

Q21.If the sum of the series …

Q22.A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct cod …

Q23.Let the plane P contain the line
$2\mathrm{x}+\mathrm{y}-\mathrm{z}-3=0=5\mathrm{x}-3\mathrm{y}+4\mathrm{z}+9$ and be parallel to the line $\frac{x+2}{2}=\frac{3-y}{-4}=\frac{z-7}{5}$. Then the distance of the point $\mathrm{A}(8,-1,-19)$ from the plane P measured paral …

Q24.Let an ellipse with centre $(1,0)$ and latus rectum of length $\frac{1}{2}$ have its major axis along $x$-axis. If its minor axis subtends an angle $60^{\circ }$ at the foci, then the square of the sum of the lengths of its minor and major axes is equal to

Q25.Let $\mathrm{A}=\{1,2,3,4\}$ and R be a relation on the set $A\times A$ defined by $\mathrm{R}=\{((\mathrm{a},\mathrm{b}),(\mathrm{c},\mathrm{d})):2\mathrm{a}+3\mathrm{b}=4\mathrm{c}+5\mathrm{d}\}$. Then the number of elements in R is:

Q26.The number of elements in the set $\{\mathrm{n}\in \mathbb{N}:10\le \mathrm{n}\le 100$ and $3^{\mathrm{n}}-3$ is a multiple of 7$\}$ is ____

Q27.If the line $\mathrm{x}=\mathrm{y}=\mathrm{z}$ intersects the line $\mathrm{x}\sin \mathrm{A}+\mathrm{y}\sin \mathrm{B}+\mathrm{z}\sin \mathrm{C}-18=0=\mathrm{x}\sin 2\mathrm{A}+\mathrm{y}\sin 2\mathrm{B}+\mathrm{z}\sin 2\mathrm{C}-9$, where …

Q28.If the area bounded by the curve $2y^2=3x$, lines $x+y=3,y=0$ and outside the circle $(x-3{)}^2+y^2=2$ is A, then $4(\pi +4\mathrm{A})$ is equal to ____

Q29.Consider the triangles with vertices $\mathrm{A}(2,1)$ $\mathrm{B}(0,0)$ and $\mathrm{C}(\mathrm{t},4),\mathrm{t}\in [0,4]$. If the maximum and the minimum perimeters of such triangles are obtained at $\mathrm{t}=\alpha$ and $\mathrm{t}=\beta$ respectively, then …

Q30.Let $\mathrm{f}(\mathrm{x})=\int \frac{\mathrm{dx}}{\left(3+4{\mathrm{x}}^2\right)\sqrt{4-3{\mathrm{x}}^2}},|\mathrm{x}|<\frac{2}{\sqrt{3}}$. If $\mathrm{f}(0)=0$ and $f(1)=\frac{1}{\alpha \beta }{\tan }^{-1}\left(\frac{\alpha }{\beta }\right),\alpha ,\beta >0$, then …