JEE Main 2023 · 10 Apr 2023 · Shift 1

Q1.A physical quantity $P$ is given as


The percentage error in the measurement of $\mathrm{a},\mathrm{b},\mathrm{c}$ and d are $1\%,2\%,3\%$ and $4\%$ respectively. The percentage error in the measurement of quantity P will be

Q2.Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth $\mathrm{d}=\frac{\mathrm{R}}{2}$ from the surface of earth, if its weight on the surface of earth is 200 N, will be:
(Given $\mathrm{R}=$ Radius of earth)

Q3.A zener diode of power rating 1.6 W is to be used as voltage regulator. If the zener diode has a breakdown of 8 V and it has to regulate voltage fluctuating between 3 V and 10 V. The value of resistance $R_s$ for safe operation of diode will be:

Q4.The range of the projectile projected at an angle of $15^{\circ }$ with horizontal is 50 m. If the projectile is projected with same velocity at an angle of $45^{\circ }$ with horizontal, then its range will be:

Q5.A carrier wave of amplitude 15 V is modulated by a sinusoidal base band signal of amplitude 3 V. The ratio of maximum amplitude to minimum amplitude in an amplitude modulated wave is:

Q6.The angular momentum for the electron in Bohr's orbit is L. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be:

Q7.A particle of mass m moving with velocity v collides with a stationary particle of mass 2m. After collision, they stick together and continue to move together with velocity

Q8.Given below are two statement:

Statement I: If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes double.
Statement II: Increasing current sensitivity of a moving coil galvanometer by only increasing the number of turns …

Q9.The equivalent resistance of the circuit shown below between points a and b is:

Q10.Consider two containers A and B containing monoatomic gases at the same Pressure (P), Volume (V) and Temperature (T). The gas in A is compressed isothermally to $\frac{1}{8}$ of its original volume while the gas B is compressed adiabatically to $\frac{1}{8}$ of its original v …

Q11.Given below are two statements:

Statement I: Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an AC source, when resonance occurs
Statement II: Maximum power is dissipated in a circuit containing pure resistor d …

Q12.Two satellites of masses m and 3 m revolve around the earth in circular orbits of radii $r\&3r$ respectively. The ratio of orbital speeds of the satellites respectively is :

Q13.Given below are two statements:

Statement I: Pressure in a reservoir of water is same at all points at the same level of water.
Statement II : The pressure applied to enclosed water is transmitted in all directions equally.
In the light of the above statements, choose the correc …

Q14.The equivalent capacitance of the combination shown is

Q15.The energy of an electromagnetic wave contained in a small volume oscillates with

Q16.An object is placed at a distance of 12 cm in front of a plane mirror. The virtual and erect image is formed by the mirror. Now the mirror is moved by 4 cm towards the stationary object. The distance by which the position of image would be shifted, will be:

Q17.The de Broglie wavelength of a molecule in a gas at room temperature ( 300 K ) is ${\lambda }_1$. If the temperature of the gas is increased to 600 K , then the de Broglie wavelength of the same gas molecule becomes

Q18.A particle executes S.H.M. of amplitude A along $x$-axis. At $t=0$, the position of the particle is $\mathrm{x}=\frac{\mathrm{A}}{2}$ and it moves along positive x-axis. The displacement of particle in time $t$ is $\mathrm{x}=\mathrm{A}\sin (\omega \mathrm{t}+\delta )$, …

Q19.The position-time graphs for two students A and B returning from the school to their homes are shown in figure :

(A) A lives closer to the school
(B) B lives closer to the school
(C) A takes lesser time to reach home
(D) A travels faster than B
(E) B travels faster than A

Choos …

Q20.A closed circular tube of average radius 15 cm , whose inner walls are rough, is kept in vertical plane. A block of mass 1 kg just fit inside the tube. The speed of block is $22\mathrm{m}/\mathrm{s}$, when it is introduced at the top of tube. After completing five oscillati …

Q21.If the earth suddenly shrinks to $\frac{1}{64}$ th of its original volume with its mass remaining the same, the period of rotation of earth becomes $\frac{24}{x}h$. The value of $x$ is ____ .

Q22.The current required to be passed through a solenoid of 15 cm length and 60 turns in order to demagnetise a bar magnet of magnetic intensity $2.4\times 10^3{\mathrm{Am}}^{-1}$ is ____ A.

Q23.A 1 m long metal rod XY completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the circuit is $5\Omega$, the force needed to move the rod in direction, as indicated, with a constant s …

Q24.A transverse harmonic wave on a string is given by $y(x,t)=5\sin (6t+0.003x)$ where $x$ and $y$ are in cm and $t$ in sec. The wave velocity is $\_\_\_\_$ ${\mathrm{ms}}^{-1}$.

Q25.The decay constant for a radioactive nuclide is $1.5\times 10^{-5}{\mathrm{s}}^{-1}$. Atomic mass of the substance is 60 g mole${}^{-1}$, $({\mathrm{N}}_{\mathrm{A}}=6\times 10^{23})$. The activity of $1.0\mu \mathrm{g}$ of the substance is $\_\_\_\_$ $\times 10^{10}\mathrm{Bq}$.

Q26.Three concentric spherical metallic shells $\mathrm{X}$, $\mathrm{Y}$ and $\mathrm{Z}$ of radius $\mathrm{a}$, $\mathrm{b}$ and $\mathrm{c}$ respectively $[\mathrm{a}<\mathrm{b}<\mathrm{c}]$ have surface charge densities $\sigma$, $-\sigma$ and $\sigma$, respectively. The shells …

Q27.10 resistors each of resistance $10\Omega$ can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be $\_\_\_\_$.

Q28.Two wires each of radius 0.2 cm and negligible mass, one made of steel and other made of brass are loaded as shown in the figure. The elongation of the steel wire is $\_\_\_\_$ $\times 10^{-6}\mathrm{m}$. [Young's modulus for steel $=2\times 10^{11}{\mathrm{Nm}}^{-2}$ and …

Q1.Using column chromatography, mixture of two compounds 'A' and 'B' was separated. 'A' eluted first, this indicates 'B' has

Q2.Prolonged heating is avoided during the preparation of ferrous ammonium sulphate to

Q3.Lime reacts exothermally with water to give 'A' which has low solubility in water. Aqueous solution of 'A' is often used for the test of ${\mathrm{CO}}_2$, a test in which insoluble B is formed. If B is further reacted with ${\mathrm{CO}}_2$ then soluble compound is formed 'A' is

Q4.The pair from the following pairs having both compounds with net non-zero dipole moment is

Q5.Match List-I with List-II

List-I (Industry):
(A) Steel plants
(B) Thermal power plants
(C) Fertilizer industries
(D) Paper mills

List-II (Waste Generated):
(I) Gypsum
(II) Fly ash
(III) Slag
(IV) Bio-degradable Wastes

Choose the correct answer from the options given below:

Q6.Isomeric amines with molecular formula ${\mathrm{C}}_8{\mathrm{H}}_{11}\mathrm{N}$ give the following tests
Isomer (P) ⇒ Can be prepared by Gabriel phthalimide synthesis
Isomer (Q) ⇒ Reacts with Hinsberg's reagent to give solid insoluble in NaOH
Isomer (R) ⇒ Reacts with HONO follo …

Q7.Given below are two statements

Statement I : Aqueous solution of ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$ is preferred as a primary standard in volumetric analysis over ${\mathrm{Na}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$ aqueous solution
Statement II : …

Q8.The one that does not stabilize $2^{\circ }$ and $3^{\circ }$ structures of proteins is

Q9.Given below are two reactions, involved in the commercial production of dihydrogen $({\mathrm{H}}_2)$.
The two reactions are carried out at temperature "${\mathrm{T}}_1$" and "${\mathrm{T}}_2$" respectively …

Q10.Which of the following statements are correct?
(A) The ${\mathrm{M}}^{3+}/{\mathrm{M}}^{2+}$ reduction potential for iron is greater than manganese
(B) The higher oxidation states of first row d-block elements get stabilized by oxide ion.
(C) Aqueous solution of ${\mathrm{Cr}}^{2+}$ …

Q11.Which of the following is used as a stabilizer during the concentration of sulphide ores?

Q12.The octahedral diamagnetic low spin complex among the following is

Q13.Given
(A) $2\mathrm{CO}(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})\to 2{\mathrm{CO}}_2(\mathrm{g})\Delta {\mathrm{H}}_1^{\theta }=-\mathrm{x}\mathrm{kJ}{\mathrm{mol}}^{-1}$
(B) C(graphite) …

Q14.The compound which does not exist is

Q15.The number of molecules and moles in 2.8375 litres of ${\mathrm{O}}_2$ at STP are respectively

Q16.The enthalpy change for the adsorption process and micelle formation respectively are

Q17.Suitable reaction condition for preparation of Methyl phenyl ether is

Q18.Identify the correct order of reactivity for the following pairs towards the respective mechanism
(A)
(B)
(C) Electrophilic substitution
(D) Nucleophilic substitution

Choose the correct answer from the options given below :

Q19.The number of correct statement/s involving equilibria in physical process from the following is
(A) Equilibrium is possible only in a closed system at a given temperature
(B) Both the opposing processes occur at the same rate.
(C) When equilibrium is attained at a given temperat …

Q20.The number of bent-shaped molecule/s from the following is ____
${\mathrm{N}}_3^{-},{\mathrm{NO}}_2^{-},{\mathrm{I}}_3^{-},{\mathrm{O}}_3,{\mathrm{SO}}_2$

Q21.A molecule undergoes two independent first order reactions whose respective half lives are 12 min and 3 min . If both the reactions are occurring then the time taken for the $50\%$ consumption of the reactant is ____ min. (Nearest integer)

Q22.The number of incorrect statement/s about the black body from the following is ____
(A) Emit or absorb energy in the form of electromagnetic radiation
(B) Frequency distribution of the emitted radiation depends on temperature
(C) At a given temperature, intensity vs frequency cur …

Q23.In the following reactions, the total number of oxygen atoms in X and Y is ____
${\mathrm{Na}}_2\mathrm{O}+{\mathrm{H}}_2\mathrm{O}\to 2\mathrm{X}$
${\mathrm{Cl}}_2{\mathrm{O}}_7+{\mathrm{H}}_2\mathrm{O}\to 2\mathrm{Y}$

Q24.${\mathrm{FeO}}_4^{2-}\stackrel{+2.2\mathrm{V}}{\to }{\mathrm{Fe}}^{3+}\stackrel{+0.70\mathrm{V}}{\to }{\mathrm{Fe}}^{2+}\stackrel{-0.45\mathrm{V}}{\to }{\mathrm{Fe}}^0$

${\mathrm{E}}_{{\mathrm{FeO}}_4^{2-}/{\mathrm{Fe}}^{2+}}^{\theta }$ is $\mathrm{x}\times 10^{-3}\mathrm{V}$. T …

Q25.If the degree of dissociation of an aqueous solution of a weak monobasic acid is determined to be 0.3, then the observed depression in freezing point will be _____ % higher than the expected / theoretical depression in freezing point. (Nearest integer)

Q26.In potassium ferrocyanide, there are ____ pairs of electrons in the ${\mathrm{t}}_{2\mathrm{g}}$ set of orbitals

Q27.At constant temperature a gas is at a pressure of 940.3 mm Hg. The pressure at which its volume decreases by 40% is ____ mm Hg.
(Nearest Integer)

Q28.The sum of lone pairs present on the central atom of the interhalogen ${\mathrm{IF}}_5$ and ${\mathrm{IF}}_7$ is ____

Q1.Let O be the origin and the position vector of the point P be $-\hat{i}-2\hat{j}+3\hat{k}$. If the position vectors of the points $\mathrm{A},\mathrm{B}$ and C are $-2\hat{i}+\hat{j}-3\hat{k},2\hat{i}+4\hat{j}-2\hat{k}$ and $-4\hat{i}+2\hat{j}-\hat{k}$ respecti …

Q2.Let the ellipse $\mathrm{E}:{\mathrm{x}}^2+9{\mathrm{y}}^2=9$ intersect the positive x - and y -axes at the points A and B respectively Let the major axis of E be a diameter of the circle C . Let the line passing through A and B meet the circle C at the point P . If the area …

Q3.If $f(x)=\frac{\left(\tan 1^o\right)x+{\log }_e(123)}{x{\log }_e(1234)-\left(\tan 1^o\right)},x>0$, then the least value of $f(f(x))+f\left(f\left(\frac{4}{x}\right)\right)$ is

Q4.A square piece of tin of side 30 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. If the volume of the box is maximum, then its surface area ( $\mathrm{in}{\mathrm{cm}}^2$ ) is equal to

Q5.Let $f$ be a differentiable function such that ${\mathrm{x}}^2\mathrm{f}(\mathrm{x})-\mathrm{x}=4{\int }_0^{x}tf(t)dt,f(1)=\frac{2}{3}$.

Then $18f(3)$ is equal to

Q6.A line segment AB of length $\lambda$ moves such that the points A and B remain on the periphery of a circle of radius $\lambda$. Then the locus of the point, that divides the line segment AB in the ratio $2:3$, is a circle of radius

Q7.Let the complex number $\mathrm{z}=\mathrm{x}+$ iy be such that $\frac{2z-3i}{2z+i}$ is purely imaginary. If $x+y^2=0$, then $y^4+y^2-y$ is equal to :

Q8.$96\cos \frac{\pi }{33}\cos \frac{2\pi }{33}\cos \frac{4\pi }{33}\cos \frac{8\pi }{33}\cos \frac{16\pi }{33}$ is equal to

Q9.If A is a $3\times 3$ matrix and $|\mathrm{A}|=2$, then $\left|3adj\left(|3A|A^2\right)\right|$ is equal to

Q10.The slope of tangent at any point $(\mathrm{x},\mathrm{y})$ on a curve $y=y(x)$ is $\frac{x^2+y^2}{2xy},x>0$. If $y(2)=0$, then a value of $y(8)$ is

Q11.For the system of linear equations


Which of the following is NOT correct?

Q12.Let N denotes the sum of the numbers obtained when two dice are rolled. If the probability that $2^{\mathrm{N}}<\mathrm{N}!$ is $\frac{m}{n}$, where m and n are coprime, then $4m-3n$ is equal to

Q13.Let P be the point of intersection of the line $\frac{x+3}{3}=\frac{y+2}{1}=\frac{1-z}{2}$ and the plane $x+y+z=2$.

If the distance of the point P from the plane $3x-4y+12z=32$ is $q$, then $q$ and $2q$ are the roots of the equation

Q14.The negation of the statement $(p\vee q)\wedge (q\vee (\sim r))$ is

Q15.If the coefficient of $x^7$ in ${\left(ax-\frac{1}{b{x}^2}\right)}^{13}$ and the coefficient of $x^{-5}$ in ${\left(ax+\frac{1}{b{x}^2}\right)}^{13}$ are equal, then $a^4{b}^4$ is equal to :

Q16.Let two vertices of triangle ABC be $(2,4,6)$ and $(0,-2,-5)$, and its centroid be $(2,1,-1)$. If the image of third vertex in the plane $x+2y+4z=11$ is $(\alpha ,\beta ,\gamma )$, then $\alpha \beta +\beta \gamma +\gamma \alpha$ is equal to

Q17.The shortest distance between the lines $\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2}$ and $\frac{x-4}{1}=\frac{y-1}{2}=\frac{z+3}{0}$ is

Q18.If $I(x)=\int e^{{\sin }^{2}x}(\cos x\sin 2x-\sin x)dx$ and $I(0)=1$, then $I\left(\frac{\pi }{3}\right)$ is equal to

Q19.Let the first term $a$ and the common ratio r of a geometric progression be positive integers. If the sum of its squares of first three terms is 33033, then the sum of these three terms is equal to

Q20.An arc PQ of a circle subtends a right angle at its centre O. The mid point of the arc PQ is R. If $\overrightarrow{OP}=\vec{u}$, $\overrightarrow{OR}=\vec{v}$ and $\overrightarrow{OQ}=\alpha \vec{u}+\beta \vec{v}$, then $\alpha ,{\beta }^2$ are the roots of the equation

Q21.The coefficient of $x^7$ in $(1-x+2x^3{)}^{10}$ is ______.

Q22.Let $f:(-2,2)\to \mathbb{R}$ be defined by

Where $[x]$ denotes the greatest integer function. If m and n respectively are the number of points in $(-2,2)$ at which $y=|f(x)|$ is not continuous a …

Q23.The sum of all those terms, of the arithmetic progression $3,8,13,\dots ,373$, which are not divisible by 3, is equal to ______.

Q24.Let a common tangent to the curves $y^2=4x$ and $(x-4{)}^2+y^2=16$ touch the curves at the points P and Q. Then $(PQ{)}^2$ is equal to ______.

Q25.The number of permutations, of the digits $1,2,3$, ..... 7 without repetition, which neither contain the string 153 nor the string 2467, is ______.

Q26.Let $\mathrm{y}=\mathrm{p}(\mathrm{x})$ be the parabola passing through the points $(-1,0),(0,1)$ and $(1,0)$. If the area of the region $\left\{(x,y):(x+1{)}^2+(y-1{)}^2\le 1,y\le p(x)\right\}$ is A , then $12(\pi -4\mathrm{A})$ is equal to ____.

Q27.If the mean of the frequency distribution

\begin{tabular}{|l|l|l|l|l|l|}
\hline Class: & $0-10$ & $10-20$ & $20-30$ & $30-40$ & $40-50$ \\
\hline Frequency & 2 & 3 & x & 5 & 4 \\
\hline
\end{tabular}

is 28 , then its variance is ____.

Q28.Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840 , then the total numbers of persons, who participated in the tournament, is ____.

Q29.The number of elements in the set $\left\{n\in \mathbb{Z}:\left|n^2-10n+19\right|<6\right\}$ is ____.