JEE Main 2023 · 01 Feb 2023 · Shift 1

Q1.An object moves with speed $v_1,v_2$, and $v_3$ along a line segment $\mathrm{AB},\mathrm{BC}$ and CD respectively as shown in figure. Where $\mathrm{AB}=\mathrm{BC}$ and $\mathrm{AD}=3\mathrm{AB}$, then average speed of the object will be :

Q2.Given below are two statements:
Statement-I: Acceleration due to gravity is different at different places on the surface of earth.
Statement-II: Acceleration due to gravity increases as we go down below the earth's surface.
In the light of the above statements, choose the correct …

Q3.If earth has a mass nine times and radius twice to the of a planet P. Then $\frac{v_e}{3}\sqrt{x}{\mathrm{ms}}^{-1}$ will be the minimum velocity required by a rocket to pull out of gravitational force of P, where $v_e$ is escape velocity on earth. The value of $x$ is

Q4.'$n$' polarizing sheets are arranged such that each makes an angle $45^{\circ }$ with the proceeding sheet. An unpolarized light of intensity $I$ is incident into this arrangement. The output intensity is found to be $\frac{I}{64}$. The value of $n$ will be:

Q5.Find the magnetic field at the point P in figure. The curved portion is a semicircle connected to two long straight wires.

Q6.Which of the following frequencies does not belong to FM broadcast.

Q7.A steel wire with mass per unit length $7.0\times 10^{-3}\mathrm{kg}{\mathrm{m}}^{-1}$ is under tension of 70 N. The speed of transverse waves in the wire will be:

Q8.A child stands on the edge of the cliff 10 m above the ground and throws a stone horizontally with an initial speed of $5{\mathrm{ms}}^{-1}$. Neglecting the air resistance, the speed with which the stone hits the ground will be ____ ${\mathrm{ms}}^{-1}$ (given, …

Q9.A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $\lambda$. An alpha particle having certain kinetic energy has the same de-Brogle wavelength $\lambda$. The ratio of kinetic energy of proton and that of alpha particle is:

Q10.A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is (given, $\gamma =\frac{3}{2}$):

Q11.The equivalent resistance between $A$ and $B$ of the network shown in figure:

Q12.Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region $E_{\mathrm{I}}$, $E_{\mathrm{II}}$ and $E_{\mathrm{III}}$ are:

Q13.A mercury drop of radius $10^{-3}\mathrm{m}$ is broken into 125 equal size droplets. Surface tension of mercury is $0.45{\mathrm{Nm}}^{-1}$. The gain in surface energy is:

Q14.The mass of proton, neutron and helium nucleus are respectively $1.0073\mathrm{u},1.0087\mathrm{u}$ and 4.0015u.
The binding energy of helium nucleus is:

Q15.$\left(P+\frac{a}{V^2}\right)(V-b)=RT$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a,b,R$ are the constants. The physical quantity, which has dimensional formula as that of …

Q16.The average kinetic energy of a molecule of the gas is

Q17.A block of mass 5 kg is placed at rest on a table of rough surface. Now, if a force of 30 N is applied in the direction parallel to surface of the table, the block slides through a distance of 50 m in an interval of time 10s. Coefficient of kinetic friction is (given, …

Q18.A charge particle of $2\mu \mathrm{C}$ accelerated by a potential difference of 100 V enters a region of uniform magnetic field of magnitude 4 mT at right angle to the direction of field. The charge particle completes semicircle of radius 3 cm inside magnetic field. The mass o …

Q19.In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of emf 1.5 V is found to be 60 cm . If this cell is replaced by another cell of emf $E$. the length-of null point increases by 40 cm . The value of $E$ is …

Q20.A small particle moves to position $5\hat{i}-2\hat{j}+\hat{k}$ from its initial position $2\hat{i}+3\hat{j}-4\hat{k}$ under the action of force $5\hat{i}+2\hat{j}+7\hat{k}\mathrm{N}$. The value of work done will be ____ J.

Q21.A light of energy 12.75 eV is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $\frac{x}{\pi }\times 10^{-17}\mathrm{eVs}$. The value of $x$ is \ …

Q22.A certain pressure ' $P$ ' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to $0.01\%$ whereas the liquid gets compressed to $0.03\%$. The ratio of Bulk modulus of water to that of the liquid is $\frac{3}{x}$. The value of $x$ …

Q23.Two equal positive point charges are separated by a distance $2a$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $q_0$ becomes maximum is $\frac{a}{\sqrt{x}}$. …

Q24.A thin cylindrical rod of length 10 cm is placed horizontally on the principle axis of a concave mirror of focal length 20 cm. The rod is placed in a such a way that mid point of the rod is at 40 cm from the pole of mirror. The length of the image formed by the mirror will be …

Q25.A solid cylinder is released from rest from the top of an inclined plane of inclination $30^{\circ }$ and length 60 cm. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ______ ${\mathrm{ms}}^{-1}$. (Given …

Q26.The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy will be 25% more than the potential energy is: ______ cm.

Q27.A series LCR circuit is connected to an ac source of 220 V, 50 Hz. The circuit contain a resistance $R=100\Omega$ and an inductor of inductive reactance $X_L=79.6\Omega$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be …

Q28.Match List I with List II :

Q1.Which of the following represents the lattice structure of ${\mathrm{A}}_{0.95}\mathrm{O}$ containing ${\mathrm{A}}^{2+},{\mathrm{A}}^{3+}$ and ${\mathrm{O}}^{2-}$ ions?
$\odot {\mathrm{A}}^{2+}\odot {\mathrm{A}}^{3+}\odot {\mathrm{O}}^{2-}$
A. (see structure)
B. (see structure)
C. …

Q2.The correct representation in six membered pyranose form for the following sugar [ X ] is

Q3.Highest oxidation state of Mn is exhibited in ${\mathrm{Mn}}_2{\mathrm{O}}_7$. The correct statements about ${\mathrm{Mn}}_2{\mathrm{O}}_7$ are
(A) Mn is tetrahedrally surrounded by oxygen atoms
(B) Mn is octahedrally surrounded by oxygen atoms
(C) Contains …

Q4.Decreasing order of dehydration of the following alcohols is
a (see structure)
b (see structure)
c (see structure)
d (see structure)

Q5.Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Amongst $\mathrm{He},\mathrm{Ne},\mathrm{Ar}$ and Kr ;
1 g of activated charcoal adsorbs more of Kr .
Reason R : The critical volume …

Q6.In the following reaction, ' $A$ ' is

Q7.Given below are two statements:

Statement I: Chlorine can easily combine with oxygen to from oxides; and the product has a tendency to explode.
Statement II: Chemical reactivity of an element can be determined by its reaction with oxygen and halogens.
In the light of the above s …

Q8.Resonance in carbonate ion $\left({\mathrm{CO}}_3^{2-}\right)$ is

Which of the following is true?

Q9.Identify the incorrect option from the following:

Q10.A solution of ${\mathrm{FeCl}}_3$ when treated with ${\mathrm{K}}_4\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]$ gives a prussiun blue precipitate due to the formation of

Q11.Which of the following are the example of double salt?
(A) ${\mathrm{FeSO}}_4\cdot {\left({\mathrm{NH}}_4\right)}_2{\mathrm{SO}}_4\cdot 6{\mathrm{H}}_2\mathrm{O}$
(B) ${\mathrm{CuSO}}_4\cdot 4{\mathrm{NH}}_3\cdot {\mathrm{H}}_2\mathrm{O}$
(C) …

Q12.Which of the following complex will show largest splitting of d-orbitals?

Q13.How can photochemical smog be controlled?

Q14.Choose the correct statement(s):
(A) Beryllium oxide is purely acidic in nature.
(B) Beryllium carbonate is kept in the atmosphere of ${\mathrm{CO}}_2$.
(C) Beryllium sulphate is readily soluble in water.
(D) Beryllium shows anomalous behavior.

Choose the correct answer from t …

Q15.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: In an Ellingham diagram, the oxidation of carbon to carbon monoxide shows a negative slope with respect to temperature.
Reason R: CO tends to get decomposed at higher …

Q16.But-2-yne is reacted separately with one mole of Hydrogen as shown below: …

Q17.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Hydrogen is an environment friendly fuel.
Reason R: Atomic number of hydrogen is 1 and it is a very light element.
In the light of the above statements, choose the co …

Q18.Match List I and List II.

Choose the correct answer from the options given below:

Q19.The density of 3 M solution of NaCl is $1.0\mathrm{g}{\mathrm{mL}}^{-1}$. Molality of the solution is ____ $\times 10^{-2}\mathrm{m}$. (Nearest integer).

Given: Molar mass of Na and Cl is 23 and $35.5\mathrm{g}{\mathrm{mol}}^{-1}$ respectively.

Q20.Electrons in a cathode ray tube have been emitted with a velocity of $1000{\mathrm{ms}}^{-1}$. The number of following statements which is/are true about the emitted radiation is ____.

Given : …

Q21.Sum of oxidation states of bromine in bromic acid and perbromic acid is ____.

Q22.At what pH , given half cell ${\mathrm{MnO}}_4^{-}(0.1\mathrm{M})\mid {\mathrm{Mn}}^{2+}(0.001\mathrm{M})$ will have electrode potential of 1.282 V ?
____ (Nearest Integer)

Given …

Q23.Number of isomeric compounds with molecular formula ${\mathrm{C}}_9{\mathrm{H}}_{10}\mathrm{O}$ which
(i) do not dissolve in NaOH
(ii) do not dissolve in HCl.
(iii) do not give orange precipitate with 2, $4-\mathrm{DNP}$
(iv) on hydrogenation give identical compound with mole …

Q24.(i) $\mathrm{X}(\mathrm{g})\rightleftharpoons \mathrm{Y}(\mathrm{g})+\mathrm{Z}(\mathrm{g}){\mathrm{K}}_{\mathrm{p}1}=3$
(ii) $\mathrm{A}(\mathrm{g})\rightleftharpoons 2\mathrm{B}(\mathrm{g}){\mathrm{K}}_{\mathrm{p}2}=1$

If the degree of dissociation and ini …

Q25.The total number of chiral compound/s from the following is ____.

Q26.A and B are two substances undergoing radioactive decay in a container. The half life of A is 15 min and that of B is 5 min. If the initial concentration of B is 4 times that of A and they both start decaying at the same time, how much time will it take for the concentration of b …

Q27.At $25^{\circ }\mathrm{C}$, the enthalpy of the following processes are given:
${\mathrm{H}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})\to 2\mathrm{OH}(\mathrm{g})\Delta {\mathrm{H}}^{\mathrm{o}}=78\mathrm{kJ}{\mathrm{mol}}^{-1}$ …

Q28.25 mL of an aqueous solution of KCl was found to require 20 mL of $1\mathrm{M}{\mathrm{AgNO}}_3$ solution when titrated using ${\mathrm{K}}_2{\mathrm{CrO}}_4$ as an indicator. What is the depression in freezing point of KCl solution of the given concentration? ____ (Neares …

Q1.${\lim }_{n\to \infty }\left(\frac{1}{1+n}+\frac{1}{2+n}+\frac{1}{3+n}+\dots +\frac{1}{2n}\right)$ is equal to :-

Q2.The negation of the expression $\mathrm{q}\vee ((\sim \mathrm{q})\wedge \mathrm{p})$ is equivalent to

Q3.In a binomial distribution $\mathrm{B}(\mathrm{n},\mathrm{p})$, the sum and product of the mean & variance are 5 and 6 respectively, then find $6(\mathrm{n}+\mathrm{p}-\mathrm{q})$ is equal to :-

Q4.The sum to 10 terms of the series $\frac{1}{1+1^2+1^4}+\frac{2}{1+2^2+2^4}+\frac{3}{1+3^2+3^4}+\dots$. is:-

Q5.The value of
$\frac{1}{1!50!}+\frac{1}{3!48!}+\frac{1}{5!46!}+\dots .+\frac{1}{49!2!}+\frac{1}{51!1!}$ is

Q6.If the orthocentre of the triangle, whose vertices are $(1,2),(2,3)$ and $(3,1)$ is $(\alpha ,\beta )$, then the quadratic equation whose roots are $\alpha +4\beta$ and $4\alpha +\beta$, is

Q7.For a triangle ABC , the value of $\cos 2\mathrm{A}+\cos 2\mathrm{B}+\cos 2\mathrm{C}$ is least. If its inradius is 3 and incentre is M , then which of the following is NOT correct?

Q8.The combined equation of the two lines $\mathrm{ax}+\mathrm{by}+\mathrm{c}=0$ and ${\mathrm{a}}^{\prime }\mathrm{x}+{\mathrm{b}}^{\prime }\mathrm{y}+{\mathrm{c}}^{\prime }=0$ can be written as …

Q9.The shortest distance between the lines $\frac{x-5}{1}=\frac{y-2}{2}=\frac{z-4}{-3}$ and $\frac{x+3}{1}=\frac{y+5}{4}=\frac{z-1}{-5}$ is

Q10.Let S denote the set of all real values of $\lambda$ such that the system of equations
$\lambda \mathrm{x}+\mathrm{y}+\mathrm{z}=1$
$\mathrm{x}+\lambda \mathrm{y}+\mathrm{z}=1$
$\mathrm{x}+\mathrm{y}+\lambda \mathrm{z}=1$
is inconsistent, then …

Q11.Let
$S=\left\{x:x\in \mathbb{R}\text{ and }(\sqrt{3}+\sqrt{2}{)}^{x^2-4}+(\sqrt{3}-\sqrt{2}{)}^{x^2-4}=10\right\}$

Then $\mathrm{n}(\mathrm{S})$ is equal to

Q12.Let S be the set of all solutions of the equation ${\cos }^{-1}(2\mathrm{x})-2{\cos }^{-1}\left(\sqrt{1-{\mathrm{x}}^2}\right)=\pi ,\mathrm{x}\in \left[-\frac{1}{2},\frac{1}{2}\right]$. Then ${\sum }_{\mathrm{x}\in \mathrm{S}}2{\sin }^{-1}\left({\mathrm{x}}^2-1\right)$ is equal to

Q13.If the center and radius of the circle $\left|\frac{z-2}{z-3}\right|=2$ are respectively ( $\alpha ,\beta$ ) and $\gamma$, then $3(\alpha +\beta +\gamma )$ is equal to

Q14.If $y=y(x)$ is the solution curve of the differential equation $\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y}\tan \mathrm{x}=\mathrm{x}\sec \mathrm{x},0\le \mathrm{x}\le \frac{\pi }{3}$, $y(0)=1$, then $y\left(\frac{\pi }{6}\right)$ is equal to

Q15.Let $R$ be a relation on $\mathbb{R}$, given by $\mathrm{R}=\{(\mathrm{a},\mathrm{b}):3\mathrm{a}-3\mathrm{b}+\sqrt{7}$ is an irrational number}. Then $R$ is

Q16.Let $f(\mathrm{x})=\left|\begin{array}{ccc}1+{\sin }^2\mathrm{x}& {\cos }^2\mathrm{x}& \sin 2\mathrm{x}\\ {\sin }^2\mathrm{x}& 1+{\cos }^2\mathrm{x}& \sin 2\mathrm{x}\\ {\sin }^2\mathrm{x}& {\cos }^2\mathrm{x}& 1+\sin 2\mathrm{x}\end{array}\right|$, …

Q17.Let $\mathrm{f}(\mathrm{x})=2\mathrm{x}+{\tan }^{-1}\mathrm{x}$ and $\mathrm{g}(\mathrm{x})={\log }_{\mathrm{e}}\left(\sqrt{1+{\mathrm{x}}^2}+\mathrm{x}\right)$, $x\in [0,3]$. Then

Q18.The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are $1,3,5$, then the sum of cubes of the remaining two observations is

Q19.The area enclosed by the closed curve C given by the differential equation $\frac{dy}{dx}+\frac{x+a}{y-2}=0,y(1)=0$ is $4\pi$.

Let P and Q be the points of intersection of the curve C and the y -axis. If normals at P and Q on the curve C intersect x -axis at points R and …

Q20.Let ${\mathrm{a}}_1=8,{\mathrm{a}}_2,{\mathrm{a}}_3,\dots {\mathrm{a}}_{\mathrm{n}}$ be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170 , then the product of its middle two terms is ______.

Q21.$\mathrm{A}(2,6,2),\mathrm{B}(-4,0,\lambda ),\mathrm{C}(2,3,-1)$ and $\mathrm{D}(4,5,0)$, $|\lambda |\le 5$ are the vertices of a quadrilateral ABCD . If its area is 18 square units, then $5-6\lambda$ is equal to ______.

Q22.The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7 is ______.

Q23.The remainder when $19^{200}+23^{200}$ is divided by 49 , is ______.

Q24.If

where $l,m,n\in \mathbb{N}$, $m$ and $n$ are coprime then $l+m+n$ is equal to ____.

Q25.If $f(x)=x^2+g^{\prime }(1)x+g^{\prime \prime }(2)$ and
$g(x)=f(1)x^2+x{f}^{\prime }(x)+f^{\prime \prime }(x)$,
then the value of $f(4)-g(4)$ is equal to ____.

Q26.Let $\vec{v}=\alpha \hat{i}+2\hat{j}-3\hat{k}$, $\vec{w}=2\alpha \hat{i}+\hat{j}-\hat{k}$, and $\vec{u}$ be a vector such that $|\vec{u}|=\alpha >0$. If the minimum value of the scalar triple product $[\vec{u}\vec{v}\vec{w}]$ is $-\alpha \sqrt{3401}$, and …

Q27.The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is ____.

Q28.Let $A$ be the area bounded by the curve $y=x|x-3|$, the $x$-axis and the ordinates $x=-1$ and $x=2$. Then $12A$ is equal to ____.

Q29.Let $f:\mathbb{R}\to \mathbb{R}$ be a differentiable function such that $f^{\prime }(x)+f(x)={\int }_0^{2}f(t)dt$. If $f(0)=e^{-2}$, then $2f(0)-f(2)$ is equal to ____.