JEE Main 2023 · 06 Apr 2023 · Shift 2

Q1.A 2 meter long scale with least count of 0.2 cm is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at 80 cm mark and lm mark, respectively. The image of the object pin o …

Q2.A capacitor of capacitance $150.0\mu \mathrm{F}$ is connected to an alternating source of emf given by $\mathrm{E}=36\sin (120\pi \mathrm{t})$ V. The maximum value of current in the circuit is approximately equal to :

Q3.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed.
Reason R: A change in the pressure applied to an enclosed …

Q4.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The phase difference of two light waves change if they travel through different media having same thickness, but different indices of refraction.
Reason R: The wavele …

Q5.Figure shows a part of an electric circuit. The potentials at points $\mathrm{a}$, $\mathrm{b}$ and c are $30\mathrm{V}$, $12\mathrm{V}$ and 2 V respectively. The current through the $20\Omega$ resistor will be.

Q6.As shown in the figure, a particle is moving with constant speed $\pi \mathrm{m}/\mathrm{s}$. Considering its motion from A to B, the magnitude of the average velocity is:

Q7.The work functions of Aluminium and Gold are 4.1 eV and 5.1 eV respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is

Q8.The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

Q9.A child of mass 5 kg is going round a merry-go-round that makes 1 rotation in 3.14 s. The radius of the merry-go-round is 2 m. The centrifugal force on the child will be

Q10.A particle starts with an initial velocity of $10.0{\mathrm{ms}}^{-1}$ along x-direction and accelerates uniformly at the rate of $2.0{\mathrm{ms}}^{-2}$. The time taken by the particle to reach the velocity of $60.0{\mathrm{ms}}^{-1}$ is ______.

Q11.Choose the incorrect statement from the following:

Q12.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Diffusion current in a p-n junction is greater than the drift current in magnitude if the junction is forward biased.
Reason R: Diffusion current in a p-n junction is …

Q13.The energy density associated with electric field $\vec{E}$ and magnetic field $\overrightarrow{\mathrm{B}}$ of an electromagnetic wave in free space is given by (${ϵ}_0$ - permittivity of free space, ${\mu }_0$ - permeability of free space)

Q14.The temperature of an ideal gas is increased from 200 K to 800 K. If r.m.s. speed of gas at 200 K is ${\mathrm{v}}_0$. Then, r.m.s. speed of the gas at 800 K will be:

Q15.A student is provided with a variable voltage source V, a test resistor ${\mathrm{R}}_{\mathrm{r}}=10\Omega$, two identical galvanometers ${\mathrm{G}}_1$ and ${\mathrm{G}}_2$ and two additional resistors, ${\mathrm{R}}_1=10\mathrm{M}\Omega$ and ${\mathrm{R}}_2=0.001\Omega$. Fo …

Q16.A body cools in 7 minutes from $60^{\circ }\mathrm{C}$ to $40^{\circ }\mathrm{C}$. The temperature of the surrounding is $10^{\circ }\mathrm{C}$. The temperature of the body after the next 7 minutes will be:

Q17.A small particle of mass $m$ moves in such a way that its potential energy $U=\frac{1}{2}m{\omega }^2{r}^2$ where $\omega$ is constant and $r$ is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of …

Q18.For an amplitude modulated wave the minimum amplitude is 3 V, while the modulation index is $60\%$. The maximum amplitude of the modulated wave is:

Q19.The weight of a body on the surface of the earth is 100 N. The gravitational force on it when taken at a height, from the surface of earth, equal to onefourth the radius of the earth is:

Q20.As shown in the figure, the voltmeter reads 2 V across $5\Omega$ resistor. The resistance of the voltmeter is ______ $\Omega$.

Q21.A metal block of mass $m$ is suspended from a rigid support through a metal wire of diameter 14 mm. The tensile stress developed in the wire under equilibrium state is $7\times 10^5{\mathrm{Nm}}^{-2}$. The value of mass $m$ is ______ kg.
(Take, …

Q22.As shown in the figure, two parallel plate capacitors having equal plate area of $200{\mathrm{cm}}^2$ are joined in such a way that $\mathrm{a}\ne \mathrm{b}$. The equivalent capacitance of the combination is $\mathrm{x}{\in }_0\mathrm{F}$. The value of $x$ is ______.

Q23.A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is $\sqrt{\frac{2}{x}}$. The value of $x$ is ______

Q24.A simple pendulum with length 100 cm and bob of mass 250 g is executing S.H.M. of amplitude 10 cm. The maximum tension in the string is found to be $\frac{x}{40}$ N. The value of x is ____.

Q25.Two concentric circular coils with radii 1 cm and 1000 cm, and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be ____ $\times 10^{-8}$ H.
(Take, ${\pi }^2=10$)

Q26.A beam of light consisting of two wavelengths 7000 Å and 5500 Å is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is 2.5 mm and the distance between the plane of slits and the screen is 150 cm. The least distance from the cen …

Q27.A body is dropped on ground from a height '$h_1$' and after hitting the ground, it rebounds to a height '$h_2$'. If the ratio of velocities of the body just before and after hitting ground is 4, then percentage loss in kinetic energy of the body is $\frac{x}{4}$. The value of $x$ …

Q28.Experimentally it is found that 12.8 eV energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is $\frac{9}{x}\times 10^{-10}$ m. The value of the $x$ is ____.
($1\text{ eV}=1.6\times 10^{-19}$ J, …

Q29.A proton with a kinetic energy of 2.0 eV moves into a region of uniform magnetic field of magnitude $\frac{\pi }{2}\times 10^{-3}$ T. The angle between the direction of magnetic field and velocity of proton is $60^{\circ }$. The pitch of the helical path taken by the proton is ____ …

Q1.Ion having highest hydration enthalpy among the given alkaline earth metal ions is:-

Q2.The IUPAC name of ${\mathrm{K}}_3[\mathrm{Co}({\mathrm{C}}_2{\mathrm{O}}_4{)}_3]$ is :-

Q3.Element not present in Nessler's reagent is:-

Q4.Structure of ${\mathrm{BeCl}}_2$ in solid state, vapour phase and at very high temperature respectively are :-

Q5.The strongest acid from the following is

Q6.Group-13 elements react with ${\mathrm{O}}_2$ in amorphous form to form oxides of type ${\mathrm{M}}_2{\mathrm{O}}_3$ ($\mathrm{M}=$ element). Which among the following is the most basic oxide?

Q7.Consider the following reaction that goes from A to B in three steps as shown below:-

Choose the correct

Q8.Given below are two statements : one is labelled as "Assertion A" and the other is labelled as "Reason R".

Assertion A : In the complex $\mathrm{Ni}(\mathrm{CO}{)}_4$ and $\mathrm{Fe}(\mathrm{CO}{)}_5$, the metals have zero oxidation state.

Reason R: Low oxidation states ar …

Q9.During the reaction of permanganate with thiosulphate, the change in oxidation of manganese occurs by value of 3. Identify which of the below medium will favour the reaction.

Q10.Find out the major product from the following reaction:

3-methylcyclohex-2-en-1-one --(1) MeMgBr / CuI; (2) n-PrI--> ?

Q11.Formation of which complex, among the following, is not a confirmatory test of ${\mathrm{Pb}}^{2+}$ ions

Q12.From the figure of column chromatography given below, identify incorrect statements.
A. Compound 'c' is more polar than 'a' and 'b'
B. Compound 'a' is least polar
C. Compound 'b' comes out of the column before 'c' and after 'a'
D. Compound 'a' spends more time in the column
Choos …

Q13.Given below are two statements:-
Statement-I: Morphine is a narcotic analgesis. It helps in relieving pain without producing sleep.
Statement-II: Morphine and its derivatives are obtained from opium poppy.
In the light of the above statements, choose the correct answer from the o …

Q14.The volume of 0.02 M aqueous HBr required to neutralize 10.0 mL of 0.01 M aqueous $\mathrm{Ba}(\mathrm{OH}{)}_2$ is (Assume complete neutralization)

Q15.The product, which is not obtained during the electrolysis of brine solution is

Q16.The group of chemicals used as pesticide is

Q17.In the following reaction, 'B' is

Q18.Which one of the following elements will remain as liquid inside pure boiling water?

Q19.If the radius of the first orbit of hydrogen atom ${\mathbf{a}}_0$, then de Broglie's wavelength of electron in $3^{\text{rd}}$ orbit is

Q20.In an ice crystal, each water molecule is hydrogen bonded to _____ neighbouring molecules.

Q21.The equilibrium composition for the reaction ${\mathrm{PCl}}_3+{\mathrm{Cl}}_2\rightleftharpoons {\mathrm{PCl}}_5$ at 298 K is given below.
$[{\mathrm{PCl}}_3{]}_{\mathrm{eq}}=0.2\mathrm{mol}{\mathrm{L}}^{-1}$ …

Q22.Consider the following pairs of solution which will be isotonic at the same temperature. The number of pairs of solutions is/are _____
A. 1 M aq. NaCl and 2 M aq. Urea
B. 1 M aq. ${\mathrm{CaCl}}_2$ and 1.5 M aq. KCl
C. 1.5 M aq. ${\mathrm{AlCl}}_3$ and 2 M aq. …

Q23.The standard reduction potential at 298 K for the following half cells are given below:-
${\mathrm{NO}}_3^{-}+4{\mathrm{H}}^{+}+3{\mathrm{e}}^{-}\to \mathrm{NO}(\mathrm{g})+2{\mathrm{H}}_2\mathrm{O}{\mathrm{E}}^0=0.97\mathrm{V}$ …

Q24.The number of colloidal systems from the following, which will have 'liquid' as the dispersion medium, is ____

Gem stones, paints, smoke, cheese, milk, hair cream, insecticide sprays, froth, soap lather.

Q25.The number of species having a square planar shape from the following is ____

${\mathrm{XeF}}_4$, ${\mathrm{SF}}_4$, ${\mathrm{SiF}}_4$, ${\mathrm{BF}}_4^{-}$, ${\mathrm{BrF}}_4^{-}$, ${\left[\mathrm{Cu}{\left({\mathrm{NH}}_3\right)}_4\right]}^{2+}$, …

Q26.Consider the following date

Heat of combustion of ${\mathrm{H}}_2(\mathrm{g})=-241.8\mathrm{kJ}{\mathrm{mol}}^{-1}$

Heat of combustion of $\mathrm{C}(\mathrm{s})=-393.5\mathrm{kJ}{\mathrm{mol}}^{-1}$

Heat of combustion of …

Q27.Among the following, the number of compounds which will give positive iodoform reaction is ____

(a) 1-Phenylbutan-2-one
(b) 2-Methylbutan-2-ol
(c) 3-Methylbutan-2-ol
(d) 1-Phenylethanol
(e) 3,3-dimethylbutan-2-one
(f) 1-Phenylpropan-2-ol

Q28.Number of isomeric aromatic amines with molecular formula ${\mathrm{C}}_8{\mathrm{H}}_{11}\mathrm{N}$, which can be synthesized by Gabriel Phthalimide synthesis is ____

Q29.Number of crystal systems from the following where body centred unit cell can be found, is.....

Cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, triclinic.

Q1.Three dice are rolled. If the probability of getting different numbers on the three dice is $\frac{p}{q}$, where $p$ and q are co-prime, then $q-p$ is equal to

Q2.Among the statements:
(S1): $2023^{2022}-1999^{2022}$ is divisible by 8.
(S2): $13(13{)}^n-11n-13$ is divisible by 144 for infinitely many $n\in \mathbb{N}$.

Q3.${\lim }_{n\to \infty }\left\{\left(2^{\frac{1}{2}}-2^{\frac{1}{3}}\right)\left(2^{\frac{1}{2}}-2^{\frac{1}{5}}\right)\dots \left(2^{\frac{1}{2}}-2^{\frac{1}{2n+1}}\right)\right\}$ is equal to

Q4.Let $a\ne b$ be two non-zero real numbers. Then the number of elements in the set $X=\{z\in \mathbb{C}:\mathrm{Re}(a{z}^2+bz)=a\text{ and }\mathrm{Re}(b{z}^2+az)=b\}$ is equal to

Q5.Let the sets A and B denote the domain and range respectively of the function $f(x)=\frac{1}{\sqrt{\lceil x\rceil -x}}$, where $\lceil x\rceil$ denotes the smallest integer greater than or equal to x. Then among the statements
(S1): $A\cap B=(1,\infty )-\mathbb{N}$ and
(S2): …

Q6.If the solution curve $f(x,y)=0$ of the differential equation $(1+{\log }_{e}x)\frac{dx}{dy}-x{\log }_{e}x=e^y$, $x>0$, passes through the points $(1,0)$ and $(\alpha ,2)$ then ${\alpha }^{\alpha }$ is equal to

Q7.The sum of all values of $\alpha$, for which the points whose position vectors $\hat{i}-2\hat{j}+3\hat{k}$, $2\hat{i}-3\hat{j}+4\hat{k}$, $(\alpha +1)\hat{i}+2\hat{k}$ and $9\hat{i}+(\alpha -8)\hat{j}+6\hat{k}$ are coplanar, is equal to

Q8.For the system of equations
$x+y+z=6$
$x+2y+\alpha z=10$
$x+3y+5z=\beta$, which one of the following is NOT true?

Q9.The area bounded by the curves $y=|x-1|+|x-2|$ and $y=3$ is equal to

Q10.Let P be a square matrix such that $P^2=I-P$. For $\alpha ,\beta ,\gamma ,\delta \in \mathbb{N}$, if $P^{\alpha }+P^{\beta }=\gamma I-29P$ and $P^{\alpha }-P^{\beta }=\delta I-13P$, then $\alpha +\beta +\gamma -\delta$ is equal to

Q11.All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is

Q12.Let the line L pass through the point $(0,1,2)$, intersect the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and be parallel to the plane $2x+y-3z=4$. Then the distance of the point $P(1,-9,2)$ from the line L is

Q13.A plane P contains the line of intersection of the plane $\vec{r}\cdot (\hat{i}+\hat{j}+\hat{k})=6$ and $\vec{r}\cdot (2\hat{i}+3\hat{j}+4\hat{k})=-5$. If P passes through the point $(0,2,-2)$, then the square of distance of the point (12, 12, 18) from the plane P is

Q14.Let $\mathrm{f}(\mathrm{x})$ be a function satisfying $\mathrm{f}(\mathrm{x})+\mathrm{f}(\pi -\mathrm{x})={\pi }^2,\forall \mathrm{x}\in \mathrm{R}$. Then ${\int }_0^{\pi }\mathrm{f}(\mathrm{x})\sin \mathrm{x}\mathrm{dx}$ is equal to

Q15.If the coefficients of $x^7$ in ${\left(a{x}^2+\frac{1}{2bx}\right)}^{11}$ and $x^{-7}$ in ${\left(ax-\frac{1}{3b{x}^2}\right)}^{11}$ are equal, then

Q16.Among the statements
(S1): $(p\Rightarrow q)\vee ((\sim p)\wedge q)$ is a tautology
(S2): $(q\Rightarrow p)\Rightarrow ((\sim p)\wedge q)$ is a contradiction

Q17.If the tangents at the points P and Q on the circle ${\mathrm{x}}^2+{\mathrm{y}}^2-2\mathrm{x}+\mathrm{y}=5$ meet at the point $\mathrm{R}\left(\frac{9}{4},2\right)$, then the area of the triangle PQR is

Q18.Let the vectors $\vec{a},\vec{b},\vec{c}$ represent three coterminous edges of a parallelopiped of volume V. Then the volume of the parallelopiped, whose coterminous edges are represented by $\vec{a},\vec{b}+\vec{c}$ and $\vec{a}+2\vec{b}+3\vec{c}$ is equal to

Q19.If $\gcd (\mathrm{m},\mathrm{n})=1$ and $1^2-2^2+3^2-4^2+\dots +(2021{)}^2-(2022{)}^2+(2023{)}^2=1012{\mathrm{m}}^2\mathrm{n}$, then ${\mathrm{m}}^2-{\mathrm{n}}^2$ is equal to

Q20.In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons, who speak only English is $\alpha$ and the number of persons who speak only Hindi is $\beta$, then the eccentricity of the ellipse …

Q21.Let $\mathrm{f}(\mathrm{x})=\frac{\mathrm{x}}{(1+x^n{)}^{1/n}},\mathrm{x}\in \mathrm{R}-\{-1\},\mathrm{n}\in \mathrm{N},\mathrm{n}>2$. If ${\mathrm{f}}^{\mathrm{n}}(\mathrm{x})=$ (fofof ...... upto n times) ( x ), then …

Q22.The value of $\tan 9^{\circ }-\tan 27^{\circ }-\tan 63^{\circ }+\tan 81^{\circ }$ is

Q23.If the lines $\frac{x-1}{2}=\frac{2-y}{-3}=\frac{z-3}{\alpha }$ and $\frac{x-4}{5}=\frac{y-1}{2}=\frac{z}{\beta }$ intersect, then the magnitude of the minimum value of $8\alpha \beta$ is

Q24.If $(20{)}^{19}+2(21)(20{)}^{18}+3(21{)}^2(20{)}^{17}+\dots +20(21{)}^{19}=\mathrm{k}(20{)}^{19}$, then k is equal to

Q25.The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is ____.

Q26.The number of points, where the curve $y=x^5-20x^3+50x+2$ crosses the $x$-axis, is ____.

Q27.For $\alpha ,\beta ,z\in \mathbb{C}$ and $\lambda >1$, if $\sqrt{\lambda -1}$ is the radius of the circle $|z-\alpha {|}^2+|z-\beta {|}^2=2\lambda$, then $|\alpha -\beta |$ is equal to ____.

Q28.Let a curve $y=f(x),x\in (0,\infty )$ pass through the points $P\left(1,\frac{3}{2}\right)$ and $Q\left(a,\frac{1}{2}\right)$. If the tangent at any point $R(b,f(b))$ to the given curve cuts the y-axis at the point $S(0,c)$ such that $bc=3$, then $(PQ{)}^2$ is equal to ____.

Q29.Let the eccentricity of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is reciprocal to that of the hyperbola $2x^2-2y^2=1$. If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is ____.

Q30.If the mean and variance of the frequency distribution

are 9 and 15.08 respectively, then the value of …