JEE Main 2023 · 11 Apr 2023 · Shift 1

Q1.The electric field in an electromagnetic wave is given as $\vec{E}=20\sin \omega \left(t-\frac{x}{c}\right)\vec{j}{\mathrm{NC}}^{-1}$, where $\omega$ and $c$ are the angular frequency and the velocity of the electromagnetic wave. The total energy contained in a volume of cross-s …

Q2.From the v - t graph shown. the ratio of distance to displacement in 25 s of motion

Q3.The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are $\rho$ and $\rho /3$ respectively. The ratio of acceleration due to gravity at their surfaces $({\mathrm{g}}_{\mathrm{A}}:{\mathrm{g}}_{\mathrm{B}})$ will be:

Q4.A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of ______ from the centre:

Q5.The logic performed by the circuit shown in figure is equivalent to :

Q6.A parallel plate capacitor of capacitance 2 F is charged to a potential V. The energy stored in the capacitor is ${\mathrm{E}}_1$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is $E_2$. The …

Q7.Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:

Q8.A transmitting antenna is kept on the surface of the earth. The minimum height of receiving antenna required to receive the signal in line of sight at 4 km distance from it is $\mathrm{x}\times 10^{-2}\mathrm{m}$. The value of x is (Let. radius of earth …

Q9.As per the given graph choose the correct representation for curve A and curve B.
{Where ${\mathrm{X}}_{\mathrm{C}}=$ reactance of pure capacitive circuit connected with A.C. source
XL $=$ reactance of pure inductive circuit connected with A.C. source
$\mathrm{R}=$ impedance of pur …

Q10.1 kg of water at $100^{\circ }\mathrm{C}$ is converted into steam at $100^{\circ }\mathrm{C}$ by boiling at atmospheric pressure. The volume of water changes from $1.00\times 10^{-3}{\mathrm{m}}^3$ as a liquid to $1.671{\mathrm{m}}^3$ as steam. The change in internal energy …

Q11.The critical angle for a denser-rarer interface is $45^{\circ }$. The speed of light in rarer medium is $3\times 10^8$ ms. The speed of light in the denser medium is:

Q12.A metallic surface is illuminated with radiation of wavelength $\lambda$, the stopping potential is ${\mathrm{V}}_{\mathrm{o}}$. If the same surface is illuminated with radiation of wavelength $2\lambda$, the stopping potential becomes $\frac{{\mathrm{V}}_{\mathrm{o}}}{4}$. The thre …

Q13.The free space inside a current carrying toroid is filled with a material of susceptibility $2\times 10^{-2}$. The percentage increase in the value of magnetic field inside the toroid will be

Q14.The current sensitivity of moving coil galvanometer is increased by $25\%$. This increase is achieved only by changing in the number of turns of coils and area of cross section of the wire while keeping the resistance of galvanometer coil constant. The percentage change in the …

Q15.The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement ( x ) starting from mean position to extreme position (A) is given by

Q16.On a temperature scale ' X '. The boiling point of water is $65^{\circ }\mathrm{X}$ and the freezing point is $-15^{\circ }\mathrm{X}$. Assume that the X scale is linear. The equivalent temperature corresponding to $-95^{\circ }\mathrm{X}$ on the Farenheit scale would be:

Q17.Given below are two statements :
Statements I : Astronomical unit (Au). Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.
Statements II: Au < Parsec (Pc) < ly
In the light of the above statements. choose the most appropriate answer from the options g …

Q18.Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic). the second contains chlorine (diatomic) and third contains uranium hexafloride polyatomic). Arrange these on the basis of their root mean square speed ( …

Q19.An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of $250\mathrm{m}/\mathrm{s}$ to keep it in position. The number of bullets fired per second by the machine gun is :

Q20.Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B . If and B are decay constants of A and B respectively, then choose the correct relation from the given options.

Q21.A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is $\mathrm{x}\times 10^{15})\mathrm{Hz}$. The value of …

Q22.The radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 cm . The lens is now immersed in a liquid of refractive index 1.5. The ratio of power of lens in air to its power in the liquid will be $\mathrm{x}:1$. The value of x is ____ .

Q23.The equation of wave is given by
$\mathrm{Y}=10^{-2}\sin 2\pi \left(160\mathrm{t}-0.5\mathrm{x}+\frac{\pi }{4}\right)$
Where $x$ and $Y$ are in $m$ and $t$ is $s$. The speed of the wave is ____ $\mathrm{km}{\mathrm{h}}^{-1}$

Q24.A force $\overrightarrow{\mathrm{F}}=(2+3\mathrm{x})\hat{\mathrm{i}}$ acts on a particle in the x direction where F is in newton and x is in meter. The work done by this force during a displacement from $\mathrm{x}=0$ to $\mathrm{x}=4\mathrm{m}$, is ____ J.

Q25.As shown in the figure, a configuration of two equal point charges ($q_0=-2\mu \mathrm{C}$) is placed on an inclined plane. Mass of each point charge is 20 g. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (a …

Q26.A solid sphere of mass 500 g and radius 5 cm is rotated about one of its diameter with angular speed of $10{\mathrm{rad}\mathrm{s}}^{-1}$. If the moment of inertia of the sphere about its tangent is $x\times 10^{-2}$ times its angular momentum about the diameter. Then the value of $x$ wi …

Q27.The length of wire becomes ${\ell }_1$ and ${\ell }_2$ when 100 N and 120 N tensions are applied respectively. If ${\ell }_2=\frac{11}{10}{\ell }_1$, the natural length of wire will be $\frac{1}{x}{\ell }_1$. Here the value of $x$ is ______.

Q28.The magnetic field B crossing normally a square metallic plate of area $4{\mathrm{m}}^2$ is changing with time as shown in figure. The magnitude of induced emf in the plate during $t=2\mathrm{s}$ to $t=4\mathrm{s}$, is ______ mV

Q29.A projectile fired at $30^{\circ }$ to the ground is observed to be at same height at time 3 s and 5 s after projection, during its flight. The speed of projection of the projectile is ______ ${\mathrm{ms}}^{-1}$
(Given $g=10{\mathrm{m}\mathrm{s}}^{-2}$)

Q30.In the circuit diagram shown in figure given below, the current flowing through resistance $3\Omega$ is $\frac{x}{3}\mathrm{A}$. The value of $x$ is ______.

Q1.L-isomer of tetrose $\mathrm{X}\left({\mathrm{C}}_4{\mathrm{H}}_8{\mathrm{O}}_4\right)$ gives positive Schiff's test and has two chiral carbons. On acetylation. ' X ' yields triacetate. ' X ' also undergoes following reactions …

Q2.The polymer X - consists of linear molecules and is closely packed. It is prepared in the presence of triethylaluminium and titanium tetrachloride under low pressure. The polymer X is -

Q3.When a solution of mixture having two inorganic salts was treated with freshly prepared ferrous sulphate in acidic medium, a dark brown ring was formed whereas on treatment with neutral ${\mathrm{FeCl}}_3$, it gave deep red colour which disappeared on boiling and a brown red ppt …

Q4.Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R :

Assertion A : In the photoelectric effect, the electrons are ejected from the metal surface as soon as the beam of light of frequency greater than threshold frequency strikes …

Q5.25 mL of silver nitrate solution ( 1 M ) is added dropwise to 25 mL of potassium iodide ( 1.05 M ) solution. The ion(s) present in very small quantity in the solution is/are

Q6.'A' and 'B' in the below reactions are :

Q7.The set which does not have ambidentate ligand(s) is

Q8.Where Nu $=$ Nucleophile
Find out the correct statement from the options given below for the above 2 reactions.

Q9.For elements $\mathrm{B},\mathrm{C},\mathrm{N},\mathrm{Li},\mathrm{Be},\mathrm{O}$ and F the correct order of first ionization enthalpy is

Q10.For compound having the formula ${\mathrm{GaAlCl}}_4$, the correct option from the following is

Q11.In the extraction process of copper, the product obtained after carrying out the reactions
(i) $2{\mathrm{Cu}}_2\mathrm{S}+3{\mathrm{O}}_2\to 2{\mathrm{Cu}}_2\mathrm{O}+2{\mathrm{SO}}_2$
(ii) …

Q12.Thin layer chromatography of a mixture shows the following observation :

Q13.Which of the following complex has a possibility to exist as meridional isomer?

Q14.Given below are two statements :

Statement-I : Methane and steam passed over a heated Ni catalyst produces hydrogen gas.
Statement-II : Sodium nitrite reacts with ${\mathrm{NH}}_4\mathrm{Cl}$ to give ${\mathrm{H}}_2\mathrm{O},{\mathrm{N}}_2$ and NaCl .
In the light of the …

Q15.Given below are two statements :

Statement I : If BOD is 4 ppm and dissolved oxygen is 8 ppm , then it is a good quality water.
Statement II : If the concentration of zinc and nitrate salts are 5 ppm each, then it can be a good quality water.
In the light of the above statements …

Q16.Arrange the following compounds in increasing order of rate of aromatic electrophilic substitution reaction
(a) (see structure)
(b) (see structure)
(c) (see structure)
(d) (see structure)

Q17.The complex that dissolves in water is

Q18.o-Phenylenediamine $\stackrel{{\mathrm{HNO}}_2}{\to }$ ' X '

Major Product
' X ' is

Q19.A mixture of 1 mole of ${\mathrm{H}}_2\mathrm{O}$ and 1 mole of CO is taken in a 10 litre container and heated to 725 K . At equilibrium $40\%$ of water by mass reacts with carbon monoxide according to the equation : …

Q20.The ratio of spin-only magnetic moment values ${\mu }_{\text{eff }}{\left[\mathrm{Cr}(\mathrm{CN}{)}_6\right]}^{3-}/{\mu }_{\text{eff }}{\left[\mathrm{Cr}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{3+}$ is ____.

Q21.An atomic substance A of molar mass $12\mathrm{g}{\mathrm{mol}}^{-1}$ has a cubic crystal structure with edge length of 300 pm . The no. of atoms present in one unit cell of A is ____. (Nearest integer)

Given the density of A is $3.0\mathrm{g}{\mathrm{mL}}^{-1}$ and …

Q22.The ratio $\mathrm{x}/\mathrm{y}$ on completion of the above reaction is ____.

Q23.The number of hyperconjugation structures involved to stabilize carbocation formed in the above reaction is ____.

Q24.Solid fuel used in rocket is a mixture of ${\mathrm{Fe}}_2{\mathrm{O}}_3$ and Al (in ratio $1:2$ ). The heat evolved ( kJ ) per gram of the mixture is ____ (Neatest integer)

Given : …

Q25.A solution of sugar is obtained by mixing 200 g of its $25\%$ solution and 500 g of its $40\%$ solution (both by mass). The mass percentage of the resulting sugar solution is ____. (Nearest integer)

Q26.$\mathrm{KClO}{}_3+6\mathrm{FeSO}{}_4+3\mathrm{H}{}_2\mathrm{SO}{}_4\to \mathrm{KCl}+3\mathrm{Fe}{}_2(\mathrm{SO}{}_4){}_3+3\mathrm{H}{}_2\mathrm{O}$

The above reaction was studied at 300 K by monitoring the concentration of $\mathrm{FeSO}{}_4$ in which initial concentration was 10 M and after half an hour became 8.8 M. The rate of production of $\mathrm{Fe}{}_2(\mathrm{SO}{}_4){}_3$ is …

Q27.$0.004$ M $\mathrm{K}{}_2\mathrm{SO}{}_4$ solution is isotonic with $0.01$ M glucose solution. Percentage dissociation of $\mathrm{K}{}_2\mathrm{SO}{}_4$ is $\_\_\_\_$ (Nearest integer)

Q28.In an electrochemical reaction of lead, at standard temperature, if $E_{(\mathrm{Pb}{}^{2+}/\mathrm{Pb})}^0=m$ Volt and $E_{(\mathrm{Pb}{}^{4+}/\mathrm{Pb})}^0=n$ Volt, then the value of $E_{(\mathrm{Pb}{}^{2+}/\mathrm{Pb}{}^{4+})}^0$ is given by $m-xn$. The value of $x$ is $\_\_\_\_$.
(Nearest integer)

Q29.Match List-I with List-II :

Q1.The value of the integral ${\int }_{-{\log }_{e}2}^{{\log }_{e}2}{e}^x\left({\log }_e\left(e^x+\sqrt{1+e^{2x}}\right)\right)dx$ is equal to

Q2.If equation of the plane that contains the point $(-2,3,5)$ and is perpendicular to each of the planes $2x+4y+5z=8$ and $3x-2y+3z=5$ is $\alpha x+\beta y+\gamma z+97=0$ then $\alpha +\beta +\gamma =$

Q3.Let R be a rectangle given by the lines $x=0,x=2$, $y=0$ and $y=5$. Let $A(\alpha ,0)$ and $B(0,\beta ),\alpha \in [0,2]$ and $\beta \in [0,5]$, be such that the line segment AB divides the area of the rectangle R in the ratio 4:1. Then, the mid-point of AB lies on a

Q4.Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of A and adding 2 to eac …

Q5.Let $f(x)=[x^2-x]+|-x+[x]|$, where $x\in \mathbb{R}$ and [t] denotes the greatest integer less than or equal to t. Then, f is

Q6.The number of triplets $(x,y,z)$, where $x,y,z$ are distinct non negative integers satisfying $x+y+z=15$, is

Q7.For any vector $\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}$, with $|a_i|<1,i=1,2,3$, consider the following statements:
(A): $\max \{|a_1|,|a_2|,|a_3|\}\le |\vec{a}|$
(B): $|\vec{a}|\le 3\max \{|a_1|,|a_2|,|a_3|\}$

Q8.Let $w_1$ be the point obtained by the rotation of $z_1=5+4i$ about the origin through a right angle in the anticlockwise direction, and $w_2$ be the point obtained by the rotation of $z_2=3+5i$ about the origin through a right angle in the clockwise direction. Th …

Q9.An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?

Q10.Let $S=\{M=[a_{ij}],a_{ij}\in \{0,1,2\},1\le i,j\le 2\}$ be a sample space and $A=\{M\in S:M\text{ is invertible}\}$ be an event. Then $P(A)$ is equal to

Q11.Consider ellipses $E_k:k{x}^2+k^2{y}^2=1,k=1,2,\dots ,20$. Let $C_k$ be the circle which touches the four chords joining the end points (one on minor axis and another on major axis) of the ellipse $E_k$. If $r_k$ is the radius of the circle $C_k$, then the …

Q12.The number of integral solutions $x$ of ${\log }_{\left(x+\frac{7}{2}\right)}{\left(\frac{x-7}{2x-3}\right)}^2\ge 0$ is

Q13.Area of the region $\left\{(x,y):x^2+(y-2{)}^2\le 4,x^2\ge 2y\right\}$ is

Q14.Let $y=y(x)$ be a solution curve of the differential equation, $(1-x^2{y}^2)dx=ydx+xdy$.

If the line $\mathrm{x}=1$ intersects the curve $\mathrm{y}=\mathrm{y}(\mathrm{x})$ at $\mathrm{y}=2$ and the line $\mathrm{x}=2$ intersects the curve …

Q15.Let A be a $2\times 2$ matrix with real entries such that ${\mathrm{A}}^{\prime }=\alpha \mathrm{A}+\mathrm{I}$, where $\alpha \in \mathbb{R}-\{-1,1\}$. If $\det (A^2-A)=4$, then the sum of all possible values of $\alpha$ is equal to

Q16.Let $(\alpha ,\beta ,\gamma )$ be the image of the point $\mathrm{P}(2,3,5)$ in the plane $2\mathrm{x}+\mathrm{y}-3\mathrm{z}=6$. Then $\alpha +\beta +\gamma$ is equal to

Q17.Let $\vec{a}$ be a non-zero vector parallel to the line of intersection of the two planes described by $\hat{i}+\hat{j},\hat{i}+\hat{k}$ and $\hat{i}-\hat{j},\hat{j}-\hat{k}$. If $\theta$ is the angle between the vector $\vec{a}$ and the vector …

Q18.The number of elements in the set $\mathrm{S}=\left\{\theta \in [0,2\pi ]:3{\cos }^4\theta -5{\cos }^2\theta -2{\sin }^6\theta +2=0\right\}$ is

Q19.Let ${\mathrm{x}}_1,{\mathrm{x}}_2,\dots ,{\mathrm{x}}_{100}$ be in an arithmetic progression, with ${\mathrm{x}}_1=2$ and their mean equal to 200. If $y_i=i(x_i-i)$, $1\le i\le 100$, then the mean of ${\mathrm{y}}_1,{\mathrm{y}}_2,\dots ,{\mathrm{y}}_{100}$ is

Q20.The mean of the coefficients of $x,x^2,\dots ,x^7$ in the binomial expansion of $(2+\mathrm{x}{)}^9$ is

Q21.Let $\mathrm{S}=109+\frac{108}{5}+\frac{107}{5^2}+\dots +\frac{2}{5^{107}}+\frac{1}{5^{108}}$. Then the value of $(16\mathrm{S}-(25{)}^{-54})$ is equal to

Q22.For $\mathrm{m},\mathrm{n}>0$, let $\alpha (\mathrm{m},\mathrm{n})={\int }_0^2{\mathrm{t}}^{\mathrm{m}}(1+3\mathrm{t}{)}^{\mathrm{n}}dt$. If $11\alpha (10,6)+18\alpha (11,5)=\mathrm{p}(14{)}^6$, then p is equal to

Q23.In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the allotted seat, is

Q24.Let a line $l$ pass through the origin and be perpendicular to the lines
$l_1:\overrightarrow{\mathrm{r}}=(\hat{\mathrm{i}}-11\hat{\mathrm{j}}-7\hat{\mathrm{k}})+\lambda (\hat{\mathrm{i}}+2\hat{\mathrm{j}}+3\hat{\mathrm{k}}),\lambda \in \mathbb{R}$
and …

Q25.The number of integral terms in the expansion of ${\left(3^{\frac{1}{2}}+5^{\frac{1}{4}}\right)}^{680}$ is equal to

Q26.The number of ordered triplets of the truth values of $p,q$ and $r$ such that the truth value of the statement $(p\vee q)\wedge (p\vee r)\Rightarrow (q\vee r)$ is True, is equal to

Q27.Let $H_n=\frac{x^2}{1+n}-\frac{y^2}{3+n}=1,n\in N$. Let $k$ be the smallest even value of n such that the eccentricity of ${\mathrm{H}}_{\mathrm{k}}$ is a rational number. If $l$ is length of the latus rectum of ${\mathrm{H}}_{\mathrm{k}}$, then $21l$ is equal to

Q28.If $a$ and $b$ are the roots of equation $x^2-7x-1=0$, then the value of $\frac{a^{21}+b^{21}+a^{17}+b^{17}}{a^{19}+b^{19}}$ is equal to

Q29.Let $\mathrm{A}=\left[\begin{array}{lll}0& 1& 2\\ \mathrm{a}& 0& 3\\ 1& \mathrm{c}& 0\end{array}\right]$, where $\mathrm{a},\mathrm{c}\in \mathrm{R}$. If ${\mathrm{A}}^3=\mathrm{A}$ and the positive value of a belongs to the interval $(\mathrm{n}-1,\mathrm{n}]$ …