JEE Main 2022 · 28 Jun 2022 · Shift 2

Q1.Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as ${\mathrm{v}}_2=\frac{\mathrm{n}}{{\mathrm{m}}^2}{\mathrm{v}}_1$ and ${\mathrm{a}}_2=\frac{{\mathrm{a}}_1}{\mathrm{mn}}$ respectively. Here m and n are constants. The relations for distance and …

Q2.A ball is spun with angular acceleration $\alpha =6{\mathrm{t}}^2-2\mathrm{t}$ where t is in second and $\alpha$ is in rads ${}^{-2}$. At $\mathrm{t}=0$, the ball has angular velocity of 10 rads ${}^{-1}$ and angular position of 4 rad. The most appropriate expression for t …

Q3.A block of mass 2 kg moving on a horizontal surface with speed of $4{\mathrm{ms}}^{-1}$ enters a rough surface ranging from $\mathrm{x}=0.5\mathrm{m}$ to $\mathrm{x}=1.5\mathrm{m}$. The retarding force in this range of rough surface is related to distance by …

Q4.A $\sqrt{34}\mathrm{m}$ long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If ${\mathrm{F}}_{\mathrm{f}}$ and ${\mathrm{F}}_{\mathrm{w}}$ are the reaction forces of the floor and the wall, then ra …

Q5.Water fall from a 40 m high dam at the rate of $9\times 10^4\mathrm{kg}$ per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100 W lamps, that can be lit, is:
(Take …

Q6.Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be:

Q7.A water drop of radius $1\mu \mathrm{m}$ falls in a situation where the effect of buoyant force is negligible. Coefficient of viscosity of air is $1.8\times 10^{-5}{\mathrm{Nsm}}^{-2}$ and its density is negligible as compared to that of water $10^6{\mathrm{gm}}^{-3}$. T …

Q8.A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 …

Q9.What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

Q10.Two point charges $A$ and $B$ of magnitude $+8\times 10^{-6}\mathrm{C}$ and $-8\times 10^{-6}\mathrm{C}$ respectively are placed at a distance d apart. The electric field at the middle point O between the charges is $6.4\times 10^4{\mathrm{NC}}^{-1}$. The distance …

Q11.Resistance of the wire is measured as $2\Omega$ and $3\Omega$ at $10^{\circ }\mathrm{C}$ and $30^{\circ }\mathrm{C}$ respectively. Temperature cocoefficient of resistance of the material of the wire is:

Q12.The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to $1.2\times 10^{-5}$. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?

Q13.Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of x A in the same direction. If the force of attraction per meter of each wire is $2\times 10^{-6}\mathrm{N}$, then the value of x is approximately:

Q14.A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be:
(Assume the coil to be short circuited.)

Q15.An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of $60{\mathrm{Vm}}^{-1}$. Choose the correct equations for electric and magnetic fields if the EM wave is propagating in vacuum:

Q16.In young's double slit experiment performed using a monochromatic light of wavelength $\lambda$, when a glass plate $(\mu =1.5)$ of thickness $\mathrm{x}\lambda$ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum …

Q17.Let ${\mathrm{K}}_1$ and ${\mathrm{K}}_2$ be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength ${\lambda }_1$ and ${\lambda }_2$, respectively are incident on a metallic surface. If ${\lambda }_1=3{\lambda }_2$ then:

Q18.Following statements related to radioactivity are given below:
(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.
(C) Slope of th …

Q19.In the given circuit the input voltage ${\mathrm{V}}_{\text{in }}$ is shown in figure. The cut-in voltage of $\mathrm{p}-\mathrm{n}$ junction diode ( ${\mathrm{D}}_1$ or ${\mathrm{D}}_2$ ) is 0.6 V. Which of the following output voltage ( ${\mathrm{V}}_0$ ) waveform across the dio …

Q20.Amplitude modulated wave is represented by $V_{\text{AM }}=10\left[1+0.4\cos \left(2\pi \times 10^4\mathrm{t}\right)\right]\cos \left(2\pi \times 10^7\mathrm{t}\right)$.

The total bandwidth of the amplitude modulated wave is:

Q21.A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 $\mathrm{mm}$, 1.23 $\mathrm{mm}$, 1.19 $\mathrm{mm}$ and 1.20 mm. The percentage error is $\frac{\mathrm{x}}{121}\%$. The value of x is

Q22.A Zener of breakdown voltage ${\mathrm{V}}_{\mathrm{Z}}=8\mathrm{V}$ and maximum zener current, ${\mathrm{I}}_{\mathrm{ZM}}=10\mathrm{mA}$ is subjected to an input voltage ${\mathrm{V}}_{\mathrm{i}}=10\mathrm{V}$ with series resistance $\mathrm{R}=100\Omega$. In the given circui …

Q23.In a Young's double slit experiment, an angular width of the fringe is $0.35^{\circ }$ on a screen placed at 2 m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index $7/5$, is $\frac{1}{\alpha }$. …

Q24.In the given circuit, the magnitude of ${\mathrm{V}}_{\mathrm{L}}$ and ${\mathrm{V}}_{\mathrm{C}}$ are twice that of ${\mathrm{V}}_{\mathrm{R}}$. Given that $\mathrm{f}=50\mathrm{Hz}$, the inductance of the coil is $\frac{1}{\mathrm{K}\pi }\mathrm{mH}$. The value of K is

Q25.All resistances in figure are $1\Omega$ each. The value of current ' I ' is $\frac{\mathrm{a}}{5}\mathrm{A}$. The value of a is ______

Q26.A capacitor ${\mathrm{C}}_1$ of capacitance $5\mu \mathrm{F}$ is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor ${\mathrm{C}}_2$ of capacitance $10\mu \mathrm{F}$ as shown in …

Q27.A tuning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ______ cm.
(Velocity of s …

Q28.A liquid of density $750{\mathrm{kgm}}^{-3}$ flows smoothly through a horizontal pipe that tapers in cross-sectional area from ${\mathrm{A}}_1=1.2\times 10^{-2}{\mathrm{m}}^2$ to $A_2=\frac{A_1}{2}$. The pressure difference between the wide and narrow sections of the …

Q29.A uniform disc with mass $\mathrm{M}=4\mathrm{kg}$ and radius $\mathrm{R}=10\mathrm{cm}$ is mounted on a fixed horizontal axle as shown in figure. A block with mass $\mathrm{m}=2\mathrm{kg}$ hangs from a massless cord that is wrapped around the rim of the disc. During …

Q30.A car covers AB distance with first one-third at velocity ${\mathrm{v}}_1{\mathrm{ms}}^{-1}$, second one-third at ${\mathrm{v}}_2{\mathrm{ms}}^{-1}$ and last one-third at ${\mathrm{v}}_3{\mathrm{ms}}^{-1}$. If …

Q1.Compound A contains $8.7\%$ Hydrogen, $74\%$ Carbon and 17.3% Nitrogen. The molecular formula of the compound is,

Given : Atomic masses of $\mathrm{C},\mathrm{H}$ and N are 12, 1 and 14 amu respectively.

The molar mass of the compound A is …

Q2.Consider the following statements:
(A) The principal quantum number ' $n$ ' is a positive integer with values of ' n ' $=1,2,3,\dots$.
(B) The azimuthal quantum number ' $l$ ' for a given ' $n$ ' (principal quantum number) can have values as …

Q3.In the structure of ${\mathrm{SF}}_4$, the lone pair of electrons on $S$ is in.

Q4.A student needs to prepare a buffer solution of propanoic acid and its sodium salt with pH 4 . The ratio of $\frac{\left[{\mathrm{CH}}_3{\mathrm{CH}}_2{\mathrm{COO}}^{-}\right]}{\left[{\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{COOH}\right]}$ required to make buffer is ____

Gi …

Q5.In the metallurgical extraction of copper, following reaction is used :
$\mathrm{FeO}+{\mathrm{SiO}}_2\to {\mathrm{FeSiO}}_3$
FeO and ${\mathrm{FeSiO}}_3$ respectively are.

Q6.Hydrogen has three isotopes : protium ( ${}^1\mathrm{H}$ ), deuterium ( ${}^2\mathrm{H}$ or D ) and tritium ( ${}^3\mathrm{H}$ or T ). They have nearly same chemical properties but different physical properties. They differ in

Q7.Among the following basic oxide is :

Q8.Among the given oxides of nitrogen; ${\mathrm{N}}_2\mathrm{O},{\mathrm{N}}_2{\mathrm{O}}_3$, ${\mathrm{N}}_2{\mathrm{O}}_4$ and ${\mathrm{N}}_2{\mathrm{O}}_5$, the number of compound/(s) having $\mathrm{N}-\mathrm{N}$ bond is :

Q9.Which of the following oxoacids of sulphur contains "S" in two different oxidation states?

Q10.Correct statement about photo-chemical smog is :

Q11.The correct IUPAC name of the following compound is :

Q12.The major product (P) of the given reaction is (where, Me is $-{\mathrm{CH}}_3$)

Q13.Isobutyraldehyde on reaction with formaldehyde and ${\mathrm{K}}_2{\mathrm{CO}}_3$ gives compound 'A'. Compound 'A' reacts with KCN and yields compound 'B', which on hydrolysis gives a stable compound 'C'. The compound 'C' is :

Q14.With respect to the following reaction, consider the given statements :
(A) o-Nitroaniline and p-nitroaniline are the predominant products
(B) p-Nitroaniline and m-nitroaniline are the predominant products
(C) ${\mathrm{HNO}}_3$ acts as an acid
(D) …

Q15.Given below are two statements, one is Assertion (A) and other is Reason (R).

Assertion (A) : Natural rubber is a linear polymer of isoprene called cis-polyisoprene with elastic properties.
Reason (R) : The cis-polyisoprene molecules consist of various chains held together by st …

Q16.When sugar 'X' is boiled with dilute ${\mathrm{H}}_2{\mathrm{SO}}_4$ in alcoholic solution, two isomers 'A' and 'B' are formed. 'A' on oxidation with ${\mathrm{HNO}}_3$ yields saccharic acid where as 'B' is laevorotatory. The compound 'X' is :

Q17.The drug tegamet is :

Q18.100 g of an ideal gas is kept in a cylinder of 416 L volume at $27^{\circ }\mathrm{C}$ under 1.5 bar pressure. The molar mass of the gas is ______ $\mathrm{g}{\mathrm{mol}}^{-1}$. (Nearest integer)
(Given : $\mathrm{R}=0.083\mathrm{L}$ bar ${\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$)

Q19.For combustion of one mole of magnesium in an open container at 300 K and 1 bar pressure, ${\Delta }_{\mathrm{C}}{\mathrm{H}}^{\ominus }=-601.70\mathrm{kJ}{\mathrm{mol}}^{-1}$, the magnitude of change in internal energy for the reaction is ______ kJ. (Nearest integer)
(Given : …

Q20.2.5 g of protein containing only glycine $\left({\mathrm{C}}_2{\mathrm{H}}_5{\mathrm{NO}}_2\right)$ is dissolved in water to make 500 mL of solution. The osmotic pressure of this solution at 300 K is found to be $5.03\times 10^{-3}$ bar. The total number of glycine units prese …

Q21.For the given reactions
${\mathrm{Sn}}^{2+}+2{\mathrm{e}}^{-}\to \mathrm{Sn}$
${\mathrm{Sn}}^{4+}+4{\mathrm{e}}^{-}\to \mathrm{Sn}$
The electrode potentials are; ${\mathrm{E}}_{{\mathrm{Sn}}^{2+}/\mathrm{Sn}}^{\mathrm{o}}=-0.140\mathrm{V}$ and …

Q22.A radioactive element has a half life of 200 days. The percentage of original activity remaining after 83 days is ______. (Nearest integer)
(Given : antilog $0.125=1.333$, antilog $0.693=4.93$)

Q23.$[\mathrm{Fe}(\mathrm{CN}){}_6{]}^{4-}$
$[\mathrm{Fe}(\mathrm{CN}){}_6{]}^{3-}$
$[\mathrm{Ti}(\mathrm{CN}){}_6{]}^{3-}$
$[\mathrm{Ni}(\mathrm{CN}){}_4{]}^{2-}$
$[\mathrm{Co}(\mathrm{CN}){}_6{]}^{3-}$

Among the given complexes, number of paramagnetic complexes is ______.

Q24.(a) $\mathrm{CoCl}{}_3\cdot 4\mathrm{NH}{}_3$
(b) $\mathrm{CoCl}{}_3\cdot 5\mathrm{NH}{}_3$
(c) $\mathrm{CoCl}{}_3\cdot 6\mathrm{NH}{}_3$ and
(d) $\mathrm{CoCl}(\mathrm{NO}{}_3){}_2\cdot 5\mathrm{NH}{}_3$

Number of complex(es) which will exist in cis-trans is/are

Q25.The complete combustion of 0.492 g of an organic compound containing 'C', 'H' and 'O' gives 0.793 g of $\mathrm{CO}{}_2$ and 0.442 g of $\mathrm{H}{}_2\mathrm{O}$. The percentage of oxygen composition in the organic compound is ______. (nearest integer)

Q26.The major product of the following reaction contains ______ bromine atom(s).

Q27.$0.01$ M $\mathrm{KMnO}{}_4$ solution was added to 20.0 mL of 0.05 M Mohr's salt solution through a burette. The initial reading of 50 mL burette is zero. The volume of $\mathrm{KMnO}{}_4$ solution left in the burette after the end point is ______ mL. (nearest integer)

Q1.Let ${\mathrm{R}}_1=\{(\mathrm{a},\mathrm{b})\in \mathrm{N}\times \mathrm{N}:|\mathrm{a}-\mathrm{b}|\le 13\}$ and

Q2.Let $\mathrm{f}(\mathrm{x})$ be a quadratic polynomial such that $\mathrm{f}(-2)+f(3)=0$. If one of the roots of $f(x)=0$ is -1 , then the sum of the roots of $\mathrm{f}(\mathrm{x})=0$ is equal to :

Q3.The number of ways to distribute 30 identical candies among four children ${\mathrm{C}}_1,{\mathrm{C}}_2,{\mathrm{C}}_3$ and ${\mathrm{C}}_4$ so that ${\mathrm{C}}_2$ receives atleast 4 and atmost 7 candies, ${\mathrm{C}}_3$ receives atleast 2 and atmost 6 candies, is e …

Q4.The term independent of $x$ in the expression of $\left(1-x^2+3x^3\right){\left(\frac{5}{2}{x}^3-\frac{1}{5x^2}\right)}^{11},x\ne 0$ is

Q5.If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is $1:7$ and $\mathrm{a}+\mathrm{n}=33$, then the value of n is

Q6.Let $\mathrm{f},\mathrm{g}:\mathbf{R}\to \mathbf{R}$ be functions defined by
$f(x)=\{\begin{array}{ll}[x]& ,x<0\\ |1-x|,& x\ge 0\end{array}$ and
$g(x)=\{\begin{array}{ll}{e}^x-x& x<0\\ (x-1{)}^2-1& ,x\ge 0\end{array}$
where $[x]$ deno …

Q7.Let $\mathrm{f}:\mathbf{R}\to \mathbf{R}$ be a differentiable function such that $\mathrm{f}\left(\frac{\pi }{4}\right)=\sqrt{2},\mathrm{f}\left(\frac{\pi }{2}\right)=0$ and ${\mathrm{f}}^{\prime }\left(\frac{\pi }{2}\right)=1$ and let …

Q8.Let $\mathrm{f}:\mathbf{R}\to \mathbf{R}$ be continuous function satisfying $\mathrm{f}(\mathrm{x})+\mathrm{f}(\mathrm{x}+\mathrm{k})=\mathrm{n}$, for all $\mathrm{x}\in \mathbf{R}$ where $\mathrm{k}>0$ and n is a positive integer. If …

Q9.The area of the bounded region enclosed by the curve $\mathrm{y}=3-\left|\mathrm{x}-\frac{1}{2}\right|-|\mathrm{x}+1|$ and the x -axis is

Q10.Let $\mathrm{x}=\mathrm{x}(\mathrm{y})$ be the solution of the differential equation $2{\mathrm{ye}}^{\mathrm{x}/{\mathrm{y}}^2}\mathrm{dx}+\left({\mathrm{y}}^2-4{\mathrm{xe}}^{\mathrm{x}/{\mathrm{y}}^2}\right)\mathrm{dy}=0$ such that $x(1)=0$. Then, $x(e)$ is equal t …

Q11.Let the slope of the tangent to a curve $y=f(x)$ at $(\mathrm{x},\mathrm{y})$ be given by $2\tan \mathrm{x}(\cos \mathrm{x}-\mathrm{y})$. if the curve passes through the point $(\pi /4,0)$, then the value of ${\int }_0^{\pi /2}ydx$ is equal to

Q12.Let a triangle be bounded by the lines ${\mathrm{L}}_1:2\mathrm{x}+5\mathrm{y}=10$; ${\mathrm{L}}_2:-4\mathrm{x}+3\mathrm{y}=12$ and the line ${\mathrm{L}}_3$, which passes through the point $\mathrm{P}(2,3)$, intersect ${\mathrm{L}}_2$ at A and ${\mathrm{L}}_1$ …

Q13.Let $\mathrm{a}>0,\mathrm{b}>0$. Let e and $\ell$ respectively be the eccentricity and length of the latus rectum of the hyperbola $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}-\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$. Let ${\mathrm{e}}^{\prime }$ and ${\ell }^{\prime }$ respectively the ec …

Q14.Let $\vec{a}=\alpha \hat{i}+2\hat{j}-\hat{k}$ and $\vec{b}=-2\hat{i}+\alpha \hat{j}+\hat{k}$, where $\alpha \in \mathbf{R}$. If the area of the parallelogram whose adjacent sides are represented by the vectors $\vec{a}$ and $\vec{b}$ is $\sqrt{15\left({\alpha }^2+4\right)}$, the …

Q15.If vertex of a parabola is $(2,-1)$ and the equation of its directrix is $4x-3y=21$, then the length of its latus rectum is

Q16.Let the plane $\mathrm{ax}+\mathrm{by}+\mathrm{cz}=\mathrm{d}$ pass through $(2,3,-5)$ and is perpendicular to the planes $2x+y-5z=10$ and $3x+5y-7z=12$. If $\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}$ are integers $\mathrm{d}>0$ and …

Q17.The probability that a randomly chosen one-one function from the set $\{\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\}$ to the set $\{1,2,3,4,5\}$ satisfies $\mathrm{f}(\mathrm{a})+2\mathrm{f}(\mathrm{b})-\mathrm{f}(\mathrm{c})=\mathrm{f}(\mathrm{d})$ is :

Q18.The value of ${\lim }_{n\to \infty }6\tan \left\{{\sum }_{r=1}^n{\tan }^{-1}\left(\frac{1}{r^2+3r+3}\right)\right\}$ is equal to

Q19.Let $\overrightarrow{\mathrm{a}}$ be a vector which is perpendicular to the vector $3\hat{i}+\frac{1}{2}\hat{j}+2\hat{k}$. If $\vec{a}\times (2\hat{i}+\hat{k})=2\hat{i}-13\hat{j}-4\hat{k}$, then the projection of the vector $\overrightarrow{\mathrm{a}}$ on the vector …

Q20.If $\cot \alpha =1$ and $\sec \beta =-\frac{5}{3}$, where $\pi <\alpha <\frac{3\pi }{2}$ and $\frac{\pi }{2}<\beta <\pi$, then the value of $\tan (\alpha +\beta )$ and the quadrant in which $\alpha +\beta$ lies, respectively are

Q21.Let the image of the point $\mathrm{P}(1,2,3)$ in the line $\mathrm{L}:\frac{\mathrm{x}-6}{3}=\frac{\mathrm{y}-1}{2}=\frac{\mathrm{z}-2}{3}$ be Q. Let $\mathrm{R}(\alpha ,\beta ,\gamma )$ be a point that divides internally the line segment PQ in the ratio $1:3$. Then the value o …

Q22.Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in the examination if he/she gets less than 50 marks, then in worst case, the number of students can fail is

Q23.If one of the diameters of the circle $x^2+y^2-2\sqrt{2}x-6\sqrt{2}y+14=0$ is a chord of the circle $(x-2\sqrt{2}{)}^2+(y-2\sqrt{2}{)}^2=r^2$, then the value of $r^2$ is equal to

Q24.If ${\lim }_{x\to 1}\frac{\sin \left(3x^2-4x+1\right)-x^2+1}{2x^3-7x^2+ax+b}=-2$, then the value of $(a-b)$ is equal to

Q25.Let for $\mathrm{n}=1,2,\dots ,50,{\mathrm{S}}_{\mathrm{n}}$ be the sum of the infinite geometric progression whose first term is ${\mathrm{n}}^2$ and whose common ratio is $\frac{1}{(\mathrm{n}+1{)}^2}$. Then the value of …

Q26.If the system of linear equations
$2\mathrm{x}-3\mathrm{y}=\gamma +5$,
$\alpha \mathrm{x}+5\mathrm{y}=\beta +1$, where $\alpha ,\beta ,\gamma \in \mathbf{R}$ has infinitely many solutions, then the value of $|9\alpha +3\beta +5\gamma |$ is equal to

Q27.Let $\mathrm{A}=\left(\begin{array}{cc}1+\mathrm{i}& 1\\ -\mathrm{i}& 0\end{array}\right)$ where $\mathrm{i}=\sqrt{-1}$.

Then, the number of elements in the set
$\left\{\mathrm{n}\in \{1,2,\dots ,100\}:{\mathrm{A}}^{\mathrm{n}}=\mathrm{A}\right\}$ is

Q28.Sum of squares of modulus of all the complex numbers z satisfying $\overline{\mathrm{z}}=i{\mathrm{z}}^2+{\mathrm{z}}^2-\mathrm{z}$ is equal to

Q29.Let $\mathrm{S}=\{1,2,3,4\}$. Then the number of elements in the set $\{f:S\times S\to S:f$ is onto and $f(a,b)=f(b,a)\ge \mathrm{a}\forall (\mathrm{a},\mathrm{b})\in \mathrm{S}\times \mathrm{S}\}$ is

Q30.The maximum number of compound propositions, out of $\mathrm{p}\vee \mathrm{r}\vee \mathrm{s},\mathrm{p}\vee \mathrm{r}\vee \sim \mathrm{s},\mathrm{p}\vee \sim \mathrm{q}\vee \mathrm{s}$, …