JEE Main 2024 — 27 Jan Shift 2 (Previous Year Paper)

An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is:

1. A.$\frac{3}{715}$✓
2. B.$\frac{5}{256}$
3. C.$\frac{5}{715}$
4. D.$\frac{3}{256}$

Correct answer: A

If $y=y(x)$ is the solution curve of the differential equation $(x^2-4)\,dy-(y^2-3y)\,dx=0$, $x>2$, $y(4)=\frac32$ and the slope of the curve is never zero, then the value of $y(10)$ equals:

1. A.$\frac{3}{1+(8)^{1/4}}$✓
2. B.$\frac{3}{1-2\sqrt2}$
3. C.$\frac{3}{1+2\sqrt2}$
4. D.$\frac{3}{1-(8)^{1/4}}$

Correct answer: A

The values of $\alpha$, for which $\begin{vmatrix}1&\frac32&\alpha+\frac32\\1&\frac13&\alpha+\frac13\\2\alpha+3&3\alpha+1&0\end{vmatrix}=0$, lie in the interval.

1. A.$(-3,0)$✓
2. B.$(-2,1)$
3. C.$(0,3)$
4. D.$\left(-\frac32,\frac32\right)$

Correct answer: A

The position vectors of the vertices $A$, $B$ and $C$ of a triangle are $2\hat i-3\hat j+3\hat k$, $2\hat i+2\hat j+3\hat k$ and $-\hat i+\hat j+3\hat k$ respectively. Let $l$ denotes the length of the angle bisector $AD$ of $\angle BAC$ where $D$ is on the line segment $BC$, then $2l^2$ equals:

1. A.50
2. B.49
3. C.42
4. D.45✓

Correct answer: D

Let $g(x)=3f\left(\frac x3\right)+f(3-x)$ and $f''(x)>0$ for all $x\in(0,3)$. If $g$ is decreasing in $(0,\alpha)$ and increasing in $(\alpha,3)$, then $8\alpha$ is:

1. A.18✓
2. B.24
3. C.0
4. D.20

Correct answer: A

Let $\alpha=\frac{(4!)!}{(4!)^{3!}}$ and $\beta=\frac{(5!)!}{(5!)^{4!}}$. Then:

1. A.$\alpha\in N$ and $\beta\notin N$
2. B.$\alpha\notin N$ and $\beta\in N$
3. C.$\alpha\in N$ and $\beta\in N$✓
4. D.$\alpha\notin N$ and $\beta\notin N$

Correct answer: C

Consider the function $f:(0,2)\to\mathbb{R}$ defined by $f(x)=\frac x2+\frac2x$ and the function $g(x)$ defined by $g(x)=\begin{cases}\min\{f(t)\}, & 0<t\le x \text{ and } 0<x\le1\\ \frac32+x, & 1<x<2\end{cases}$. Then,

1. A.$g$ is continuous but not differentiable at $x=1$✓
2. B.$g$ is not continuous for all $x\in(0,2)$
3. C.$g$ is continuous and differentiable for all $x\in(0,2)$
4. D.$g$ is neither continuous nor differentiable at $x=1$

Correct answer: A

Let the position vectors of vertices $A$, $B$ and $C$ of a triangle be $2\hat i+2\hat j+\hat k$, $\hat i+2\hat j+2\hat k$ and $2\hat i+\hat j+2\hat k$ respectively. Let $l_1,l_2$ and $l_3$ be the lengths of perpendiculars drawn from the ortho centre of the triangle on the sides $AB$, $BC$ and $CA$ respectively, then $l_1^2+l_2^2+l_3^2$ equals:

1. A.$\frac13$
2. B.$\frac15$
3. C.$\frac14$
4. D.$\frac12$✓

Correct answer: D

Let the image of the point $(1,0,7)$ in the line $\frac x1=\frac{y-1}{2}=\frac{z-2}{3}$ be the point $(\alpha,\beta,\gamma)$. Then which one of the following points lies on the line passing through $(\alpha,\beta,\gamma)$ and making angles $\frac{2\pi}{3}$ and $\frac{3\pi}{4}$ with $y$-axis and $z$-axis respectively and an acute angle with $x$-axis ?

1. A.$(1,2,1-\sqrt2)$
2. B.$(3,-4,3+2\sqrt2)$
3. C.$(3,4,3-2\sqrt2)$✓
4. D.$(1,-2,1+\sqrt2)$

Correct answer: C

Let $A$ and $B$ be two finite sets with $m$ and $n$ elements respectively. The total number of subsets of the set $A$ is 56 more than the total number of subsets of $B$. Then the distance of the point $P(m,n)$ from the point $Q(-2,-3)$ is:

1. A.8
2. B.4
3. C.10✓
4. D.6

Correct answer: C

Let $f:\mathbb{R}-\left\{\frac{-1}{2}\right\}\to\mathbb{R}$ and $g:\mathbb{R}-\left\{\frac{-5}{2}\right\}\to\mathbb{R}$ be defined as $f(x)=\frac{2x+3}{2x+1}$ and $g(x)=\frac{|x|+1}{2x+5}$. Then, the domain of the function $f\circ g$ is:

1. A.$\mathbb{R}-\left\{-\frac74\right\}$
2. B.$\mathbb{R}-\left\{-\frac52\right\}$✓
3. C.$\mathbb{R}-\left\{-\frac52,-\frac74\right\}$
4. D.$\mathbb{R}$

Correct answer: B

Let $R$ be the interior region between the lines $3x-y+1=0$ and $x+2y-5=0$ containing the origin. The set of all values of $a$, for which the points $(a^2,a+1)$ lie in $R$, is:

1. A.$(-3,-1)\cup\left(\frac13,1\right)$
2. B.$(-3,-1)\cup\left(-\frac13,1\right)$
3. C.$(-3,0)\cup\left(\frac23,1\right)$
4. D.$(-3,0)\cup\left(\frac13,1\right)$✓

Correct answer: D

The integral $\int\frac{(x^8-x^2)\,dx}{(x^{12}+3x^6+1)\tan^{-1}\left(x^3+\frac{1}{x^3}\right)}$ is equal to:

1. A.$\log_e\left(\left|\tan^{-1}\left(x^3+\frac1{x^3}\right)\right|\right)+C$
2. B.$\log_e\left(\left|\tan^{-1}\left(x^3+\frac1{x^3}\right)\right|\right)^{\frac13}+C$✓
3. C.$\log_e\left(\left|\tan^{-1}\left(x^3+\frac1{x^3}\right)\right|\right)^{\frac12}+C$
4. D.$\log_e\left(\left|\tan^{-1}\left(x^3+\frac1{x^3}\right)\right|\right)^{3}+C$

Correct answer: B

If $2\tan^2\theta-5\sec\theta=1$ has exactly 7 solutions in the interval $\left[0,\frac{n\pi}{2}\right]$, for the least value of $n\in N$, then $\sum_{k=1}^{n}\frac{k}{2^k}$ is equal to:

1. A.$\frac{1}{2^{13}}\left(2^{14}-15\right)$✓
2. B.$\frac{1}{2^{15}}\left(2^{14}-14\right)$
3. C.$1-\frac{15}{2^{13}}$
4. D.$\frac{1}{2^{14}}\left(2^{15}-15\right)$

Correct answer: A

If $\alpha,\beta$ are the roots of the equation, $x^2-x-1=0$ and $S_n=2023\alpha^n+2024\beta^n$, then:

1. A.$2S_{11}=S_{12}+S_{10}$
2. B.$S_{11}=S_{10}+S_{12}$
3. C.$2S_{12}=S_{11}+S_{10}$
4. D.$S_{12}=S_{11}+S_{10}$✓

Correct answer: D

Let $e_1$ be the eccentricity of the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$ and $e_2$ be the eccentricity of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, $a>b$, which passes through the foci of the hyperbola. If $e_1e_2=1$, then the length of the chord of the ellipse parallel to the $x$-axis and passing through $(0,2)$ is:

1. A.$4\sqrt5$
2. B.$\frac{10\sqrt5}{3}$✓
3. C.$\frac{8\sqrt5}{3}$
4. D.$3\sqrt5$

Correct answer: B

For $0<a<1$, the value of the integral $\int_0^\pi\frac{dx}{1-2a\cos x+a^2}$ is:

1. A.$\frac{\pi^2}{\pi+a^2}$
2. B.$\frac{\pi}{1+a^2}$
3. C.$\frac{\pi^2}{\pi-a^2}$
4. D.$\frac{\pi}{1-a^2}$✓

Correct answer: D

If $\lim_{x\to0}\frac{3+\alpha\sin x+\beta\cos x+\log_e(1-x)}{3\tan^2x}=\frac13$, then $2\alpha-\beta$ is equal to:

1. A.2
2. B.1
3. C.7
4. D.5✓

Correct answer: D

The $20^{th}$ term from the end of the progression $20,19\frac14,18\frac12,17\frac34,\ldots,-129\frac14$ is:

1. A.−100
2. B.−110
3. C.−118
4. D.−115✓

Correct answer: D

Considering only the principal values of inverse trigonometric functions, the number of positive real values of $x$ satisfying $\tan^{-1}(x)+\tan^{-1}(2x)=\frac\pi4$ is:

1. A.2
2. B.more than 2
3. C.1✓
4. D.0

Correct answer: C

If the area of the region $\{(x,y):0\le y\le\min\{2x,6x-x^2\}\}$ is $A$, then $12A$ is equal to ______.

Correct answer: 304

If the solution curve, of the differential equation $\frac{dy}{dx}=\frac{x+y-2}{x-y}$ passing through the point $(2,1)$ is $\tan^{-1}\left(\frac{y-1}{x-1}\right)-\frac1\beta\log_e\left(\alpha+\left(\frac{y-1}{x-1}\right)^2\right)=\log_e|x-1|$, then $5\beta+\alpha$ is equal to:

Correct answer: 11

The coefficient of $x^{2012}$ in the expansion of $(1-x)^{2008}(1+x+x^2)^{2007}$ is equal to ______.

Correct answer: 0

The lines $\frac{x-2}{2}=\frac{y}{-2}=\frac{z-7}{16}$ and $\frac{x+3}{4}=\frac{y+2}{3}=\frac{z+2}{1}$ intersect at the point $P$. If the distance of $P$ from the line $\frac{x+1}{2}=\frac{y-1}{3}=\frac{z-1}{1}$ is $l$, then $14l^2$ is equal to ______.

Correct answer: 108

Let the complex numbers $\alpha$ and $\frac1{\bar\alpha}$ lie on the circles $|z-z_0|^2=4$ and $|z-z_0|^2=16$ respectively, where $z_0=1+i$. Then, the value of $100|\alpha|^2$ is ______.

Correct answer: 20

Let $f(x)=\int_0^x g(t)\log_e\left(\frac{1-t}{1+t}\right)dt$, where $g$ is a continuous odd function. If $\int_{-\pi/2}^{\pi/2}\left(f(x)+\frac{x^2\cos x}{1+e^x}\right)dx=\left(\frac\pi\alpha\right)^2-\alpha$, then $\alpha$ is equal to ______.

Correct answer: 2

Let $A$ be a $2\times2$ real matrix and $I$ be the identity matrix of order 2. If the roots of the equation $|A-xI|=0$ be $-1$ and 3, then the sum of the diagonal elements of the matrix $A^2$ is ______.

Correct answer: 10

If the sum of squares of all real values of $\alpha$, for which the lines $2x-y+3=0$, $6x+3y+1=0$ and $\alpha x+2y-2=0$ do not form a triangle is $p$, then the greatest integer less than or equal to $p$ is ______.

Correct answer: 32

Consider a circle $(x-\alpha)^2+(y-\beta)^2=50$, where $\alpha,\beta>0$. If the circle touches the line $y+x=0$ at the point $P$, whose distance from the origin is $4\sqrt2$, then $(\alpha+\beta)^2$ is equal to ______.

Correct answer: 100

The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12. If $\mu$ and $\sigma^2$ denote the mean and variance of the correct observations respectively, then $15(\mu+\mu^2+\sigma^2)$ is equal to ______.

Correct answer: 2521

An object is placed in a medium of refractive index 3. An electromagnetic wave of intensity $6\times10^8$ W/m² falls normally on the object and it is absorbed completely. The radiation pressure on the object would be (speed of light in free space $3\times10^8$ m/s):

1. A.2 N m$^{-2}$
2. B.6 N m$^{-2}$✓
3. C.36 N m$^{-2}$
4. D.18 N m$^{-2}$

Correct answer: B

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Work done by electric field on moving a positive charge on an equipotential surface is always zero. Reason (R): Electric lines of forces are always perpendicular to equipotential surfaces. In the light of the above statements, choose the most appropriate answer from the options given below:

1. A.(A) is not correct but (R) is correct
2. B.(A) is correct but (R) is not correct
3. C.Both (A) and (R) are correct and (R) is the correct explanation of (A)✓
4. D.Both (A) and (R) are correct but (R) is not the correct explanation of (A)

Correct answer: C

Primary side of a transformer is connected to 230 V, 50 Hz supply. Turns ratio of primary to secondary winding is 10 : 1. Load resistance connected to secondary side is 46 Ω. The power consumed in it is:

1. A.10.0 W
2. B.11.5 W✓
3. C.12.0 W
4. D.12.5 W

Correct answer: B

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $\frac{C_p}{C_v}$ for the gas is:

1. A.$\frac75$
2. B.$\frac32$✓
3. C.$\frac97$
4. D.$\frac53$

Correct answer: B

The threshold frequency of a metal with work function 6.63 eV is:

1. A.$1.6\times10^{15}$ Hz✓
2. B.$16\times10^{12}$ Hz
3. C.$1.6\times10^{12}$ Hz
4. D.$16\times10^{15}$ Hz

Correct answer: A

Given below are two statements: Statement (I): The limiting force of static friction depends on the area of contact and independent of materials. Statement (II): The limiting forces of kinetic friction is independent of the area of contact and depends on materials. In the light of the above statements, choose the most appropriate answer from the options given below:

1. A.Both Statement I and Statement II are correct
2. B.Statement I is correct and Statement II is incorrect
3. C.Both Statement I and Statement II are incorrect
4. D.Statement I is incorrect and Statement II is correct✓

Correct answer: D

The atomic mass of ${}_6C^{12}$ is 12.000000 u and that of ${}_6C^{13}$ is 13.003354 u. The required energy to remove a neutron from ${}_6C^{13}$, if mass of neutron is 1.008665 u, will be:

1. A.4.95 MeV✓
2. B.62.5 MeV
3. C.49.5 MeV
4. D.6.25 MeV

Correct answer: A

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity. Reason (R): The restoring force depends upon the bonded inter atomic and inter molecular force of solid. In the light of the above statements, choose the most appropriate answer from the options given below:

1. A.Both (A) and (R) are true and (R) is the correct explanation of (A)✓
2. B.Both (A) and (R) are true but (R) is not the correct explanation of (A)
3. C.(A) is true but (R) is false
4. D.(A) is false but (R) is true

Correct answer: A

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun. Reason (R): The moon takes less time to move around the earth than the time taken by the earth to move around the sun. In the light of the above statements, choose the correct answer from the options given below:

1. A.(A) is not correct but (R) is correct
2. B.Both (A) and (R) are correct but (R) is not the correct explanation of (A)
3. C.(A) is correct but (R) is not correct
4. D.Both (A) and (R) are correct and (R) is the correct explanation of (A)✓

Correct answer: D

The truth table of the given circuit diagram is:

1. A.A B Y: 0 0 0; 0 1 0; 1 0 0; 1 1 1
2. B.A B Y: 0 0 0; 0 1 1; 1 0 1; 1 1 0✓
3. C.A B Y: 0 0 1; 0 1 1; 1 0 1; 1 1 0
4. D.A B Y: 0 0 1; 0 1 0; 1 0 0; 1 1 1

Correct answer: B

A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle 60° with the horizontal, the weight experienced by the man is:

1. A.3 kg✓
2. B.$6\sqrt3$ kg
3. C.6 kg
4. D.12 kg

Correct answer: A

When a polaroid sheet is rotated between two crossed polaroids then the transmitted light intensity will be maximum for a rotation of:

1. A.45°✓
2. B.30°
3. C.60°
4. D.90°

Correct answer: A

A current of 200 μA deflects the coil of a moving coil galvanometer through 60°. The current to cause deflection through $\frac{\pi}{10}$ radian is:

1. A.60 μA✓
2. B.120 μA
3. C.30 μA
4. D.180 μA

Correct answer: A

Three voltmeters, all having different internal resistances are joined as shown in figure. When some potential difference is applied across A and B, their readings are $V_1$, $V_2$ and $V_3$. Choose the correct option.

1. A.$V_1=V_2$
2. B.$V_1+V_2=V_3$✓
3. C.$V_1+V_2>V_3$
4. D.$V_1\ne V_3-V_2$

Correct answer: B

The equation of state of a real gas is given by $\left(P+\frac{a}{V^2}\right)(V-b)=RT$, where P, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of $\frac{a}{b^2}$ is similar to that of:

1. A.$PV$
2. B.$R$
3. C.$RT$
4. D.$P$✓

Correct answer: D

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): In Vernier Calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading. Reason (R): The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling. In the light of the above statements, choose the correct answer from the options give below:

1. A.Both (A) and (R) are correct and (R) is the correct explanation of (A)
2. B.(A) is true but (R) is false
3. C.(A) is false but (R) is true
4. D.Both (A) and (R) are correct but (R) is not the correct explanation of (A)✓

Correct answer: D

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle $(\theta)$ of thread deflection in the extreme position will be:

1. A.$2\tan^{-1}\left(\frac1{\sqrt5}\right)$
2. B.$2\tan^{-1}\left(\frac12\right)$✓
3. C.$\tan^{-1}\left(\frac12\right)$
4. D.$\tan^{-1}(\sqrt2)$

Correct answer: B

The total kinetic energy of 1 mole of oxygen at 27°C is: [Use universal gas constant (R) = 8.31 J/mole K]

1. A.5670.5 J
2. B.5942.0 J
3. C.6845.5 J
4. D.6232.5 J✓

Correct answer: D

Wheatstone bridge principle is used to measure the specific resistance $(S_1)$ of given wire, having length $L$, radius $r$. If $X$ is the resistance of wire, then specific resistance is; $S_1=X\left(\frac{\pi r^2}{L}\right)$. If the length of the wire gets doubled then the value of specific resistance will be:

1. A.$\frac{S_1}{4}$
2. B.$S_1$✓
3. C.$\frac{S_1}{2}$
4. D.$2S_1$

Correct answer: B

A parallel beam of monochromatic light of wavelength 5000 Å is incident normally on a single narrow slit of width 0.001 mm. The light is focused by convex lens on screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of ______ (degree).

Correct answer: 30

Two charges of $-4\ \mu C$ and $+4\ \mu C$ are placed at the points $A(1,0,4)$ m and $B(2,-1,5)$ m located in an electric field $\vec E=0.20\,\hat i$ V/cm. The magnitude of the torque acting on the dipole is $8\sqrt\alpha\times10^{-5}$ N m, where $\alpha=$ ______.

Correct answer: 2

A closed organ pipe 150 cm long gives 7 beats per second with an open organ pipe of length 350 cm, both vibrating in fundamental mode. The velocity of sound is ______ m/s.

Correct answer: 294

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $R_1=2\pi$ m and $R_2=4\pi$ m, carrying current $I=4$ A as per figure given below is $\alpha\times10^{-7}$ T. The value of $\alpha$ is ______. (Centre O is common for all segments)

Correct answer: 3

A series LCR circuit with $L=\frac{100}{\pi}$ mH, $C=\frac{10^{-3}}{\pi}$ F and $R=10\ \Omega$, is connected across an ac source of 220 V, 50 Hz supply. The power factor of the circuit would be ______.

Correct answer: 1

A body falling under gravity covers two points A and B separated by 80 m in 2 s. The distance of upper point A from the starting point is ______ m (use $g=10$ m s$^{-2}$).

Correct answer: 45

The reading of pressure metre attached with a closed pipe is $4.5\times10^4$ N/m². On opening the valve, water starts flowing and the reading of pressure metre falls to $2.0\times10^4$ N/m². The velocity of water is found to be $\sqrt V$ m/s. The value of $V$ is ______.

Correct answer: 50

The electric potential at the surface of an atomic nucleus $(z=50)$ of radius $9\times10^{-13}$ cm is ______ $\times10^6$ V.

Correct answer: 8

If Rydberg's constant is $R$, the longest wavelength of radiation in Paschen series will be $\frac{\alpha}{7R}$, where $\alpha=$ ______.

Correct answer: 144

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is $\frac7x$, where $x$ is ______.

Correct answer: 7

The final product A, formed in the following reaction sequence is: $\text{Ph-CH=CH}_2\xrightarrow{\text{(i) BH}_3\ \text{(ii) H}_2\text{O}_2,\ \overset{\ominus}{\text{O}}\text{H}\ \text{(iii) HBr}\ \text{(iv) Mg, ether, then HCHO/H}_3\text{O}^+}A$

1. A.$\text{Ph-CH(CH}_3\text{)-CH}_3$
2. B.$\text{Ph-CH}_2\text{-CH}_2\text{-CH}_2\text{-OH}$✓
3. C.$\text{Ph-CH(CH}_3\text{)-CH}_2\text{OH}$
4. D.$\text{Ph-CH}_2\text{-CH}_2\text{-CH}_3$

Correct answer: B

Which of the following cannot function as an oxidizing agent?

1. A.$\text{SO}_4^{2-}$
2. B.$\text{MnO}_4^-$
3. C.$\text{N}^{3-}$✓
4. D.$\text{BrO}_3^-$

Correct answer: C

Which among the following halide/s will not show $S_N1$ reaction: (A) $\text{H}_2\text{C=CH-CH}_2\text{Cl}$ (B) $\text{CH}_3\text{-CH=CH-Cl}$ (C) benzyl chloride ($\text{C}_6\text{H}_5\text{CH}_2\text{Cl}$) (D) $(\text{CH}_3)_2\text{CH-Cl}$ Choose the most appropriate answer from the options given below:

1. A.(A), (B) and (D) only
2. B.(B) and (C) only
3. C.(A) and (B) only
4. D.(B) only✓

Correct answer: D

Identify B formed in the reaction. $\text{Cl-(CH}_2)_4\text{-Cl}\xrightarrow{\text{excess NH}_3}A\xrightarrow{\text{NaOH}}B+\text{H}_2\text{O}+\text{NaCl}$

1. A.$\text{Cl}^-\,\overset{+}{\text{N}}\text{H}_3\text{-(CH}_2)_4\text{-}\overset{+}{\text{N}}\text{H}_3\,\text{Cl}^-$
2. B.1,1'-bipiperidine (two piperidine rings joined N–N)
3. C.$\text{H}_2\text{N-(CH}_2)_4\text{-NH}_2$✓
4. D.Piperidine

Correct answer: C

The molecular formula of second homologue in the homologous series of mono carboxylic acid is:

1. A.$\text{C}_2\text{H}_2\text{O}_2$
2. B.$\text{C}_3\text{H}_6\text{O}_2$
3. C.$\text{CH}_2\text{O}$
4. D.$\text{C}_2\text{H}_4\text{O}_2$✓