JEE Main 2023 8 April Shift 1 Question Paper with Solution PDF- Download Here

Consider the word INDEPENDENCE. The number of words such that all the vowels are together is?

• (1) 16800
• (2) 15800
• (3) 17900
• (4) 14800

Let \(f(x)=\frac{sinx+cosx-\sqrt2}{sinx-cosx},x∈[0.\pi]-\left[\frac{\pi}{4}\right]. Then f\left(\frac{7\pi}{12}\right)f^n\left(\frac{7\pi}{12}\right)\)is equal to

• (1) \(\frac{-2}{3}\)
• (2) \(\frac{-1}{3\sqrt3}\)
• (3) \(\frac{2}{3\sqrt3}\)
• (4) \(\frac{2}{9}\)

Let A =\(\left[\begin{matrix} 2 & 1 & 0 \\   1 & 2 & -1 \\   0 & -1 & 2  \end{matrix} \right]\). If |adj(adj(adj 2A)) | = (16)ⁿ, then n is equal to

• (1) 10
• (2) 8
• (3) 12
• (4) 9

\(\lim\limits_{x\rightarrow0}\left(\left(\frac{1-cos^2(3x)}{cos^3(4x)}\right)\left(\frac{sin^3(4x)}{(log_e(2x+1))^5}\right)\right)\)is equal to

• (1) 9
• (2) 15
• (3) 18
• (4) 24

A bolt manufacturing factory has three products A, B and C. 50% and 30% of the products are A and B type respectively and remaining are C type. Then probability that the product A is defective is 4%, that of B is 3% and that of C is 2%. A product is picked randomly picked and found to be defective, then the probability that it is type C.

• (1) \(\frac{4}{33}\)
• (2) \(\frac{1}{33}\)
• (3) \(\frac{2}{33}\)
• (4) \(\frac{9}{33}\)

7 boys and 5 girls are to be seated around a circular table such that no two girls sit together is?

• (1) \(126(5!)^{2}\)
• (2) \(720(5!)\)
• (3) \(720(6!)\)
• (4) 720

The shortest distance between the lines
\(\frac{x-4}{4}=\frac{y+2}{5}=\frac{z+3}{3}\)
and
\(\frac{x-1}{3}=\frac{y-3}{4}=\frac{z-4}{2}\)
is :

• (1) \(3\sqrt{6}\)
• (2) \(6\sqrt{2}\)
• (3) \(6\sqrt{3}\)
• (4) \(2\sqrt{6}\)

Let R be the focus of the parabola y² = 20x and the line y=mx+c intersect the parabola at two points Pand Q. Let the point G(10,10) be the centroid of the triangle PQR. If c-m=6, then (PQ)² is

• (1) 296
• (2) 325
• (3) 317
• (4) 346

The area of the region {(x,y): x² ≤ y ≤8-x², y≤7} is

• (1) 18
• (2) 20
• (3) 21
• (4) 24

Let C(α, β) be the circumcenter of the triangle formed by the lines
4x+3y=69,
4y-3x=17, and
x+7y=61.
Then (α-β)²+α+β is equal to

• (1) 15
• (2) 16
• (3) 17
• (4) 18

Let \(I(x)=\int\frac{x+1}{x(1+xe^x)^2} dx\), x>0. If \(\lim\limits_{x\rightarrow\infin}I(x)=0\), then I(1) is equal to

• (1) \(\frac{e+2}{e+1}-log_e(e+1)\)
• (2) \(\frac{e+2}{e+1}+log_e(e+1)\)
• (3) \(\frac{e+1}{e+2}-log_e(e+1)\)
• (4) \(\frac{e+1}{e+2}+log_e(e+1)\)

Let α, β, γ be the three roots of the equation x³+bx+c=0. If βγ =1=-α, then b³+2c³-3α³-6β³-8γ³ is equal to

• (1) \(\frac{169}{8}\)
• (2) \(\frac{155}{8}\)
• (3) 19
• (4) 28

Let the number of elements in sets \(A\) and \(B\) be five and two respectively. Then the number of subsets of \(A \times B\) each having at least 3 and at most 6 elements is:

• (1) 752
• (2) 772
• (3) 792
• (4) 782

Let S_K = \(\frac{1+2+...+ K}{K}\) and \(\displaystyle\sum_{j=1}^{n}S_j^2=\frac{n}{A}(Bn^2+Cn+D)\), where A,B,C,D∈N and A has least value. Then

• (1) A+B+C+D is divisible by 5
• (2) A+B is divisible by D
• (3) A+B=5(D-C)
• (4) A+C+D is not divisible by B

Let P = \(\left[\begin{matrix}   \frac{\sqrt3}{2} & \frac{1}{2} \\   -\frac{1}{2} & \frac{\sqrt3}{2}  \end{matrix}\right]\) A = \(\left[\begin{matrix}   1 & 1 \\   0 & 1  \end{matrix}\right]\) and Q = PAP^T. If P^TQ²⁰⁰⁷P = \(\left[\begin{matrix}   a & b \\   c & d  \end{matrix}\right]\), then 2a+b-3c-4d equal to

• (1) 2004
• (2) 2005
• (3) 2006
• (4) 2007

If for z=α+iβ, |z+2|=z+4(1+i), then α +β and αβ are the roots of the equation

• (1) x²+3x-4=0
• (2) x²+7x+12=0
• (3) x²+2x-3=0
• (4) x²+x-12=0

If the points with position vectors \(a\hat{i} +10\hat{j} +13\hat{k}, 6\hat{i} +11\hat{k} +11\hat{k},\frac{9}{2}\hat{i}+B\hat{j}−8\hat{k}\) are collinear, then (19α-6β)² is equal to

• (1) 16
• (2) 25
• (3) 36
• (4) 49

If the coefficients of three consecutive terms in the expansion of (1+x)n are in the ratio 1:5:20, then the coefficient of the fourth term of the expansion is?

• (1) 3654
• (2) 3658
• (3) 3600
• (4) 1000

If the equation of the plane containing the line x+2y+3z-4=0=2x+y-z+5 and perpendicular to the plane \(\vec{r}=(\vec{i}-\vec{j})+\lambda(\vec{i}+\vec{j}+\vec{k})+\mu(\vec{i}-2\vec{j}+3\vec{k})\) is ax+by+cz=4, then (a-b+c) is equal to

• (1) 18
• (2) 20
• (3) 22
• (4) 24

Negation of (p⇒q)⇒(q⇒p) is

• (1) p∨(∼q)
• (2) (∼p)∨q
• (3) q∧(∼p)
• (4) (∼q)∧p

Let [t] denote the greatest integer ≤t. Then \(\frac{2}{π} \int\limits_{\frac{\pi}{6}}^{\frac{5\pi}{6}} (8 [cosec x]-5[cot x]) dx\)is equal to ______.

Let A={0, 3, 4, 6, 7, 8, 9, 10 } and R be the relation defined on A such that R = {(x, y)∈A×A:x-y is odd positive integer or x-y=2}. The minimum number of elements that must be added to the relation R, so that it is a symmetric relation, is equal to _______.

If the solution curve of the differential equation \( (y - 2 \log x) dx + (x \log x^2) dy = 0 \) passes through the points \( \left( e^{4/3}, \alpha \right) \) and \( \left( e^4, \alpha \right) \), then \( \alpha \) is equal to: 
 

Let the mean and variance of 8 numbers \(x, y, 10, 12, 6, 12, 4, 8\) be \(9\) and \(9.25\) respectively. If \(x > y\), then \(3x - 2y\) is equal to:

• (1) 25
• (2) 1
• (3) 24
• (4) 13

Let \(\vec{a} = 6\hat{i} + 9\hat{j} + 12\hat{k}\), \(\vec{b} = a\hat{i} + 11\hat{j} - 2\hat{k}\), and \(\vec{c}\) be vectors such that \(\vec{a} \times \vec{c} = \vec{a} \times \vec{b}\). If \(\vec{a} \cdot \vec{c} = -12\) and \(\vec{c} \cdot (\hat{i} - 2\hat{j} + \hat{k}) = 5\), then \(\vec{c} \cdot (\hat{i} + \hat{j} + \hat{k})\) is equal to:

If a_a is the greatest term in the sequence \(a_n=\frac{n^3}{n^4+147},n=1,2,3,...,\) then a is equal to______________.

Let \([t]\) denote the greatest integer \(\le t\). If the constant term in the expansion of
\(\left(3x^{2}-\frac{1}{2x^{5}}\right)^{7}\)
is \(\alpha\), then \([\alpha]\) is equal to ____________.

Consider a circle \(C_1 : x^2 + y^2 - 4x - 2y = \alpha - 5\). Let its mirror image in the line \(y = 2x + 1\) be another circle \(C_2 : 5x^2 + 5y^2 - 10x - 10y + 36 = 0\). Let \(r\) be the radius of \(C_2\). Then \(\alpha + r\) is equal to:

The largest natural number \(n\) such that \(3^n\) divides \(66!\) is:

Let \(\lambda_1, \lambda_2\) be the values of \(\lambda\) for which the points \((1, \lambda, \frac{1}{2})\) and \((-2, 0, 1)\) are at equal distance from the plane \(2x + 3y - 6z + 7 = 0\). If \(\lambda_1 > \lambda_2\), then the distance of the point \((1 - \lambda_2, \lambda_2, \lambda_1)\) from the line \(\frac{x-5}{1} = \frac{y-1}{2} = \frac{z+7}{2}\) is:

An air bubble having volume 1 cm³ at depth 40 m inside water comes to the surface. What will be the volume of the bubble at the surface?

• (1) 5 cm³
• (2) 2 cm³
• (3) 4 cm³
• (4) 3 cm³

In a reflecting telescope, a secondary mirror is used to:

• (1) make chromatic aberration zero
• (2) remove spherical aberration
• (3) reduce the problem of mechanical support
• (4) move the eyepiece outside the telescopic tube

Certain galvanometers have a fixed core made of non magnetic metallic material. The function of this metallic material is

• (1) to oscillate the coil in magnetic field for longer period of time
• (2) to produce large deflecting torque on the coil
• (3) to make the magnetic field radial
• (4) to bring the coil to rest quickly

Given below are two statements:
Statement I: If E be the total energy of a satellite moving around the earth, then its potential energy will be \(\frac{E}{2}\)
Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy E.
In the light of the above statements, choose the most appropriate answer from the options given below

• (1) Both Statement I and Statement II are correct
• (2) Both Statement I and Statement II are incorrect
• (3) Statement I is correct but Statement II is incorrect
• (4) Statement I is incorrect but Statement II is correct

Dimension of \(\frac{1}{μ_0∈_0}\) should be equal to 

• (1) \(\frac{L}{T}\)
• (2) \(\frac{T}{L}\)
• (3) \(\frac{L^2}{T^2}\)
• (4) \(\frac{T^2}{L^2}\)

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius R, with distance r from the centre O is represented by

• (1)
• (2)
• (3)
• (4)

Given below are two statements:
Statement I: If heat is added to a system, its temperature must increase.
Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.
In the light of the above statements, choose the correct answer from the options given below

• (1) Both Statement I and Statement II are true
• (2) Both Statement I and Statement II are false
• (3) Statement I is true but Statement II is false
• (4) Statement I is false but Statement II is true

A charge particle moving in magnetic field \(B\), has the components of velocity along \(B\) as well as perpendicular to \(B\). The path of the charge particle will be

• (1) helical path with the axis along magnetic field \(B\)
• (2) straight along the direction of magnetic field \(B\)
• (3) circular path
• (4) helical path with the axis perpendicular to the direction of magnetic field \(B\)

Two forces of magnitude A and \(\frac{A}{2}\) act perpendicular to each other. The magnitude of the resultant force is equal to:

• (1) \(\frac{A}{2}\)
• (2) \(\frac{\sqrt{5A}}{{2}}\)
• (3) \(\frac{3A}{2}\)
• (4) \(\frac{5A}{2}\)

At any instant the velocity of a particle of mass 500 g is \((2t\hat{i}+3t^2\hat{j}) ms^{-1}\). If the force acting on the particle at t=1s is \((\hat{i} + x\hat{j})N\). Then the value of x will be:

• (1) 6
• (2) 4
• (3) 3
• (4) 2

If mass, radius of cross-section and height of a cylinder are (0.4+0.01) g, (6+0.03) m and height (8+0.04) m. The maximum percentage error in the measurement of density of cylinder is?

• (1) 1%
• (2) 4%
• (3) 8%
• (4) 7%

Two projectiles u₁ and u₂, with speed of 40 m/s and 60 m/s respectively are thrown at a certain angle, u₁ with 30^o and u₂ with 60^o, what is the ratio of range?

For a nucleus AAX having mass number A and atomic number Z
A. The surface energy per nucleon \((b_s)=−a_1A^{\frac{2}{3}} \)
B. The Coulomb contribution to the binding energy \(b_c=−a_2\frac{Z(Z−1)}{A^{\frac{4}{3}}} \)
C. The volume energy b_v=a₃A
D. Decrease in the binding energy is proportional to surface area.
E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( a₁,a₂ and a₃ are constants)
Choose the most appropriate answer from the options given below:

• (1) A, B, C, D only
• (2) B, C only
• (3) C, D only
• (4) B, C, E only

An aluminium rod with Young's modulus Y=7.0×10¹⁰ N/m² undergoes elastic strain of 0.04%. The energy per unit volume stored in the rod in SI unit is:

• (1) 2800
• (2) 5600
• (3) 8400
• (4) 11200

For the logic circuit shown, the output waveform at Y is:

• (1)

• (2)

• (3)

• (4)

The weight of a body on the earth is \(400\ \mathrm{N}\). Then weight of the body when taken to a depth half of the radius of the earth will be:

• (1) \(300\ \mathrm{N}\)
• (2) \(200\ \mathrm{N}\)
• (3) \(100\ \mathrm{N}\)
• (4) Zero

Proton \((\mathrm{P})\) and electron \((\mathrm{e})\) will have same de-Broglie wavelength when the ratio of their momentum is (assume, \(m_p=1849\,m_e\)):

• (1) 1 : 1
• (2) 1 : 43
• (3) 1 : 1849
• (4) 43 : 1

In this figure the resistance of the coil of galvanometer G is 2Ω. The emf of the cell is 4 V. The ratio of potential difference across C₁ and C₂ is

• (1) \(\frac{4}{5}\)
• (2) 1
• (3) \(\frac{5}{4}\)
• (4) \(\frac{3}{4}\)

A train is moving with a speed of \(10 m/s\) towards a platform and blows a horn with frequency \(400 Hz\). Find the frequency heard by a passenger standing on the platform. Take speed of sound = \(310 m/s\).

• (1) 405 Hz
• (2) 425 Hz
• (3) 380 Hz
• (4) 413 Hz

The height of the antenna is 98 m. The radius of Earth is 6400 km. The area up to which it will transmit signal is:

• (1) 3642 km²
• (2) 3942 km²
• (3) 11200 km²
• (4) 22400 km²

The magnetic intensity at the centre of a long current carrying solenoid is found to be 1.6 x 10³ Am^-1. If the number of turns is 8 per cm, then the current flowing through the solenoid is_____A.

An organ pipe 40cm long is open at both ends. The speed of sound in air is 360ms^-1 . The frequency of the second harmonic is ____Hz.

A current of 2 A flows through a wire of crosssectional area 25.0 mm2 . The number of free electrons in a cubic meter are 2.0 x 10²⁸ . The drift velocity of the electrons is _____ x 10^-6 ms^-1 (Given, charge on electron = 1.6 x 10^-19C)

A nucleus with mass number 242 and binding energy per nucleon as 7.6 MeV breaks into fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as 8.1 MeV, the total gain in binding energy is ____MeV.

The momentum of a body is increased by 50%. The percentage increase in the kinetic energy of the body is ______%

An electric dipole of dipole moment is 6.0 x 10^-6 Cm placed in a uniform electric field of 1.5 x 10³ NC^-1 in such a way that dipole moment is along electric field. The work done in rotating dipole by 180º in this field will be _____mJ.

Two vertical parallel mirrors A and B are separated by 10 cm. A point object O is placed at a distance of 2 cm from mirror A. The distance of the second nearest image behind mirror A from the mirror A is ___cm

An air bubble of diameter 6 mm rises steadily through a solution of density 1750kg / m³ at the rate of 0.35 cm/s. The co-efficient of viscosity of the solution (neglect density of air) is ____Pas (given, g = 10ms^-2)

An oscillating LC circuit consists of a 75 mH inductor and a 1.2 uF capacitor. If the maximum charge to the capacitor is 2.7μC. The maximum current in the circuit will be _____mA.

The moment of inertia of semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is \(\frac{1}{x} \)MR² , where R is the radius and M is the mass of semicircular ring. The value of x will be___

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.  
Assertion A: Butan -1- ol has higher boiling point than ethoxyethane.  
Reason R: Extensive hydrogen bonding leads to stronger association of molecules.  
In the light of the above statements, choose the correct answer from the options given below: 

• (1) Both A and R are true and R is the correct explanation of A
• (2) A is true but R is false
• (3) Both A and R are true but R is not the correct explanation of A
• (4) A is false but R is true

Which of the following complex is octahedral, diamagnetic and the most stable?

• (1) K₃[CO(CN)₆]
• (2) [Ni(NH₃)₆]Cl₂
• (3) The correct option is(A): Na₃[COCl₆]
• (4) [Co(H₂O)₆]Cl₂

Select the correct order of electronegativity of the elements: B, C, At, S

• (1) B > C > S > At
• (2) S > C > B > At
• (3) C > B > S > At
• (4) S > C > At > B

The correct order of spin only magnetic moments for the following complex ions is

• (1) [Fe(CN)₆]^3-< [CoF6]^3- < [MnBr₄]^2- < [Mn(CN)₆]^3-
• (2) [Fe(CN)₆]^3-< [Mn(CN)₆]^3- < CoF₆]^3- < [MnBr₄]^2-
• (3) [COF₆]^3- < [MnBr₄]^2- < [Fe(CN)₆]^3- < [Mn(CN)₆]^3-
• (4) [MnBr₄]^2- < [CoF₆]^3- < [Fe(CN)₆]^3- < [Mn(CN)₆]^3-

\(2 I O^ − _3 + x I ^− + 12 H ^+ ⟶ 6 I_ 2 + 6 H _2 O\) What is the value of x?

• (1) 2
• (2) 10
• (3) 6
• (4) 12

	List-I (Reagent)		List-II (Products)
A		I
B	HBF4 \(\triangle\)	II
C	Cu, HCI	III
D	CuCN/ KCN	IV

• (1) A-IV, B-III, C-II, D-I
• (2) A-III, B-I, C-IV, D-II
• (3) A-I, B-III, C-IV, D-II
• (4) A-III, B-I, C-II, D-IV

Consider the reaction \(Cu^{2+} + X^- → Cu_2X_2 + X_2\).
X² will be predominantly?

• (1) Cl₂
• (2) Br₂
• (3) I₂
• (4) All halogens are possible.

In chromyl chloride, the number of d-electrons present on chromium is same as in (Given at no. of Ti : 22, V : 23, Cr : 24, Mn : 25, Fe : 26)

• (1) Mn (VII)
• (2) Fe (III)
• (3) V (IV)
• (4) Ti (III)

The major product formed in the following reaction is

• (1)
• (2)
• (3)
• (4)

The reaction \(\frac{ 1}{2}\)H₂(g) + AgCl(s) → H⁺(aq) + Cl^-(aq) + Ag(s) occurs in which of the given galvanic cell.

• (1) Ag | AgCl(s) | KCl(sonⁿ) || AgNO₃ | Ag
• (2) Pt | H₂(g) | HCl(solⁿ) || AgNO₃ (solⁿ) | Ag
• (3) Pt | H₂(g) | HCl(solⁿ) || AgCl(s) | Ag
• (4) Pt | H₂(g) | KCl(solⁿ) || AgCl(s) | Ag

The water gas on reacting with cobalt as a catalyst forms

• (1) Methanoic acid
• (2) Methanol
• (3) Methanal
• (4) Ethanol

Choose the halogen which is most reactive towards SN1 reaction in the given compounds (A, B, C & D)

• (1) A-Br_(a) ; B-I_(a) ; C-Br_(b) ; D-Br_(a)
• (2) A-Br_(a) ; B-I_(a) ; C-Br_(a) ; D-Br_(a)
• (3) A-Br_(b) ; B-I_(a) ; C-Br_(a) ; D-Br_(a)
• (4) A-Br_(b) ; B-I_(b) ; C-Br_(b) ; D-Br_(b)

Match List-I with List-II :

	List I (Reagents Used)		List II (Compound with Functional group detected)
A	Alkaline solution of copper sulphate and sodium citrate	I
B	Neutral FeCl3 solution	II
C	Alkaline chloroform solution	III
D	Potassium iodide and sodium hypochlorite	IV

Choose the correct answer from the options given below :

• (1) A-II, B-IV, C-III, D-I
• (2) A-IV, B-I, C-II, D-III
• (3) A-III, B-IV, C-I, D-II
• (4) A-III, B-IV, C-II, D-I

• (1) A-III, B-II, C-I, D-IV
• (2) A-IV, B-III, C-II, D-I
• (3) A-II, B-I, C-III, D-IV
• (4) A-I, B-II, C-III, D-IV

• (1) A-II, B-IV, C-I, D-III
• (2) A-II, B-IV, C-III, D-I
• (3) A-II, B-III, C-IV, D-I
• (4) A-IV, B-III, C-I, D-II

Read the following two statements
Statement I: Ionic radius of Li+ is greater than Mg++
Statement II: Lithium and magnesium can't form superoxide

• (1) Both Statement I and Statement II are correct.
• (2) Both Statement I and Statement II are incorrect.
• (3) Statement I is correct but Statement II is incorrect.
• (4) Statement I is incorrect but Statement II is correct.

What is the purpose of adding gypsum to cement?

• (1) To give a hard mass
• (2) To facilitate the hydration of cement
• (3) To slow down the process of setting
• (4) To speed up the process of setting

Which of the following represent the Freundlich adsorption isotherms?




Choose the correct answer from the options given below: 

• (1) A, B only
• (2) B, C, D only
• (3) A, B, D only
• (4) A, C, D only

Which of the following metals can be extracted through alkali leaching technique?

• (1) Cu
• (2) Au
• (3) Sn
• (4) Pb

1. If there is no relation between rate constant and temperature, then activation energy is negative.
2. If the activation energy is zero, rate constant is temperature independent.
3. If rate constant increases with increase of temperature, activation energy is positive.
4. If rate constant decreases with increase in temperature, activation energy is negative.

• (1) 1 and 2
• (2) 2 and 3
• (3) 2, 3, and 4
• (4) 4

1. Polarising power of cation
2. Polarisability of the anion
3. Distortion caused by cation
4. Polarisability of cation

• (1) 1 and 2
• (2) 2 and 3
• (3) 1, 2, and 3
• (4) 4

0.5 gm of an organic compound with 60%. Carbon produce ______ gm of \(CO_{2}\) upon complete combustion

The titration curve of weak acid vs. strong base with phenolphthalein as indictor is shown below. The K_{phenolphthalein} = 4 × 10^-10 . 
Given: log2 = 0.3

The number of following statements which is/are correct about phenolphthalein is______
A. It can be used as an indicator for the titration of weak acid with weak base.
B. It begins to change colour at pH = 8.4
C. It is a weak organic base
D. It is colourless in acidic medium.

When a 60 W electric heater is immersed in a gas for 100s in a constant volume container with adiabatic walls, the temperature of the gas rises by 5°C. The heat capacity of the given gas is_____J K^-1 (Nearest integer).

Molar mass of the hydrocarbon (X) which on ozonolysis consumes one mole of O3 per mole of (X) and gives one mole each of ethanal and propanone is _______ g mol-1  
(Molar mass of C : 12 g mol-1 , H : 1 g mol-1)

The vapour pressure vs. temperature curve for a solution solvent system is shown below.

The boiling point of the solvent is _____°C.

The number of following statement/s which is/are\(\text{\underline{ incorrect}}\) is______  
(A) Line emission spectra are used to study the electronic structure  
(B) The emission spectra of atoms in the gas phase show a continuous spread of wavelength from red to violet  
(C) An absorption spectrum is like the photographic negative of an emission spectrum  
(D) The element helium was discovered in the sun by spectroscopic method.

XeF\(_4\) reacts with SbF\(_5\) to form:
\[ [\text{XeF}_m]^{n+}[\text{SbF}_y]^{z-} \] What is \(m+n+y+z\)?

Three bulbs are filled with CH4, CO2 and Ne as shown in the picture. The bulbs are connected through pipes of zero volume. When the stopcocks are opened and the temperature is kept constant throughout, the pressure of the system is found to be_______atm. (Nearest integer)