**JEE Main Session 2 28 ^{th} June 2022 Shift 2**

**PHYSICS**

**Section-A**

**IMPORTANT INSTRUCTIONS:**

(1) The test is of **3 hours** duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of **Physics**, **Chemistry** and **Mathematics** having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) **Section-A:** This section contains 20 multiple choice questions which have only one correct answer. each question carries **4 marks** for correct answer and **−1** mark for wrong answer.

(ii) **Section-B:** This section contains 10 questions. In Section-B, attempt any **five questions out of 10.** The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and **−1 mark** for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as Here m and n are constants. The relations for distance and time in two systems respectively are :

2. A ball is spun with angular acceleration α = 6t^{2} – 2t, where t is in second and α is in rads^{–2}. At t = 0, the ball has angular velocity of 10 rads^{–1} and angular position of 4 rad. The most appropriate expression for the angular position of the ball is :

3. A block of mass 2 kg moving on a horizontal surface with speed of 4 ms^{–1} enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = –kx where k = 12 Nm^{–1}. The speed of the block as it just crosses the rough surface will be :

(A) Zero

(B) 1.5 ms^{–1}

(C) 2.0 ms^{–1}

(D) 2.5 ms^{–1}

4. A √(34) 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 F_{f} and F_{w} are the reaction forces of the floor and the wall, then ratio of F_{w}/F_{f} will be:

(Use g = 10 m/s^{2})

(A) 6/√110

(B) 3/√113

(C) 3/√109

(D) 2/√109

5. Water falls from a 40 m high dam at the rate of 9 × 10^{4} kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydro electric energy number of 100 W lamps, that can be lit, is :

(Take g = 10 ms^{−}^{2})

(A) 25

(B) 50

(C) 100

(D) 18

6. 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

7. A water drop of radius 1 μm falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1.8 × 10^{–5 }Nsm^{–2} and its density is negligible as compared to that of water (10^{6}gm^{–3}). Terminal velocity of the water drop is

(Take acceleration due to gravity = 10 ms^{–2})

(A) 145.4 × 10^{–6}ms^{–1}

(B) 118.0 × 10^{–6}ms^{–1}

(C) 132.6 × 10^{–6}ms^{–1}

(D) 123.4 × 10^{–6}ms^{–1}

8. 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 of 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 J. The work done by the gas during the part CA is:

(A) 20 J

(B) 30 J

(C) −30 J

(D) −60 J

9. 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?

(A) The velocity of atomic oxygen remains same

(B) The velocity of atomic oxygen doubles

(C) The velocity of atomic oxygen becomes half

(D) The velocity of atomic oxygen becomes four times

10. Two point charges A and B of magnitude +8 × 10^{–6} C and –8 × 10^{–6} C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4 × 10^{4} NC^{–1}. The distance ‘d’ between the point charges A and B is:

(A) 2.0 m

(B) 3.0 m

(C) 1.0 m

(D) 4.0 m

11. Resistance of the wire is measured as 2 Ω and 3 Ω at 10°C and 30°C respectively. Temperature co-efficient of resistance of the material of the wire is:

(A) 0.033°C^{–1}

(B) –0.033°C^{–1}

(C) 0.011°C^{–1}

(D) 0.055°C^{–1}

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

(A) 1.2 × 10^{–5}

(B) 1.2 × 10^{–3}

(C) 1.8 × 10^{–3}

(D) 2.4 × 10^{–5}

13. 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 × 10^{–6} N, then the value of x is approximately:

(A) 1

(B) 2.4

(C) 1.4

(D) 2

14. 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.)

(A) Halved

(B) Quadrupled

(C) The same

(D) Doubled

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

16. In Young’s double slit experiment performed using a monochromatic light of wavelength λ, when a glass plate (μ = 1.5) of thickness xλ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of x will be:

(A) 3

(B) 2

(C) 1.5

(D) 0.5

17. Let K_{1} and K_{2} be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength λ_{1} and λ_{2}, respectively are incident on a metallic surface. If λ_{1} = 3λ_{2} then:

(A) K_{1}> K_{2}/3

(B) K_{1}< K_{2}/3

(C) K_{1} = K_{2}/3

(D) K_{2} = K_{1}/3

18. 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 the graph of loge (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time (τ).

(D) Product of decay constant (λ) and half-life time (T1/2) is not constant.

Choose the most appropriate answer from the options given below:

(A) (A) and (B) only

(B) (B) and (D) only

(C) (B) and (C) only

(D) (C) and (D) only

19. In the given circuit the input voltage Vin is shown in figure. The cut-in voltage of p–n junction diode (D_{1} or D_{2}) is 0.6 V. Which of the following output voltage (V_{0}) waveform across the diode is correct?

20. Amplitude modulated wave is represented by V_{AM} = 10[1 + 0.4 cos(2π × 10^{4}t] cos(2π × 10^{7}t). The total bandwidth of the amplitude modulated wave is:

(A) 10 kHz

(B) 20 MHz

(C) 20 kHz

(D) 10 MHz

**SECTION-B**

21. A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is . Then value of x is _______.

22. A zener of breakdown voltage V_{Z} = 8 V and maximum Zener current, I_{ZM} = 10 mA is subjected to an input voltage V_{i} = 10 V with series resistance R = 100 Ω. In the given circuit R_{L} represents the variable load resistance. The ratio of maximum and minimum value of R_{L} is __________.

23. In a Young’s double slit experiment, an angular width of the fringe is 0.35° 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 1/α. The value of α is _________.

24. In the given circuit, the magnitude of V_{L} and V_{C} are twice that of V_{R}. Given that f = 50 Hz, the inductance of the coil is 1/(Kπ) mH. The value of K is ________.

25. All resistances in figure are 1 Ω each. The value of current ‘I‘ is (a/5) A. The value of a is _________.

26. A capacitor C_{1} of capacitance 5 μF 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 C_{2} of capacitance 10 μF as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor C_{2} is ____ μC.

27. 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 sound in air is 340 ms^{–1})

28. A liquid of density 750 kgm^{–3} flows smoothly through a horizontal pipe that tapers incross-sectional area from A1 = 1.2 × 10^{–2} m^{2} to The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ________ × 10^{–3} m^{3}s^{–1}.

29. A uniform disc with mass M = 4 kg and radius R = 10 cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m = 2 kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is ________ N.

(Take g = 10 ms^{–2})

30. A car covers AB distance with first one-third at velocity v_{1}ms^{–1}, second one-third at v_{2}ms^{–1} and last one-third at v_{3}ms^{–1}. If v_{3} = 3v_{1}, v_{2} = 2v_{1} and v_{1} = 11 ms^{–1} then the average velocity of the car is ____ ms^{–1}.

**CHEMISTRY**

**SECTION-A**

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

Given : Atomic masses of C, H and N are 12, 1 and 14 amu, respectively.

The molar mass of the compound A is 162 g mol^{–1}.

(A) C_{4}H_{6}N_{2}

(B) C_{2}H_{3}N

(C) C_{5}H_{7}N

(D) C_{10}H_{14}N_{2}

2. Consider the following statements :

(A) The principal quantum number ‘n’ is a positive integer with values of ‘n’ = 1, 2, 3, ….

(B) The azimuthal quantum number ‘l’ for a given ‘n’ (principal quantum number) can have values as ‘l’ = 0, 1, 2, …n

(C) Magnetic orbital quantum number ‘ml’ for a particular ‘l’ (azimuthal quantum number) has (2l + 1) values.

(D) ±1/2 are the two possible orientations of electron spin.

(E) For l = 5, there will be a total of 9 orbital

Which of the above statements are correct?

(A) (A), (B) and (C)

(B) (A), (C), (D) and (E)

(C) (A), (C) and (D)

(D) (A), (B), (C) and (D)

3. In the structure of SF_{4}, the lone pair of electrons on S is in.

(A) Equatorial position and there are two lone pair – bond pair repulsions at 90º

(B) Equatorial position and there are three lone pair – bond pair repulsions at 90º

(C) Axial position and there are three lone pair – bond pair repulsion at 90º

(D) Axial position and there are two lone pair – bond pair repulsion at 90º

4. A student needs to prepare a buffer solution of propanoic acid and its sodium salt with pH 4. The ratio of required to make buffer is _____.

Given :Ka(CH_{3}CH_{2}COOH) = 1.3 × 10^{–5}

(A) 0.03

(B) 0.13

(C) 0.23

(D) 0.33

5. Match List-I with List-II.

Choose the correct answer from the options given below:

(A) (A) – (II), (B) – (III), (C) – (IV), (D) – (I)

(B) (A) – (II), (B) – (I), (C) – (III), (D) – (IV)

(C) (A) – (II), (B) – (III), (C) – (I), (D) – (IV)

(D) (A) – (I), (B) – (III), (C) – (II), (D) – (IV)

6. Match List-I with List-II:

Choose the correct answer from the options given below:

(A) A-IV, B-III, C-I, D-II

(B) A-IV, B-II, C-I, D-III

(C) A-II, B-IV, C-III, D-I

(D) A-I, B-II, C-III, D-IV

7. In the metallurgical extraction of copper, following reaction is used :

FeO + SiO_{2} → FeSiO_{3}

FeO and FeSiO_{3} respectively are.

(A) Gangue and flux

(B) Flux and slag

(C) Slag and flux

(D) Gangue and slag

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

(A) Number of protons

(B) Atomic number

(C) Electronic configuration

(D) Atomic mass

9. Among the following, basic oxide is:

(A) SO_{3}

(B) SiO_{2}

(C) CaO

(D) Al_{2}O_{3}

10. Among the given oxides of nitrogen; N_{2}O, N_{2}O_{3}, N_{2}O_{4} and N_{2}O_{5}, the number of compound/(s) having N – N bond is:

(A) 1

(B) 2

(C) 3

(D) 4

11. Which of the following oxoacids of sulphur contains ‘‘S’’ in two different oxidation states?

(A) H_{2}S_{2}O_{3}

(B) H_{2}S_{2}O_{6}

(C) H_{2}S_{2}O_{7}

(D) H_{2}S_{2}O_{8}

12. Correct statement about photo-chemical smog is:

(A) It occurs in humid climate.

(B) It is a mixture of smoke, fog and SO_{2}.

(C) It is reducing smog.

(D) It results from reaction of unsaturated hydrocarbons.

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

(A) 4-methyl-2-nitro-5-oxohept-3-enal

(B) 4-methyl-5-oxo-2-nitrohept-3-enal

(C) 4-methyl-6-nitro-3-oxohept-4-enal

(D) 6-formyl-4-methyl-2-nitrohex-3-enal

14. The major product (P) of the given reaction is (where, Me is –CH_{3})

15. 4-Bromophenyl acetic acid.

In the above reaction ‘A’ is

16. Isobutyraldehyde on reaction with formaldehyde and K_{2}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

17. 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) HNO_{3} acts as an acid.

(D) H_{2}SO_{4} acts as an acid.

Choose the correct option.

(A) (A) and (C) are correct statements.

(B) (A) and (D) are correct statements.

(C) (B) and (D) are correct statements.

(D) (B) and (C) are correct statements.

18. 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 strong polar interactions with coiled structure.

In the light of the above statements, choose the correct one from the options given below:

(A) Both (A) and (R) are true and (R) is the correct explanation of (A).

(B) Both (A) and (R) are true but (R) is not the correct explanation of (A).

(C) (A) is true but (R) is false.

(D) (A) is false but (R) is true.

19. When sugar ‘X’ is boiled with dilute H_{2}SO_{4} in alcoholic solution, two isomers ‘A’ and ‘B’ are formed. ‘A’ on oxidation with HNO_{3} yields saccharic acid whereas ‘B’ is laevorotatory. The compound ‘X’ is :

(A) Maltose

(B) Sucrose

(C) Lactose

(D) Starch

20. The drug tegamet is:

**SECTION-B**

21. 100 g of an ideal gas is kept in a cylinder of 416 L volume at 27°C under 1.5 bar pressure. The molar mass of the gas is ________ g mol^{–1}. (Nearest integer).

22. For combustion of one mole of magnesium in an open container at 300 K and 1 bar pressure, Δ_{C}H^{Θ} = –601.70 kJ mol^{–1}, the magnitude of change in internal energy for the reaction is ______ kJ. (Nearest integer)

(Given : R = 8.3 J K^{–1}mol^{–1})

23. 2.5 g of protein containing only glycine (C_{2}H_{5}NO_{2}) 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 × 10^{–3} bar. The total number of glycine units present in the protein is _______.

(Given : R = 0.083 L bar K^{–1}mol^{–1})

24. For the given reactions

Sn^{2+} + 2e– → Sn

Sn^{4+} + 4e– → Sn

The electrode potentials are; and The magnitude of standard electrode potential for Sn^{4+}/Sn^{2+} i.e. is _______ × 10^{−}^{2} V. (Nearest integer)

25. 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)

26. [Fe(CN)_{6}]^{4–}

[Fe(CN)_{6}]^{3–}

[Ti(CN)_{6}]^{3–}

[Ni(CN)_{4}]^{2–}

[Co(CN)_{6}]^{3–}

Among the given complexes, number of paramagnetic complexes is_______.

27. (a) CoCl_{3}⋅4 NH_{3}, (b) CoCl_{3}⋅5NH_{3}, (c) CoCl_{3}.6NH_{3} and (d) CoCl(NO_{3})_{2}⋅5NH_{3}. Number of complex(es) which will exist in cis-trans form is/are______.

28. The complete combustion of 0.492 g of an organic compound containing ‘C’, ‘H’ and ‘O’ gives 0.793 g of CO_{2} and 0.442 g of H_{2} The percentage of oxygen composition in the organic compound is_____.[nearest integer]

29. The major product of the following reaction contains______bromine atom(s).

30. 0.01 M 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 KMnO_{4} solution left in burette after the end point is _____ml. [nearest integer]

**MATHEMATICS**

**SECTION-A**

1. Let R_{1} = {(a, b) ∈ N × N : |a – b| ≤ 13} and R_{2} = {(a, b) ∈ N × N : |a – b| ≠ 13}. Then on N:

(A) Both R_{1} and R_{2} are equivalence relations

(B) Neither R_{1} nor R_{2} is an equivalence relation

(C) R_{1} is an equivalence relation but R_{2} is not

(D) R_{2} is an equivalence relation but R_{1} is not

2. Let f(x) be a quadratic polynomial such that f(–2) + f(3) = 0. If one of the roots of f(x) = 0 is –1, then the sum of the roots of f(x) = 0 is equal to:

(A) 11/3

(B) 7/3

(C) 13/3

(D) 14/3

3. The number of ways to distribute 30 identical candies among four children C_{1}, C_{2}, C_{3} and C_{4} so that C_{2} receives atleast 4 and atmost 7 candies, C_{3} receives atleast 2 and atmost 6 candies, is equal to:

(A) 205

(B) 615

(C) 510

(D) 430

4. The term independent of x in the expansion of is

(A) 7/40

(B) 33/200

(C) 39/200

(D) 11/50

5. 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 a + n = 33, then the value of n is:

(A) 21

(B) 22

(C) 23

(D) 24

6. Let f, g : R → R be functions defined by

Where [x] denotes the greatest integer less than or equal to x. Then, the function fog is discontinuous at exactly :

(A) one point

(B) two points

(C) three points

(D) four points

7. Let f : R → R be a differentiable function such that and let for is equal to

(A) 2

(B) 3

(C) 4

(D) −3

8. Let f :**R** → **R** be a continuous function satisfying f(x) + f(x + k) = n, for all x ∈ **R **where k > 0 and n is a positive integer. If then

(A) I_{1} + 2I_{2} = 4nk

(B) I_{1} + 2I_{2} = 2nk

(C) I_{1} + nI_{2} = 4n^{2}k

(D) I_{1} + nI_{2} = 6n^{2}k

9. The area of the bounded region enclosed by the curve and the x-axis is

(A) 9/4

(B) 45/16

(C) 27/8

(D) 63/16

10. Let x = x(y) be the solution of the differential equation such that x(1) = 0. Then, x(e) is equal to

(A) elog_{e}(2)

(B) −elog_{e}(2)

(C) e^{2}log_{e}(2)

(D) −e^{2}log_{e}(2)

11. Let the slope of the tangent to a curve y = f(x) at (x, y) be given by 2 tanx(cosx – y). If the curve passes through the point (π/4, 0) then the value of is equal to

12. Let a triangle be bounded by the lines L_{1} : 2x + 5y = 10; L_{2} : –4x + 3y = 12 and the line L3, which passes through the point P(2, 3), intersects L_{2} at A and L_{1} at B. If the point P divides the line-segment AB, internally in the ratio 1 : 3, then the area of the triangle is equal to

(A) 110/13

(B) 132/13

(C) 142/13

(D) 151/13

13. Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola e′ and ℓ′ respectively the eccentricity and length of the latus rectum of its conjugate hyperbola. If then the value of 77a + 44b is equal to

(A) 100

(B) 110

(C) 120

(D) 130

14. Let α ∈ where α ∈ R. If the area of the parallelogram whose adjacent sides are represented by the vectors then the value of is equal to

(A) 10

(B) 7

(C) 9

(D) 14

15. 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 :

(A) 2

(B) 8

(C) 12

(D) 16

16. Let the plane ax + by + cz = d pass through (2, 3, –5) and is perpendicular to the planes 2x + y – 5z = 10 and 3x + 5y – 7z = 12. If a, b, c, d are integers d > 0 and gcd (|a|, |b|, |c|, d) = 1, then the value of a + 7b + c + 20d is equal to :

(A) 18

(B) 20

(C) 24

(D) 22

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

(A) 1/24

(B) 1/40

(C) 1/30

(D) 1/20

18. The value of is equal to

(A) 1

(B) 2

(C) 3

(D) 6

19. Let be a vector which is perpendicular to the vector If the projection of the vector on the vector is

(A) 1/3

(B) 1

(C) 5/3

(D) 7/3

20. If cot α =1 and sec β = −5/3, where then the value of tan(α + β) and the quadrant in which α + β lies, respectively are :

(A) –1/7 and IVth quadrant

(B) 7 and Ist quadrant

(C) –7 and IVth quadrant

(D) 1/7 and Ist quadrant

**SECTION-B**

21. Let the image of the point P(1, 2, 3) in the line be Q. Let R (α, β, γ) be a point that divides internally the line segment PQ in the ratio 1 : 3. Then the value of 22(α + β + γ) is equal to ________.

22. 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 __________.

23. If one of the diameters of the circle x^{2} + y^{2} – 2√2x – 6√2y + 14 = 0 is a chord of the circle (x – 2√2)^{2} + (y – 2√2)^{2} = r^{2}, then the value of r^{2} is equal to _______.

24. If then the value of (a – b) is equal to _______.

25. Let for n = 1, 2, …, 50, S_{n} be the sum of the infinite geometric progression whose first term is n^{2} and whose common ratio is Then the value of is equal to

26. If the system of linear equations

2x – 3y = γ + 5,

αx + 5y = β + 1,

where α, β, γ ∈ R has infinitely many solutions, then the value of |9α + 3β + 5γ| is equal to _______.

27. Let Then, the number of elements in the set {n ∈ {1, 2, ……, 100} : A^{n} = A} is

28. Sum of squares of modulus of all the complex numbers z satisfying is equal to

29. Let S = {1, 2, 3, 4}. Then the number of elements in the set {f : S × S → S : f is onto and f(a, b) = f(b, a) ≥ a ∀ (a, b) ∈ S × S is ____________.

30. The maximum number of compound propositions, out of p ∨ r ∨ s, p ∨ r ∨ ~s, p ∨ ~q ∨ s, ~p ∨ ~r ∨ s, ~p ∨ ~r ∨ ~s, ~p ∨ q ∨ ~s, q ∨ r ∨ ~s, q ∨ ~r ∨ ~s, ~p ∨ ~q ∨ ~s that can be made simultaneously true by an assignment of the truth values to p, q, r and s, is equal to ____________ .

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