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JEE Main 8 April 2023 Shift 2 Question Paper with Answers

8 April 2023 · April session · 90 questions

The complete JEE Main 8 April 2023 Shift 2 paper — all 90 questions with the correct answer for each, tagged to the chapter it tests. Free to read, no account needed.

Physics
30
Chemistry
30
Mathematics
30

Physics — JEE Main 8 April 2023 Shift 2

Q1·PhysicsSingle correct
Electric potential at a point P due to a point charge of 5×10−95\times10^{-9}5×10−9 C is 50 V. The distance of P from the point charge is: (Assume 14πε0=9×109\dfrac{1}{4\pi\varepsilon_0}=9\times10^{9}4πε0​1​=9×109 Nm2^22C−2^{-2}−2)
  1. (A)3 cm
  2. (B)9 cm
  3. (C)90 cm
  4. (D)0.9 cm

Correct answer: (C)

Step-by-step solution →
Q2·PhysicsSingle correct
For a particle P revolving round the centre O with radius of circular path rrr and angular velocity ω\omegaω, as shown in the figure, the projection of OP on the x-axis at time t is
  1. (A)x(t)=rcos⁡(ωt+π6)x(t)=r\cos\left(\omega t+\dfrac{\pi}{6}\right)x(t)=rcos(ωt+6π​)
  2. (B)x(t)=rcos⁡(ωt)x(t)=r\cos(\omega t)x(t)=rcos(ωt)
  3. (C)x(t)=rsin⁡(ωt+π6)x(t)=r\sin\left(\omega t+\dfrac{\pi}{6}\right)x(t)=rsin(ωt+6π​)
  4. (D)x(t)=rcos⁡(ωt−π6)x(t)=r\cos\left(\omega t-\dfrac{\pi}{6}\right)x(t)=rcos(ωt−6π​)

Correct answer: (A)

Step-by-step solution →
Q3·PhysicsSingle correct
Match List-I (physical quantity) with List-II (dimensional formula). Choose the correct answer from the options given below:
List-I (Physical quantity)List-II (Dimensional formula)
A.TorqueI.ML−2T−2ML^{-2}T^{-2}ML−2T−2
B.StressII.ML2T−2ML^{2}T^{-2}ML2T−2
C.Pressure gradientIII.ML−1T−1ML^{-1}T^{-1}ML−1T−1
D.Coefficient of viscosityIV.ML−1T−2ML^{-1}T^{-2}ML−1T−2
  1. (A)A-III, B-IV, C-I, D-II
  2. (B)A-IV, B-II, C-III, D-I
  3. (C)A-II, B-IV, C-I, D-III
  4. (D)A-II, B-I, C-IV, D-III

Correct answer: (C)

Step-by-step solution →
Q4·PhysicsSingle correct
For a given transistor amplifier circuit in CE configuration VCC=1V_{CC}=1VCC​=1 V, Rc=1R_c=1Rc​=1 kΩ\OmegaΩ, Rb=100R_b=100Rb​=100 kΩ\OmegaΩ and β=100\beta=100β=100. The value of base current IbI_bIb​ is
  1. (A)Ib=1.0 μAI_b=1.0\ \mu AIb​=1.0 μA
  2. (B)Ib=0.10 μAI_b=0.10\ \mu AIb​=0.10 μA
  3. (C)Ib=100 μAI_b=100\ \mu AIb​=100 μA
  4. (D)Ib=10 μAI_b=10\ \mu AIb​=10 μA

Correct answer: (D)

Step-by-step solution →
Q5·PhysicsSingle correct
The trajectory of a projectile, projected from the ground is given by y=x−x220y=x-\dfrac{x^{2}}{20}y=x−20x2​, where x and y are measured in metre. The maximum height attained by the projectile will be
  1. (A)5 m
  2. (B)10210\sqrt{2}102​ m
  3. (C)200 m
  4. (D)10 m

Correct answer: (A)

Step-by-step solution →
Q6·PhysicsSingle correct
A radioactive material is reduced to 18\dfrac{1}{8}81​ of its original amount in 3 days. If 8×10−38\times10^{-3}8×10−3 kg of the material is left after 5 days, the initial amount of the material is
  1. (A)64 g
  2. (B)40 g
  3. (C)32 g
  4. (D)256 g

Correct answer: (D)

Step-by-step solution →
Q7·PhysicsSingle correct
The equivalent resistance between A and B shown in the figure is:
  1. (A)5 kΩ\OmegaΩ
  2. (B)30 kΩ\OmegaΩ
  3. (C)10 kΩ\OmegaΩ
  4. (D)20 kΩ\OmegaΩ

Correct answer: (A)

Step-by-step solution →
Q8·PhysicsSingle correct
A hydraulic automobile lift is designed to lift vehicles of mass 5000 kg. The area of cross section of the cylinder carrying the load is 250 cm2^22. The maximum pressure the smaller piston would have to bear is [Assume g=10g=10g=10 m/s2^22]:
  1. (A)200×106200\times10^{6}200×106 Pa
  2. (B)20×10620\times10^{6}20×106 Pa
  3. (C)2×1062\times10^{6}2×106 Pa
  4. (D)2×1052\times10^{5}2×105 Pa

Correct answer: (C)

Step-by-step solution →
Q9·PhysicsSingle correct
The orbital angular momentum of a satellite revolving in a circular orbit at a distance rrr from the centre of the earth is LLL. If the distance of the satellite from the centre of the earth is increased to nine times its initial value, then the new angular momentum will be
  1. (A)8L8L8L
  2. (B)4L4L4L
  3. (C)9L9L9L
  4. (D)3L3L3L

Correct answer: (D)

Step-by-step solution →
Q10·PhysicsSingle correct
The temperature at which the kinetic energy of oxygen molecules becomes double of its value at 27∘27^{\circ}27∘C is
  1. (A)1227∘1227^{\circ}1227∘C
  2. (B)927∘927^{\circ}927∘C
  3. (C)327∘327^{\circ}327∘C
  4. (D)627∘627^{\circ}627∘C

Correct answer: (C)

Step-by-step solution →
Q11·PhysicsSingle correct
The acceleration due to gravity at height h above the earth, if h≪Rh\ll Rh≪R (radius of the earth), is given by
  1. (A)g′=g(1−2hR)g'=g\left(1-\dfrac{2h}{R}\right)g′=g(1−R2h​)
  2. (B)g′=g(1−h2R2)g'=g\left(1-\dfrac{h^{2}}{R^{2}}\right)g′=g(1−R2h2​)
  3. (C)g′=g(1−h2R)g'=g\left(1-\dfrac{h}{2R}\right)g′=g(1−2Rh​)
  4. (D)g′=g(1−h22R2)g'=g\left(1-\dfrac{h^{2}}{2R^{2}}\right)g′=g(1−2R2h2​)

Correct answer: (A)

Step-by-step solution →
Q12·PhysicsSingle correct
Work done by a Carnot engine operating between temperatures 127∘127^{\circ}127∘C and 27∘27^{\circ}27∘C is 2 kJ. The amount of heat transferred to the engine by the reservoir is:
  1. (A)4 kJ
  2. (B)2 kJ
  3. (C)8 kJ
  4. (D)2.67 kJ

Correct answer: (C)

Step-by-step solution →
Q13·PhysicsSingle correct
Given below are two statements: Statement I: Area under velocity-time graph gives the distance travelled by the body in a given time. Statement II: Area under acceleration-time graph is equal to the change in velocity in the given time. In the light of the given statements, choose the correct answer from the options given below.
  1. (A)Both Statement I and Statement II are true
  2. (B)Statement I is correct but Statement II is false
  3. (C)Statement I is incorrect but Statement II is true
  4. (D)Both Statement I and Statement II are false

Correct answer: (A)

Step-by-step solution →
Q14·PhysicsSingle correct
The waves emitted when a metal target is bombarded with high energy electrons are
  1. (A)Microwaves
  2. (B)X-rays
  3. (C)Infrared rays
  4. (D)Radio Waves

Correct answer: (B)

Step-by-step solution →
Q15·PhysicsSingle correct
The width of a fringe is 2 mm on the screen in a double slit experiment for light of wavelength 400 nm. The width of the fringe for light of wavelength 600 nm will be:
  1. (A)4 mm
  2. (B)1.33 mm
  3. (C)3 mm
  4. (D)2 mm

Correct answer: (C)

Step-by-step solution →
Q16·PhysicsSingle correct
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Electromagnets are made of soft iron. Reason R: Soft iron has high permeability and low retentivity. In the light of the above statements, choose the most appropriate answer from the options given below.
  1. (A)A is false but R is true
  2. (B)Both A and R are true and R is the correct explanation of A
  3. (C)Both A and R are true but R is NOT the correct explanation of A
  4. (D)A is true but R is false

Correct answer: (B)

Step-by-step solution →
Q17·PhysicsSingle correct
In photoelectric effect: A. The photocurrent is proportional to the intensity of the incident radiation. B. Maximum kinetic energy with which photoelectrons are emitted depends on the intensity of incident light. C. Maximum K.E. with which photoelectrons are emitted depends on the frequency of incident light. D. The emission of photoelectrons requires a minimum threshold intensity of incident radiation. E. Maximum K.E. of the photoelectrons is independent of the frequency of the incident light. Choose the correct answer from the options below:
  1. (A)A and C only
  2. (B)A and E only
  3. (C)B and C only
  4. (D)A and B only

Correct answer: (A)

Step-by-step solution →
Q18·PhysicsSingle correct
An emf of 0.08 V is induced in a metal rod of length 10 cm held normal to a uniform magnetic field of 0.4 T, when it moves with a velocity of:
  1. (A)2 ms−1^{-1}−1
  2. (B)3.2 ms−1^{-1}−1
  3. (C)0.5 ms−1^{-1}−1
  4. (D)20 ms−1^{-1}−1

Correct answer: (A)

Step-by-step solution →
Q19·PhysicsSingle correct
A bullet of mass 0.1 kg moving horizontally with speed 400 ms−1^{-1}−1 hits a wooden block of mass 3.9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 m before coming to rest. The coefficient of friction between the block and the surface is ____. (Given g=10g=10g=10 m/s2^22)
  1. (A)0.50
  2. (B)0.90
  3. (C)0.65
  4. (D)0.25

Correct answer: (D)

Step-by-step solution →
Q20·PhysicsSingle correct
The power radiated from a linear antenna of length lll is proportional to (Given λ=\lambda=λ= wavelength of wave):
  1. (A)lλ\dfrac{l}{\lambda}λl​
  2. (B)lλ2\dfrac{l}{\lambda^{2}}λ2l​
  3. (C)l2λ\dfrac{l^{2}}{\lambda}λl2​
  4. (D)(lλ)2\left(\dfrac{l}{\lambda}\right)^{2}(λl​)2

Correct answer: (D)

Step-by-step solution →
Q21·PhysicsNumerical
A series combination of a resistor of resistance 100 Ω\OmegaΩ, an inductor of inductance 1 H and a capacitor of capacitance 6.25 μ\muμF is connected to an ac source. The quality factor of the circuit will be ____.

Correct answer: 4

Step-by-step solution →
Q22·PhysicsNumerical
A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be ____ cm.

Correct answer: 60

Step-by-step solution →
Q23·PhysicsNumerical
The ratio of the wavelengths of the spectral lines HαH_\alphaHα​ and HβH_\betaHβ​ in the Balmer series is x20\dfrac{x}{20}20x​. The value of x is ____.

Correct answer: 27

Step-by-step solution →
Q24·PhysicsNumerical
The number density of free electrons in copper is nearly 8×10288\times10^{28}8×1028 m−3^{-3}−3. A copper wire has its area of cross section =2×10−6=2\times10^{-6}=2×10−6 m2^22 and is carrying a current of 3.2 A. The drift speed of the electrons is ____ ×10−5\times10^{-5}×10−5 ms−1^{-1}−1.

Correct answer: 125

Step-by-step solution →
Q25·PhysicsNumerical
A steel rod of length 1 m and cross sectional area 10−410^{-4}10−4 m2^22 is heated from 0∘0^{\circ}0∘C to 200∘200^{\circ}200∘C without being allowed to extend or bend. The compressive tension produced in the rod is ____ ×104\times10^{4}×104 N. (Given Young's modulus of steel =2×1011=2\times10^{11}=2×1011 N/m2^22, coefficient of linear expansion =10−5=10^{-5}=10−5 K−1^{-1}−1.)

Correct answer: 4

Step-by-step solution →
Q26·PhysicsNumerical
A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity 3 m/s (as shown in the figure). The maximum height with respect to the initial position covered by it will be ____ cm.

Correct answer: 75

Step-by-step solution →
Q27·PhysicsNumerical
A body of mass 5 kg is moving with a momentum of 10 kg ms−1^{-1}−1. A force of 2 N acts on the body in the direction of its motion for 5 s. The increase in the kinetic energy of the body is ____ J.

Correct answer: 30

Step-by-step solution →
Q28·Physics·Capacitors and DielectricsNumerical
A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. The electrostatic energy lost in the process is ____ μ\muμJ.

Correct answer: 6

Step-by-step solution →
Q29·PhysicsNumerical
Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature 30 cm. The centre of curvature of the surface is towards the denser medium and a point object is placed on the principal axis in the rarer medium at a distance of 15 cm from the pole of the surface. The distance of the image from the pole of the surface is ____ cm.

Correct answer: 30

Step-by-step solution →
Q30·PhysicsNumerical
The ratio of the magnetic field at the centre of a current carrying coil of radius rrr to the magnetic field at a distance rrr from the centre of the coil on its axis is x:1\sqrt{x}:1x​:1. The value of x is ____.

Correct answer: 8

Step-by-step solution →

Chemistry — JEE Main 8 April 2023 Shift 2

Q31·ChemistrySingle correct
Which of the following have the same number of significant figures? A. 0.002530.002530.00253 B. 1.00031.00031.0003 C. 15.015.015.0 D. 163163163. Choose the correct answer from the options given below.
  1. (A)A, B and C only
  2. (B)C and D only
  3. (C)A, C and D only
  4. (D)B and C only

Correct answer: (C)

Step-by-step solution →
Q32·ChemistrySingle correct
Which of these reactions is not a part of the breakdown of ozone in the stratosphere?
  1. (A)ClO(g)+O(g)→Cl(g)+O2(g)ClO(g)+O(g)\rightarrow Cl(g)+O_2(g)ClO(g)+O(g)→Cl(g)+O2​(g)
  2. (B)Cl(g)+O3(g)→ClO(g)+O2(g)Cl(g)+O_3(g)\rightarrow ClO(g)+O_2(g)Cl(g)+O3​(g)→ClO(g)+O2​(g)
  3. (C)2 ClO→ClO2(g)+Cl(g)2\,ClO\rightarrow ClO_2(g)+Cl(g)2ClO→ClO2​(g)+Cl(g)
  4. (D)CF2Cl2(g)→uvCl(g)+CF2Cl(g)CF_2Cl_2(g)\xrightarrow{uv}Cl(g)+CF_2Cl(g)CF2​Cl2​(g)uv​Cl(g)+CF2​Cl(g)

Correct answer: (C)

Step-by-step solution →
Q33·ChemistrySingle correct
The correct IUPAC nomenclature for the following compound is
  1. (A)5-Formyl-2-methylhexanoic acid
  2. (B)2-Methyl-5-oxohexanoic acid
  3. (C)2-Formyl-5-methylhexan-6-oic acid
  4. (D)5-Methyl-2-oxohexan-6-oic acid

Correct answer: (B)

Step-by-step solution →
Q34·ChemistrySingle correct
Arrange the following gases in increasing order of van der Waals constant 'a': A. Ar B. CH4CH_4CH4​ C. H2OH_2OH2​O D. C6H6C_6H_6C6​H6​. Choose the correct option from the following:
  1. (A)B, C, D and A
  2. (B)C, D, B and A
  3. (C)A, B, C and D
  4. (D)D, C, B and A

Correct answer: (C)

Step-by-step solution →
Q35·ChemistrySingle correct
Given below are two statements: Statement I: Methyl orange is a weak acid. Statement II: The benzenoid form of methyl orange is more intense/deeply coloured than the quinonoid form. In the light of the above statements, choose the most appropriate answer from the options given below:
  1. (A)Statement I is correct but Statement II is incorrect
  2. (B)Statement I is incorrect but Statement II is correct
  3. (C)Both Statement I and Statement II are incorrect
  4. (D)Both Statement I and Statement II are correct

Correct answer: (C)

Step-by-step solution →
Q36·ChemistrySingle correct
Given below are two statements: Statement I: In redox titration, the indicators used are sensitive to change in pH of the solution. Statement II: In acid-base titration, the indicators used are sensitive to change in oxidation potential. 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 incorrect but Statement II is correct
  3. (C)Statement I is correct but Statement II is incorrect
  4. (D)Both Statement I and Statement II are incorrect

Correct answer: (D)

Step-by-step solution →
Q37·ChemistrySingle correct
The product (P) formed from the following multistep reaction is:
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (D)

Step-by-step solution →
Q38·ChemistrySingle correct
The correct reaction profile diagram for a positively catalysed reaction is:
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (B)

Step-by-step solution →
Q39·ChemistrySingle correct
Which of the following can reduce the decomposition of H2O2H_2O_2H2​O2​ on exposure to light?
  1. (A)Alkali
  2. (B)Urea
  3. (C)Dust
  4. (D)Glass containers

Correct answer: (B)

Step-by-step solution →
Q40·ChemistrySingle correct
The statement/s which are true about antagonists from the following is/are: A. They bind to the receptor site. B. They get transferred inside the cell for their action. C. They inhibit the natural communication of the body. D. They mimic the natural messenger. Choose the correct answer from the options given below:
  1. (A)B only
  2. (B)A, C and D
  3. (C)A and B
  4. (D)A and C

Correct answer: (D)

Step-by-step solution →
Q41·ChemistrySingle correct
Match List-I (coordination complex) with List-II (number of unpaired electrons). Choose the correct answer from the options given below:
List-I (Coordination complex)List-II (Number of unpaired electrons)
A.[Cr(CN)6]3−[Cr(CN)_6]^{3-}[Cr(CN)6​]3−I.0
B.[Fe(H2O)6]2+[Fe(H_2O)_6]^{2+}[Fe(H2​O)6​]2+II.3
C.[Co(NH3)6]3+[Co(NH_3)_6]^{3+}[Co(NH3​)6​]3+III.2
D.[Ni(NH3)6]2+[Ni(NH_3)_6]^{2+}[Ni(NH3​)6​]2+IV.4
  1. (A)A-II, B-IV, C-I, D-III
  2. (B)A-IV, B-III, C-II, D-I
  3. (C)A-III, B-IV, C-I, D-II
  4. (D)A-II, B-I, C-IV, D-III

Correct answer: (A)

Step-by-step solution →
Q42·ChemistrySingle correct
The major product 'P' formed in the following reaction is:
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (B)

Step-by-step solution →
Q43·ChemistrySingle correct
In the Hall-Heroult process, the following is used for reducing Al2O3Al_2O_3Al2​O3​:
  1. (A)Graphite
  2. (B)Magnesium
  3. (C)Na3AlF6Na_3AlF_6Na3​AlF6​
  4. (D)CaF2CaF_2CaF2​

Correct answer: (A)

Step-by-step solution →
Q44·ChemistrySingle correct
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Sodium is about 30 times as abundant as potassium in the oceans. Reason R: Potassium is bigger in size than sodium. In the light of the above statements, choose the correct answer from the options given below.
  1. (A)Both A and R are true 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 true but R is NOT the correct explanation of A

Correct answer: (A)

Step-by-step solution →
Q45·ChemistrySingle correct
Match List-I (natural amino acid) with List-II (one letter code). Choose the correct answer from the options given below:
List-I (Natural amino acid)List-II (One letter code)
A.Glutamic acidI.Q
B.GlutamineII.W
C.TyrosineIII.E
D.TryptophanIV.Y
  1. (A)A-II, B-I, C-IV, D-III
  2. (B)A-IV, B-III, C-I, D-II
  3. (C)A-III, B-I, C-IV, D-II
  4. (D)A-III, B-IV, C-I, D-II

Correct answer: (C)

Step-by-step solution →
Q46·ChemistrySingle correct
Henry Moseley studied the characteristic X-ray spectra of elements. The graph which represents his observation correctly is: (Given v=v=v= frequency of X-ray emitted; Z=Z=Z= atomic number)
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (B)

Step-by-step solution →
Q47·Chemistry·Carboxylic Acids and DerivativesSingle correct
The descending order of acidity for the following carboxylic acids is: A. CH3COOHCH_3COOHCH3​COOH B. F3C–COOHF_3C\text{--}COOHF3​C–COOH C. ClCH2–COOHClCH_2\text{--}COOHClCH2​–COOH D. FCH2–COOHFCH_2\text{--}COOHFCH2​–COOH E. BrCH2–COOHBrCH_2\text{--}COOHBrCH2​–COOH. Choose the correct answer from the options given below:
  1. (A)D > B > A > E > C
  2. (B)E > D > B > A > C
  3. (C)B > C > D > E > A
  4. (D)B > D > C > E > A

Correct answer: (D)

Step-by-step solution →
Q48·ChemistrySingle correct
The correct order of reactivity of the following haloarenes towards nucleophilic substitution with aqueous NaOH is:
  1. (A)A > B > D > C
  2. (B)C > A > D > B
  3. (C)D > C > B > A
  4. (D)D > B > A > C

Correct answer: (D)

Step-by-step solution →
Q49·ChemistrySingle correct
For a good quality cement, the ratio of lime to the total of the oxides of Si, Al and Fe should be as close as to:
  1. (A)4
  2. (B)2
  3. (C)3
  4. (D)1

Correct answer: (B)

Step-by-step solution →
Q50·ChemistrySingle correct
A compound 'X' when treated with phthalic anhydride in presence of concentrated H2SO4H_2SO_4H2​SO4​ yields 'Y'. 'Y' is used as an acid/base indicator. 'X' and 'Y' are respectively:
  1. (A)Carbolic acid, Phenolphthalein
  2. (B)Anisole, Methyl orange
  3. (C)Salicylaldehyde, Phenolphthalein
  4. (D)Toluidine, Phenolphthalein

Correct answer: (A)

Step-by-step solution →
Q51·ChemistryNumerical
The solubility product of BaSO4BaSO_4BaSO4​ is 1×10−101\times10^{-10}1×10−10 at 298 K. The solubility of BaSO4BaSO_4BaSO4​ in 0.10.10.1 M K2SO4(aq)K_2SO_4(aq)K2​SO4​(aq) solution is ____ ×10−9\times10^{-9}×10−9 g L−1^{-1}−1 (nearest integer). Given: Molar mass of BaSO4BaSO_4BaSO4​ is 233233233 g mol−1^{-1}−1.

Correct answer: 233

Step-by-step solution →
Q52·ChemistryNumerical
Coagulating values of the electrolytes AlCl3AlCl_3AlCl3​ and NaClNaClNaCl for As2S3As_2S_3As2​S3​ are 0.09 and 50.04 respectively. The coagulating power of AlCl3AlCl_3AlCl3​ is x times the coagulating power of NaClNaClNaCl. The value of x is ____.

Correct answer: 556

Step-by-step solution →
Q53·ChemistryNumerical
The number of atomic orbitals from the following having 5 radial nodes is ____. 7s, 7p, 6s, 8p, 8d

Correct answer: 3

Step-by-step solution →
Q54·ChemistryNumerical
For complete combustion of ethene, C2H4(g)+3O2(g)→2CO2(g)+2H2O(l)C_2H_4(g)+3O_2(g)\rightarrow 2CO_2(g)+2H_2O(l)C2​H4​(g)+3O2​(g)→2CO2​(g)+2H2​O(l), the amount of heat produced as measured in a bomb calorimeter is 140614061406 kJ mol−1^{-1}−1 at 300 K. The minimum value of TΔST\Delta STΔS needed to reach equilibrium is (−)(-)(−) ____ kJ (nearest integer). Given: R=8.3R=8.3R=8.3 JK−1^{-1}−1mol−1^{-1}−1.

Correct answer: 1411

Step-by-step solution →
Q55·ChemistryNumerical
The number of species from the following carrying a single lone pair on the central atom xenon is ____. XeF5+XeF_5^+XeF5+​, XeO3XeO_3XeO3​, XeO2F2XeO_2F_2XeO2​F2​, XeF5−XeF_5^-XeF5−​, XeO3F2XeO_3F_2XeO3​F2​, XeOF4XeOF_4XeOF4​, XeF4XeF_4XeF4​

Correct answer: 4

Step-by-step solution →
Q56·ChemistryNumerical
If the boiling points of two solvents X and Y (having the same molecular weights) are in the ratio 2:12:12:1 and their enthalpies of vaporization are in the ratio 1:21:21:2, then the boiling point elevation constant of X is m times the boiling point elevation constant of Y. The value of m is ____ (nearest integer).

Correct answer: 8

Step-by-step solution →
Q57·ChemistryNumerical
The sum of the oxidation states of the metals in Fe(CO)5Fe(CO)_5Fe(CO)5​, VO2+VO^{2+}VO2+ and WO3WO_3WO3​ is ____.

Correct answer: 10

Step-by-step solution →
Q58·ChemistryNumerical
The observed magnetic moment of the complex [Mn(NCS)6]x−[Mn(NCS)_6]^{x-}[Mn(NCS)6​]x− is 6.06 BM. The numerical value of x is ____.

Correct answer: 4

Step-by-step solution →
Q59·ChemistryNumerical
The number of incorrect statements from the following is ____. A. The electrical work that a reaction can perform at constant pressure and temperature is equal to the reaction Gibbs energy. B. Ecell0E^0_{cell}Ecell0​ is dependent on the pressure. C. (dEcell0dT)=ΔrS0nF\left(\dfrac{dE^0_{cell}}{dT}\right)=\dfrac{\Delta_r S^0}{nF}(dTdEcell0​​)=nFΔr​S0​. D. A cell is operating reversibly if the cell potential is exactly balanced by an opposing source of potential difference.

Correct answer: 1

Step-by-step solution →
Q60·ChemistryNumerical
The ratio of sigma and π\piπ bonds present in pyrophosphoric acid is ____.

Correct answer: 6

Step-by-step solution →

Mathematics — JEE Main 8 April 2023 Shift 2

Q61·MathematicsSingle correct
Let the mean and variance of 12 observations be 92\dfrac{9}{2}29​ and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is mn\dfrac{m}{n}nm​, where m and n are co-prime, then m+n is equal to
  1. (A)316
  2. (B)314
  3. (C)317
  4. (D)315

Correct answer: (C)

Step-by-step solution →
Q62·MathematicsSingle correct
Let ana_nan​ be the nthn^{th}nth term of the series 5+8+14+23+35+50+…5+8+14+23+35+50+\ldots5+8+14+23+35+50+… and Sn=∑k=1nakS_n=\sum_{k=1}^{n}a_kSn​=∑k=1n​ak​. Then S30−a40S_{30}-a_{40}S30​−a40​ is equal to
  1. (A)11310
  2. (B)11280
  3. (C)11290
  4. (D)11260

Correct answer: (C)

Step-by-step solution →
Q63·MathematicsSingle correct
Let P be the plane passing through the line x−11=y−2−3=z+57\dfrac{x-1}{1}=\dfrac{y-2}{-3}=\dfrac{z+5}{7}1x−1​=−3y−2​=7z+5​ and the point (2,4,−3)(2,4,-3)(2,4,−3). If the image of the point (−1,3,4)(-1,3,4)(−1,3,4) in the plane P is (α,β,γ)(\alpha,\beta,\gamma)(α,β,γ), then α+β+γ\alpha+\beta+\gammaα+β+γ is equal to
  1. (A)12
  2. (B)11
  3. (C)9
  4. (D)10

Correct answer: (D)

Step-by-step solution →
Q64·MathematicsSingle correct
Let A={θ∈(0,2π):1+2isin⁡θ1−isin⁡θ is purely imaginary}A=\left\{\theta\in(0,2\pi):\dfrac{1+2i\sin\theta}{1-i\sin\theta}\text{ is purely imaginary}\right\}A={θ∈(0,2π):1−isinθ1+2isinθ​ is purely imaginary}. Then the sum of the elements in A is
  1. (A)π\piπ
  2. (B)2π2\pi2π
  3. (C)4π4\pi4π
  4. (D)3π3\pi3π

Correct answer: (C)

Step-by-step solution →
Q65·MathematicsSingle correct
The absolute difference of the coefficients of x10x^{10}x10 and x7x^{7}x7 in the expansion of (2x2+12x)11\left(2x^{2}+\dfrac{1}{2x}\right)^{11}(2x2+2x1​)11 is equal to
  1. (A)123−1212^{3}-12123−12
  2. (B)113−1111^{3}-11113−11
  3. (C)103−1010^{3}-10103−10
  4. (D)133−1313^{3}-13133−13

Correct answer: (A)

Step-by-step solution →
Q66·MathematicsSingle correct
If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is (6!)k(6!)k(6!)k, then k is equal to
  1. (A)1890
  2. (B)945
  3. (C)2835
  4. (D)5670

Correct answer: (D)

Step-by-step solution →
Q67·Mathematics·Matrices and DeterminantsSingle correct
Let S be the set of all values of θ∈[−π,π]\theta\in[-\pi,\pi]θ∈[−π,π] for which the system of linear equations x+y+3 z=0x+y+\sqrt{3}\,z=0x+y+3​z=0, −x+(tan⁡θ)y+7 z=0-x+(\tan\theta)y+\sqrt{7}\,z=0−x+(tanθ)y+7​z=0, x+y+(tan⁡θ)z=0x+y+(\tan\theta)z=0x+y+(tanθ)z=0 has non-trivial solution. Then 120π∑θ∈Sθ\dfrac{120}{\pi}\sum_{\theta\in S}\thetaπ120​∑θ∈S​θ is equal to
  1. (A)40
  2. (B)10
  3. (C)20
  4. (D)30

Correct answer: (C)

Step-by-step solution →
Q68·MathematicsSingle correct
If the probability that the random variable X takes values x is given by P(X=x)=k(x+1)3−xP(X=x)=k(x+1)3^{-x}P(X=x)=k(x+1)3−x, x=0,1,2,3,…x=0,1,2,3,\ldotsx=0,1,2,3,…, where k is a constant, then P(X≥2)P(X\geq2)P(X≥2) is equal to
  1. (A)127\dfrac{1}{27}271​
  2. (B)1118\dfrac{11}{18}1811​
  3. (C)718\dfrac{7}{18}187​
  4. (D)2027\dfrac{20}{27}2720​

Correct answer: (A)

Step-by-step solution →
Q69·MathematicsSingle correct
The value of 36(4cos⁡29∘−1)(4cos⁡227∘−1)(4cos⁡281∘−1)(4cos⁡2243∘−1)36(4\cos^{2}9^{\circ}-1)(4\cos^{2}27^{\circ}-1)(4\cos^{2}81^{\circ}-1)(4\cos^{2}243^{\circ}-1)36(4cos29∘−1)(4cos227∘−1)(4cos281∘−1)(4cos2243∘−1) is
  1. (A)54
  2. (B)18
  3. (C)27
  4. (D)36

Correct answer: (D)

Step-by-step solution →
Q70·MathematicsSingle correct
The integral ∫((x2)x+(2x)x)log⁡2x dx\displaystyle\int\left(\left(\dfrac{x}{2}\right)^{x}+\left(\dfrac{2}{x}\right)^{x}\right)\log_{2}x\,dx∫((2x​)x+(x2​)x)log2​xdx is equal to
  1. (A)(x2)x+(2x)x+C\left(\dfrac{x}{2}\right)^{x}+\left(\dfrac{2}{x}\right)^{x}+C(2x​)x+(x2​)x+C
  2. (B)(x2)x−(2x)x+C\left(\dfrac{x}{2}\right)^{x}-\left(\dfrac{2}{x}\right)^{x}+C(2x​)x−(x2​)x+C
  3. (C)(x2)xlog⁡2(x2)+C\left(\dfrac{x}{2}\right)^{x}\log_{2}\left(\dfrac{x}{2}\right)+C(2x​)xlog2​(2x​)+C
  4. (D)(x2)xlog⁡2(2x)+C\left(\dfrac{x}{2}\right)^{x}\log_{2}\left(\dfrac{2}{x}\right)+C(2x​)xlog2​(x2​)+C

Correct answer: (B)

Step-by-step solution →
Q71·MathematicsSingle correct
The area of the quadrilateral ABCD with vertices A(2,1,1)A(2,1,1)A(2,1,1), B(1,2,5)B(1,2,5)B(1,2,5), C(−2,−3,5)C(-2,-3,5)C(−2,−3,5) and D(1,−6,−7)D(1,-6,-7)D(1,−6,−7) is equal to
  1. (A)48
  2. (B)8388\sqrt{38}838​
  3. (C)54
  4. (D)9389\sqrt{38}938​

Correct answer: (B)

Step-by-step solution →
Q72·MathematicsSingle correct
For a,b∈Za,b\in\mathbb{Z}a,b∈Z and ∣a−b∣≤10|a-b|\leq10∣a−b∣≤10, let the angle between the plane P:ax+y−z=bP:ax+y-z=bP:ax+y−z=b and the line l:x−1=a−y=z+1l:x-1=a-y=z+1l:x−1=a−y=z+1 be cos⁡−1(13)\cos^{-1}\left(\dfrac{1}{3}\right)cos−1(31​). If the distance of the point (6,−6,4)(6,-6,4)(6,−6,4) from the plane P is 363\sqrt{6}36​, then a4+b2a^{4}+b^{2}a4+b2 is equal to
  1. (A)25
  2. (B)85
  3. (C)48
  4. (D)32

Correct answer: (D)

Step-by-step solution →
Q73·MathematicsSingle correct
25190−19190−8190+219025^{190}-19^{190}-8^{190}+2^{190}25190−19190−8190+2190 is divisible by
  1. (A)34 but not by 14
  2. (B)both 14 and 34
  3. (C)neither 14 nor 34
  4. (D)14 but not by 34

Correct answer: (A)

Step-by-step solution →
Q74·MathematicsSingle correct
Let the vectors u⃗1=i^+j^+ak^\vec{u}_1=\hat{i}+\hat{j}+a\hat{k}u1​=i^+j^​+ak^, u⃗2=i^+bj^+k^\vec{u}_2=\hat{i}+b\hat{j}+\hat{k}u2​=i^+bj^​+k^ and u⃗3=ci^+j^+k^\vec{u}_3=c\hat{i}+\hat{j}+\hat{k}u3​=ci^+j^​+k^ be coplanar. If the vectors v⃗1=(a+b)i^+cj^+ck^\vec{v}_1=(a+b)\hat{i}+c\hat{j}+c\hat{k}v1​=(a+b)i^+cj^​+ck^, v⃗2=ai^+(b+c)j^+ak^\vec{v}_2=a\hat{i}+(b+c)\hat{j}+a\hat{k}v2​=ai^+(b+c)j^​+ak^ and v⃗3=bi^+bj^+(c+a)k^\vec{v}_3=b\hat{i}+b\hat{j}+(c+a)\hat{k}v3​=bi^+bj^​+(c+a)k^ are also coplanar, then 6(a+b+c)6(a+b+c)6(a+b+c) is equal to
  1. (A)0
  2. (B)6
  3. (C)12
  4. (D)4

Correct answer: (C)

Step-by-step solution →
Q75·MathematicsSingle correct
Let O be the origin and OP and OQ be the tangents to the circle x2+y2−6x+4y+8=0x^{2}+y^{2}-6x+4y+8=0x2+y2−6x+4y+8=0 at the points P and Q on it. If the circumcircle of the triangle OPQ passes through the point (α,12)\left(\alpha,\dfrac{1}{2}\right)(α,21​), then a value of α\alphaα is
  1. (A)32\dfrac{3}{2}23​
  2. (B)52\dfrac{5}{2}25​
  3. (C)111
  4. (D)−12-\dfrac{1}{2}−21​

Correct answer: (B)

Step-by-step solution →
Q76·MathematicsSingle correct
The negation of p∧(∼q)∨(∼p)p\wedge(\sim q)\vee(\sim p)p∧(∼q)∨(∼p) is equivalent to
  1. (A)p∧qp\wedge qp∧q
  2. (B)p∧(∼q)p\wedge(\sim q)p∧(∼q)
  3. (C)p∧(q∧(∼p))p\wedge(q\wedge(\sim p))p∧(q∧(∼p))
  4. (D)p∨(q∨(∼p))p\vee(q\vee(\sim p))p∨(q∨(∼p))

Correct answer: (A)

Step-by-step solution →
Q77·Mathematics·Limits and ContinuitySingle correct
If α>β>0\alpha>\beta>0α>β>0 are the roots of the equation ax2+bx+1=0ax^{2}+bx+1=0ax2+bx+1=0, and lim⁡x→1α(1−cos⁡(x2+bx+a)2(1−αx)2)12=1k(1β−1α)\displaystyle\lim_{x\to\frac{1}{\alpha}}\left(\dfrac{1-\cos(x^{2}+bx+a)}{2(1-\alpha x)^{2}}\right)^{\frac{1}{2}}=\dfrac{1}{k}\left(\dfrac{1}{\beta}-\dfrac{1}{\alpha}\right)x→α1​lim​(2(1−αx)21−cos(x2+bx+a)​)21​=k1​(β1​−α1​), then k is equal to
  1. (A)2β2\beta2β
  2. (B)2α2\alpha2α
  3. (C)α\alphaα
  4. (D)β\betaβ

Correct answer: (B)

Step-by-step solution →
Q78·MathematicsSingle correct
If A=[15λ10]A=\begin{bmatrix}1&5\\\lambda&10\end{bmatrix}A=[1λ​510​], A−1=αA+βIA^{-1}=\alpha A+\beta IA−1=αA+βI and α+β=−2\alpha+\beta=-2α+β=−2, then 4α2+β2+λ24\alpha^{2}+\beta^{2}+\lambda^{2}4α2+β2+λ2 is equal to
  1. (A)12
  2. (B)10
  3. (C)19
  4. (D)14

Correct answer: (D)

Step-by-step solution →
Q79·MathematicsSingle correct
Let A(0,1)A(0,1)A(0,1), B(1,1)B(1,1)B(1,1) and C(1,0)C(1,0)C(1,0) be the mid-points of the sides of a triangle with incentre at the point D. If the focus of the parabola y2=4axy^{2}=4axy2=4ax passing through D is (α+β2,0)(\alpha+\beta\sqrt{2},0)(α+β2​,0), where α\alphaα and β\betaβ are rational numbers, then αβ2\dfrac{\alpha}{\beta^{2}}β2α​ is equal to
  1. (A)6
  2. (B)8
  3. (C)12
  4. (D)92\dfrac{9}{2}29​

Correct answer: (B)

Step-by-step solution →
Q80·MathematicsSingle correct
Let A={1,2,3,4,5,6,7}A=\{1,2,3,4,5,6,7\}A={1,2,3,4,5,6,7}. Then the relation R={(x,y)∈A×A:x+y=7}R=\{(x,y)\in A\times A:x+y=7\}R={(x,y)∈A×A:x+y=7} is
  1. (A)transitive but neither symmetric nor reflexive
  2. (B)reflexive but neither symmetric nor transitive
  3. (C)an equivalence relation
  4. (D)symmetric but neither reflexive nor transitive

Correct answer: (D)

Step-by-step solution →
Q81·MathematicsNumerical
Let [t][t][t] denote the greatest integer function. If ∫02.4[x2]dx=α+β2+γ3+δ5\displaystyle\int_0^{2.4}\left[x^{2}\right]dx=\alpha+\beta\sqrt{2}+\gamma\sqrt{3}+\delta\sqrt{5}∫02.4​[x2]dx=α+β2​+γ3​+δ5​, then α+β+γ+δ\alpha+\beta+\gamma+\deltaα+β+γ+δ is equal to

Correct answer: 6

Step-by-step solution →
Q82·Mathematics·DifferentiabilityNumerical
Let k and m be positive real numbers such that the function f(x)={3x2+kx+1,0<x<1mx2+k2,x≥1f(x)=\begin{cases}3x^{2}+k\sqrt{x+1},&0<x<1\\mx^{2}+k^{2},&x\geq1\end{cases}f(x)={3x2+kx+1​,mx2+k2,​0<x<1x≥1​ is differentiable for all x>0x>0x>0. Then 8f′(8)f′(18)\dfrac{8f'(8)}{f'\left(\dfrac{1}{8}\right)}f′(81​)8f′(8)​ is equal to

Correct answer: 309

Step-by-step solution →
Q83·MathematicsNumerical
Let 0<z<y<x0<z<y<x0<z<y<x be three real numbers such that 1x,1y,1z\dfrac{1}{x},\dfrac{1}{y},\dfrac{1}{z}x1​,y1​,z1​ are in an arithmetic progression and x,2y,zx,\sqrt{2}y,zx,2​y,z are in a geometric progression. If xy+yz+zx=32xyzxy+yz+zx=\dfrac{3}{\sqrt{2}}xyzxy+yz+zx=2​3​xyz, then 3(x+y+z)23(x+y+z)^{2}3(x+y+z)2 is equal to

Correct answer: 150

Step-by-step solution →
Q84·MathematicsNumerical
If domain of the function log⁡e(6x2+5x+12x−1)+cos⁡−1(2x2−3x+43x−5)\log_e\left(\dfrac{6x^{2}+5x+1}{2x-1}\right)+\cos^{-1}\left(\dfrac{2x^{2}-3x+4}{3x-5}\right)loge​(2x−16x2+5x+1​)+cos−1(3x−52x2−3x+4​) is (α,β)∪(γ,δ](\alpha,\beta)\cup(\gamma,\delta](α,β)∪(γ,δ], then 18(α2+β2+γ2+δ2)18(\alpha^{2}+\beta^{2}+\gamma^{2}+\delta^{2})18(α2+β2+γ2+δ2) is equal to

Correct answer: 20

Step-by-step solution →
Q85·MathematicsNumerical
Let m and n be the numbers of real roots of the quadratic equations x2−12x+[x]+31=0x^{2}-12x+[x]+31=0x2−12x+[x]+31=0 and x2−5∣x+2∣−4=0x^{2}-5|x+2|-4=0x2−5∣x+2∣−4=0 respectively, where [x][x][x] denotes the greatest integer ≤x\leq x≤x. Then m2+mn+n2m^{2}+mn+n^{2}m2+mn+n2 is equal to

Correct answer: 9

Step-by-step solution →
Q86·MathematicsNumerical
The ordinates of the points P and Q on the parabola with focus (3,0)(3,0)(3,0) and directrix x=−3x=-3x=−3 are in the ratio 3:13:13:1. If R(α,β)R(\alpha,\beta)R(α,β) is the point of intersection of the tangents to the parabola at P and Q, then β2α\dfrac{\beta^{2}}{\alpha}αβ2​ is equal to

Correct answer: 16

Step-by-step solution →
Q87·MathematicsNumerical
Let the solution curve x=x(y)x=x(y)x=x(y), 0<y<π20<y<\dfrac{\pi}{2}0<y<2π​, of the differential equation (log⁡e(cos⁡y))2cos⁡y dx−(1+3xlog⁡e(cos⁡y))sin⁡y dy=0(\log_e(\cos y))^{2}\cos y\,dx-(1+3x\log_e(\cos y))\sin y\,dy=0(loge​(cosy))2cosydx−(1+3xloge​(cosy))sinydy=0 satisfy x(π3)=12log⁡e2x\left(\dfrac{\pi}{3}\right)=\dfrac{1}{2\log_e 2}x(3π​)=2loge​21​. If x(π6)=1log⁡em−log⁡enx\left(\dfrac{\pi}{6}\right)=\dfrac{1}{\log_e m-\log_e n}x(6π​)=loge​m−loge​n1​, where m and n are co-prime, then mn is equal to

Correct answer: 12

Step-by-step solution →
Q88·MathematicsNumerical
Let P1P_1P1​ be the plane 3x−y−7z=113x-y-7z=113x−y−7z=11 and P2P_2P2​ be the plane passing through the points (2,−1,0)(2,-1,0)(2,−1,0), (2,0,−1)(2,0,-1)(2,0,−1) and (5,1,1)(5,1,1)(5,1,1). If the foot of the perpendicular drawn from the point (7,4,−1)(7,4,-1)(7,4,−1) on the line of intersection of the planes P1P_1P1​ and P2P_2P2​ is (α,β,γ)(\alpha,\beta,\gamma)(α,β,γ), then α+β+γ\alpha+\beta+\gammaα+β+γ is equal to

Correct answer: 11

Step-by-step solution →
Q89·MathematicsNumerical
Let R={a,b,c,d,e}R=\{a,b,c,d,e\}R={a,b,c,d,e} and S={1,2,3,4}S=\{1,2,3,4\}S={1,2,3,4}. Total number of onto functions f:R→Sf:R\to Sf:R→S such that f(a)≠1f(a)\neq1f(a)=1, is equal to

Correct answer: 384

Step-by-step solution →
Q90·MathematicsNumerical
Let the area enclosed by the lines x+y=2x+y=2x+y=2, y=0y=0y=0, x=0x=0x=0 and the curve f(x)=min⁡{x2+34, 1+[x]}f(x)=\min\left\{x^{2}+\dfrac{3}{4},\,1+[x]\right\}f(x)=min{x2+43​,1+[x]}, where [x][x][x] denotes the greatest integer ≤x\leq x≤x, be A. Then the value of 12A12A12A is

Correct answer: 17

Step-by-step solution →

Chapters tested in this paper

Open any chapter to practise every past-year question on that topic across all papers, and see how often it has actually appeared.

  • Properties of Solids and Liquids 172/186
  • Three Dimensional Geometry 176/186
  • Matrices and Determinants 180/186
  • Coordination Compounds 176/186
  • Sets, Relations and Functions 165/186
  • Current Electricity 160/186
  • Sequence and Series 164/186
  • Definite Integration 168/186
  • Rotational Motion 172/186
  • Redox Reactions and Electrochemistry 177/186
  • Geometrical Optics 172/186
  • Kinematics 156/186
  • Vector Algebra 173/186
  • Differential Equations 167/186
  • Probability 176/186
  • Permutations and Combinations 162/186
  • Magnetic Field of Current 147/186
  • Binomial Theorem and Its Simple Applications 158/186
  • Electromagnetic Waves 144/186
  • Chemical Bonding and Molecular Structure 151/186
  • Limits and Continuity 149/186
  • Thermodynamics 154/186
  • Equilibrium 163/186
  • Solutions 158/186
  • Chemical Thermodynamics 165/186
  • Units and Measurements 149/186
  • Complex Numbers 165/186
  • Trigonometric Functions 144/186
  • Biomolecules 162/186
  • Chemical Kinetics 169/186
  • Gravitation 152/186
  • Atomic Structure 161/186
  • Electronic Devices 145/186
  • Circles 142/186
  • Dual Nature of Matter and Radiation 155/186
  • Quadratic Equations 148/186
  • Work, Energy and Power 132/186
  • Some Basic Concepts in Chemistry 129/186
  • Electromagnetic Induction 120/186
  • Wave Optics 130/186
  • Area Under Curves 139/186
  • Kinetic Theory of Gases 135/186
  • Alcohols and Ethers 106/186
  • Oscillations 117/186
  • Alternating Currents 108/186
  • Nuclei 116/186
  • Organic Compounds Containing Halogens 109/186
  • Waves 109/186
  • Capacitors and Dielectrics 115/186
  • Atoms 112/186
  • Parabola 101/186
  • Statistics 118/186
  • Isolation of Metals 106/186
  • Differentiability 91/186
  • s-Block Elements 88/186
  • Surface Chemistry 98/186
  • Inverse Trigonometric Functions 93/186
  • Environmental Chemistry 83/186
  • Hydrogen 81/186
  • Electric Potential 63/186
  • Indefinite Integration 66/186
  • Carboxylic Acids and Derivatives 54/186
  • Chemistry in Everyday Life 60/186
  • Diazonium Salts and Reactions 53/186
  • States of Matter: Gases and Liquids 52/186
  • Magnetism and Matter 50/186
  • IUPAC Nomenclature 37/186
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