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JEE Main 24 January 2023 Shift 1 Question Paper with Answers

24 January 2023 · January session · 90 questions

The complete JEE Main 24 January 2023 Shift 1 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 24 January 2023 Shift 1

Q1·PhysicsSingle correct
A circular loop of radius rrr is carrying current III A. The ratio of magnetic field at the centre of the circular loop and at a distance rrr from the centre of the loop on its axis is:
  1. (A)22:12\sqrt{2}:122​:1
  2. (B)1:321:3\sqrt{2}1:32​
  3. (C)1:21:\sqrt{2}1:2​
  4. (D)32:23\sqrt{2}:232​:2

Correct answer: (A)

Step-by-step solution →
Q2·PhysicsSingle correct
The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth Re=6400R_e=6400Re​=6400 km):
  1. (A)8 N
  2. (B)4.9 N
  3. (C)9.8 N
  4. (D)19.6 N

Correct answer: (A)

Step-by-step solution →
Q3·PhysicsSingle correct
Two long straight wires PPP and QQQ carrying equal current 10 A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire P is F1F_1F1​. If distance between wires is halved and currents on them are doubled, force F2F_2F2​ on 10 cm length of wire P will be:
  1. (A)F18\tfrac{F_1}{8}8F1​​
  2. (B)8F18F_18F1​
  3. (C)10F110F_110F1​
  4. (D)F110\tfrac{F_1}{10}10F1​​

Correct answer: (B)

Step-by-step solution →
Q4·PhysicsSingle correct
Given below are two statements: Statement I: The temperature of a gas is −73∘-73^{\circ}−73∘C. When the gas is heated to 527∘527^{\circ}527∘C, the root mean square speed of the molecules is doubled. Statement II: The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)Statement I is false but Statement II is true
  2. (B)Both Statement I and Statement II are false
  3. (C)Statement I is true but Statement II is false
  4. (D)Both Statement I and Statement II are true

Correct answer: (C)

Step-by-step solution →
Q5·PhysicsSingle correct
The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is:
  1. (A)272 m
  2. (B)68 m
  3. (C)192 m
  4. (D)136 m

Correct answer: (A)

Step-by-step solution →
Q6·PhysicsSingle correct
Given below are two statements: Statement I: If the Brewster's angle for the light propagating from air to glass is θB\theta_BθB​, then the Brewster's angle for the light propagating from glass to air is π2−θB\tfrac{\pi}{2}-\theta_B2π​−θB​. Statement II: The Brewster's angle for the light propagating from glass to air is tan⁡−1(μg)\tan^{-1}(\mu_g)tan−1(μg​) where μg\mu_gμg​ is the refractive index of glass. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)Both Statement I and Statement II are false
  2. (B)Statement I is true but Statement II is false
  3. (C)Statement I is false but Statement II is true
  4. (D)Both Statement I and Statement II are true

Correct answer: (B)

Step-by-step solution →
Q7·PhysicsSingle correct
A 100 m long wire having cross-sectional area 6.25×10−46.25\times10^{-4}6.25×10−4 m2^22 and Young's modulus is 101010^{10}1010 Nm−2^{-2}−2 is subjected to a load of 250 N, then the elongation in the wire will be:
  1. (A)4×10−34\times10^{-3}4×10−3 m
  2. (B)6.25×10−36.25\times10^{-3}6.25×10−3 m
  3. (C)6.25×10−66.25\times10^{-6}6.25×10−6 m
  4. (D)4×10−44\times10^{-4}4×10−4 m

Correct answer: (A)

Step-by-step solution →
Q8·PhysicsSingle correct
If two charges q1q_1q1​ and q2q_2q2​ are separated with distance ′d′'d'′d′ and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?
  1. (A)2dK2d\sqrt{K}2dK​
  2. (B)1.5 dK1.5\,d\sqrt{K}1.5dK​
  3. (C)dKd\sqrt{K}dK​
  4. (D)KdK\sqrt{d}Kd​

Correct answer: (C)

Step-by-step solution →
Q9·PhysicsSingle correct
Consider the following radioactive decay process: 84218A→αA1→β−A2→γA3→αA4→β+A5→γA6{}^{218}_{84}A \xrightarrow{\alpha} A_1 \xrightarrow{\beta^-} A_2 \xrightarrow{\gamma} A_3 \xrightarrow{\alpha} A_4 \xrightarrow{\beta^+} A_5 \xrightarrow{\gamma} A_684218​Aα​A1​β−​A2​γ​A3​α​A4​β+​A5​γ​A6​. The mass number and the atomic number of A6A_6A6​ are given by:
  1. (A)210 and 84
  2. (B)210 and 82
  3. (C)211 and 80
  4. (D)210 and 80

Correct answer: (D)

Step-by-step solution →
Q10·PhysicsSingle correct
From the photoelectric effect experiment, following observations are made. Identify which of these are correct. A. The stopping potential depends only on the work function of the metal. B. The saturation current increases as the intensity of incident light increases. C. The maximum kinetic energy of a photo electron depends on the intensity of the incident light. D. Photoelectric effect can be explained using wave theory of light. Choose the correct answer from the options given below:
  1. (A)A, C, D only
  2. (B)B, C only
  3. (C)B only
  4. (D)A, B, D only

Correct answer: (C)

Step-by-step solution →
Q11·PhysicsSingle correct
Given below are two statements: Statement I: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable. Statement II: Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed. In the light of the above 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 false but Statement II is true
  3. (C)Statement I is true but Statement II is false
  4. (D)Both Statement I and Statement II are false

Correct answer: (C)

Step-by-step solution →
Q12·PhysicsSingle correct
1 g of a liquid is converted to vapour at 3×1053\times10^53×105 Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm3^33 during this phase change, then the increase in internal energy in the process will be:
  1. (A)432000 J
  2. (B)4320 J
  3. (C)4800 J
  4. (D)4.32×1084.32\times10^84.32×108 J

Correct answer: (B)

Step-by-step solution →
Q13·PhysicsSingle correct
As shown in the figure, a network of resistors is connected to a battery of 24 V with an internal resistance of 3 Ω3\,\Omega3Ω. The currents through the resistors R4R_4R4​ and R5R_5R5​ are I4I_4I4​ and I5I_5I5​ respectively. The values of I4I_4I4​ and I5I_5I5​ are:
  1. (A)I4=25I_4=\tfrac{2}{5}I4​=52​ A and I5=85I_5=\tfrac{8}{5}I5​=58​ A
  2. (B)I4=245I_4=\tfrac{24}{5}I4​=524​ A and I5=65I_5=\tfrac{6}{5}I5​=56​ A
  3. (C)I4=85I_4=\tfrac{8}{5}I4​=58​ A and I5=25I_5=\tfrac{2}{5}I5​=52​ A
  4. (D)I4=65I_4=\tfrac{6}{5}I4​=56​ A and I5=245I_5=\tfrac{24}{5}I5​=524​ A

Correct answer: (A)

Step-by-step solution →
Q14·PhysicsSingle correct
A modulating signal is a square wave, as shown in the figure. If the carrier wave is given as c(t)=2sin⁡(8πt)c(t)=2\sin(8\pi t)c(t)=2sin(8πt) volts, the modulation index is:
  1. (A)14\tfrac{1}{4}41​
  2. (B)12\tfrac{1}{2}21​
  3. (C)111
  4. (D)13\tfrac{1}{3}31​

Correct answer: (B)

Step-by-step solution →
Q15·PhysicsSingle correct
A conducting circular loop of radius 10π\tfrac{10}{\sqrt{\pi}}π​10​ cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is:
  1. (A)emf = 1 mV
  2. (B)emf = 5 mV
  3. (C)emf = 100 mV
  4. (D)emf = 10 mV

Correct answer: (D)

Step-by-step solution →
Q16·PhysicsSingle correct
If E⃗\vec{E}E and K⃗\vec{K}K represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by (ω\omegaω - angular frequency):
  1. (A)ω(E⃗×K⃗)\omega(\vec{E}\times\vec{K})ω(E×K)
  2. (B)ω(K⃗×E⃗)\omega(\vec{K}\times\vec{E})ω(K×E)
  3. (C)K⃗×E⃗\vec{K}\times\vec{E}K×E
  4. (D)1ω(K⃗×E⃗)\tfrac{1}{\omega}(\vec{K}\times\vec{E})ω1​(K×E)

Correct answer: (D)

Step-by-step solution →
Q17·PhysicsSingle correct
Match List I (physical quantities) with List II (their dimensional formulae). Choose the correct answer from the options given below:
List IList II
A.Planck's constant (h)I.[M1L2T−2][M^1L^2T^{-2}][M1L2T−2]
B.Stopping potential (VsV_sVs​)II.[M1L1T−1][M^1L^1T^{-1}][M1L1T−1]
C.Work function (ϕ\phiϕ)III.[M1L2T−1][M^1L^2T^{-1}][M1L2T−1]
D.Momentum (p)IV.[M1L2T−3A−1][M^1L^2T^{-3}A^{-1}][M1L2T−3A−1]
  1. (A)A-I, B-III, C-IV, D-II
  2. (B)A-III, B-I, C-II, D-IV
  3. (C)A-II, B-IV, C-III, D-I
  4. (D)A-III, B-IV, C-I, D-II

Correct answer: (D)

Step-by-step solution →
Q18·PhysicsSingle correct
A travelling wave is described by the equation y(x,t)=[0.05sin⁡(8x−4t)]y(x,t)=[0.05\sin(8x-4t)]y(x,t)=[0.05sin(8x−4t)] m. The velocity of the wave is: [all the quantities are in SI unit]
  1. (A)888 ms−1^{-1}−1
  2. (B)444 ms−1^{-1}−1
  3. (C)0.50.50.5 ms−1^{-1}−1
  4. (D)222 ms−1^{-1}−1

Correct answer: (C)

Step-by-step solution →
Q19·PhysicsSingle correct
As shown in the figure, a weightless pulley PPP is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if g=10g=10g=10 m/s2^22):
  1. (A)(43+1)(4\sqrt{3}+1)(43​+1) N
  2. (B)4(3+1)4(\sqrt{3}+1)4(3​+1) N
  3. (C)(43−1)(4\sqrt{3}-1)(43​−1) N
  4. (D)4(3−1)4(\sqrt{3}-1)4(3​−1) N

Correct answer: (B)

Step-by-step solution →
Q20·PhysicsAssertion & Reason
Assertion A: Photodiodes are preferably operated in reverse bias condition for light intensity measurement. Reason R: The current in the forward bias is more than the current in the reverse bias for a p−np-np−n junction diode. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)A is true but R is false
  2. (B)A is false but R is true
  3. (C)Both A and R are true and R is the correct explanation of A
  4. (D)Both A and R are true but R is NOT the correct explanation of A

Correct answer: (D)

Step-by-step solution →
Q21·PhysicsNumerical
Vectors ai^+bj^+k^a\hat{i}+b\hat{j}+\hat{k}ai^+bj^​+k^ and 2i^−3j^+4k^2\hat{i}-3\hat{j}+4\hat{k}2i^−3j^​+4k^ are perpendicular to each other when 3a+2b=73a+2b=73a+2b=7, the ratio of aaa to bbb is x2\tfrac{x}{2}2x​. The value of xxx is _______ .

Correct answer: 1

Step-by-step solution →
Q22·PhysicsNumerical
Assume that protons and neutrons have equal masses. Mass of a nucleon is 1.6×10−271.6\times10^{-27}1.6×10−27 kg and radius of nucleus is 1.5×10−15A1/31.5\times10^{-15}A^{1/3}1.5×10−15A1/3 m. The approximate ratio of the nuclear density and water density is n×1013n\times10^{13}n×1013. The value of nnn is _______ .

Correct answer: 11

Step-by-step solution →
Q23·PhysicsNumerical
A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is n×10−3 Ωn\times10^{-3}\,\Omegan×10−3Ω. If the resistivity of the material is 2.4×10−8 Ω2.4\times10^{-8}\,\Omega2.4×10−8Ωm. The value of nnn is _______ .

Correct answer: 2

Step-by-step solution →
Q24·PhysicsNumerical
A stream of positively charged particles having qm=2×1011 Ckg\tfrac{q}{m}=2\times10^{11}\,\tfrac{\text{C}}{\text{kg}}mq​=2×1011kgC​ and velocity v⃗0=3×107 i^\vec{v}_0=3\times10^7\,\hat{i}v0​=3×107i^ m/s is deflected by an electric field 1.8 j^1.8\,\hat{j}1.8j^​ kV/m. The electric field exists in a region of 10 cm along xxx direction. Due to the electric field, the deflection of the charge particles in the yyy direction is _______ mm.

Correct answer: 2

Step-by-step solution →
Q25·PhysicsNumerical
As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and refraction index of the material for both the lenses is 1.75. Both the lenses are placed at distance of 40 cm from each other. Due to the combination, the image of the object is formed at distance = _______ cm, from concave lens.

Correct answer: 120

Step-by-step solution →
Q26·PhysicsNumerical
Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be x\sqrt{x}x​ cm. The value of xxx is _______ .

Correct answer: 110

Step-by-step solution →
Q27·PhysicsNumerical
A block of mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is πx\tfrac{\pi}{\sqrt{x}}x​π​ in SI unit. The value of xxx is _______ .

Correct answer: 5

Step-by-step solution →
Q28·PhysicsNumerical
A hole is drilled in a metal sheet. At 27∘27^{\circ}27∘C, the diameter of hole is 5 cm. When the sheet is heated to 177∘177^{\circ}177∘C, the change in the diameter of hole is d×10−3d\times10^{-3}d×10−3 cm. The value of ddd will be _______ if coefficient of linear expansion of the metal is 1.6×10−5/∘1.6\times10^{-5}/^{\circ}1.6×10−5/∘C.

Correct answer: 12

Step-by-step solution →
Q29·PhysicsNumerical
In the circuit shown in the figure, the ratio of the quality factor and the band width is _______ S.

Correct answer: 10

Step-by-step solution →
Q30·PhysicsNumerical
A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of 5th second. The force acted on the body is _______ N.

Correct answer: 40

Step-by-step solution →

Chemistry — JEE Main 24 January 2023 Shift 1

Q31·ChemistrySingle correct
'A' and 'B' formed in the following set of reactions are:
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (B)

Step-by-step solution →
Q32·ChemistrySingle correct
Decreasing order of the hydrogen bonding in following forms of water is correctly represented by: A. Liquid water B. Ice C. Impure water. Choose the correct answer from the options given below:
  1. (A)B > A > C
  2. (B)A>B>CA>B>CA>B>C
  3. (C)A=B>CA=B>CA=B>C
  4. (D)C > B > A

Correct answer: (A)

Step-by-step solution →
Q33·Chemistry·Electronic Effects and StabilitySingle correct
Increasing order of stability of the resonance structures (A, B, C, D shown in the figure) is:
  1. (A)D, C, A, B
  2. (B)D, C, B, A
  3. (C)C, D, A, B
  4. (D)C, D, B, A

Correct answer: (A)

Step-by-step solution →
Q34·ChemistrySingle correct
'R' formed in the following sequence of reactions is:
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (B)

Step-by-step solution →
Q35·ChemistrySingle correct
The primary and secondary valencies of cobalt respectively in [Co(NH3)5Cl]Cl2[\text{Co(NH}_3)_5\text{Cl}]\text{Cl}_2[Co(NH3​)5​Cl]Cl2​ are:
  1. (A)3 and 6
  2. (B)2 and 6
  3. (C)3 and 5
  4. (D)2 and 8

Correct answer: (A)

Step-by-step solution →
Q36·ChemistrySingle correct
An ammoniacal metal salt solution gives a brilliant red precipitate on addition of dimethylglyoxime. The metal ion is:
  1. (A)Co2+\text{Co}^{2+}Co2+
  2. (B)Ni2+\text{Ni}^{2+}Ni2+
  3. (C)Fe2+\text{Fe}^{2+}Fe2+
  4. (D)Cu2+\text{Cu}^{2+}Cu2+

Correct answer: (B)

Step-by-step solution →
Q37·ChemistrySingle correct
Reaction of BeO with ammonia and hydrogen fluoride gives A which on thermal decomposition gives BeF2\text{BeF}_2BeF2​ and NH4F\text{NH}_4\text{F}NH4​F. What is 'A'?
  1. (A)(NH4)2BeF4(\text{NH}_4)_2\text{BeF}_4(NH4​)2​BeF4​
  2. (B)H3NBeF3\text{H}_3\text{NBeF}_3H3​NBeF3​
  3. (C)(NH4)Be2F5(\text{NH}_4)\text{Be}_2\text{F}_5(NH4​)Be2​F5​
  4. (D)(NH4)BeF3(\text{NH}_4)\text{BeF}_3(NH4​)BeF3​

Correct answer: (A)

Step-by-step solution →
Q38·ChemistrySingle correct
Match List I (metallurgical furnace / process) with List II (the metal or element produced). Choose the correct answer from the options given below:
List IList II
A.Reverberatory furnaceI.Pig Iron
B.Electrolytic cellII.Aluminium
C.Blast furnaceIII.Silicon
D.Zone Refining furnaceIV.Copper
  1. (A)A-IV, B-II, C-I, D-III
  2. (B)A-I, B-III, C-II, D-IV
  3. (C)A-III, B-IV, C-I, D-II
  4. (D)A-I, B-IV, C-II, D-III

Correct answer: (A)

Step-by-step solution →
Q39·ChemistrySingle correct
Match List I (substance / use) with List II (the chemical species involved). Choose the correct answer from the options given below:
List IList II
A.ChlorophyllI.Na2CO3\text{Na}_2\text{CO}_3Na2​CO3​
B.Soda ashII.CaSO4\text{CaSO}_4CaSO4​
C.Dentistry, Ornamental workIII.Mg2+\text{Mg}^{2+}Mg2+
D.Used in white washingIV.Ca(OH)2\text{Ca(OH)}_2Ca(OH)2​
  1. (A)A-II, B-I, C-III, D-IV
  2. (B)A-III, B-I, C-II, D-IV
  3. (C)A-II, B-III, C-IV, D-I
  4. (D)A-III, B-IV, C-I, D-II

Correct answer: (B)

Step-by-step solution →
Q40·Chemistry·Reaction MechanismSingle correct
In the following given reaction, 'A' is:
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (C)

Step-by-step solution →
Q41·ChemistrySingle correct
It is observed that characteristic X-ray spectra of elements show regularity. When frequency to the power 'n' i.e. vnv^nvn of X-rays emitted is plotted against atomic number 'Z', the following graph is obtained. The value of 'n' is:
  1. (A)3
  2. (B)2
  3. (C)1
  4. (D)12\tfrac{1}{2}21​

Correct answer: (D)

Step-by-step solution →
Q42·ChemistrySingle correct
Given below are two statements: Statement I: Noradrenaline is a neurotransmitter. Statement II: Low level of noradrenaline is not the cause of depression in human. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)Statement I is correct but Statement II is incorrect
  2. (B)Both Statement I and Statement II are correct
  3. (C)Both Statement I and Statement II are incorrect
  4. (D)Statement I is incorrect but Statement II is correct

Correct answer: (A)

Step-by-step solution →
Q43·ChemistrySingle correct
Which of the Phosphorus oxoacid can create silver mirror from AgNO3\text{AgNO}_3AgNO3​ solution?
  1. (A)(HPO3)n(\text{HPO}_3)_n(HPO3​)n​
  2. (B)H4P2O6\text{H}_4\text{P}_2\text{O}_6H4​P2​O6​
  3. (C)H4P2O5\text{H}_4\text{P}_2\text{O}_5H4​P2​O5​
  4. (D)H4P2O7\text{H}_4\text{P}_2\text{O}_7H4​P2​O7​

Correct answer: (C)

Step-by-step solution →
Q44·ChemistrySingle correct
Compound (X) undergoes the following sequence of reactions to give the Lactone (Y). Compound (X) is:
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (D)

Step-by-step solution →
Q45·ChemistrySingle correct
Order of Covalent bond: A. KF > KI; LiF > KF. B. KF < KI; LiF > KF. C. SnCl4\text{SnCl}_4SnCl4​ > SnCl2\text{SnCl}_2SnCl2​; CuCl > NaCl. D. LiF > KF; CuCl < NaCl. E. KF < KI; CuCl > NaCl. Choose the correct answer from the options given below:
  1. (A)C, E only
  2. (B)B, C, E only
  3. (C)A, B only
  4. (D)B, C only

Correct answer: (B)

Step-by-step solution →
Q46·ChemistrySingle correct
Which of the following is true about freons?
  1. (A)These are radicals of chlorine and chlorine monoxide
  2. (B)These are chemicals causing skin cancer
  3. (C)These are chlorofluorocarbon compounds
  4. (D)All radicals are called freons

Correct answer: (C)

Step-by-step solution →
Q47·ChemistrySingle correct
In the depression of freezing point experiment: A. Vapour pressure of the solution is less than that of pure solvent. B. Vapour pressure of the solution is more than that of pure solvent. C. Only solute molecules solidify at the freezing point. D. Only solvent molecules solidify at the freezing point. Choose the most appropriate answer from the options given below:
  1. (A)A and C only
  2. (B)A only
  3. (C)A and D only
  4. (D)B and C only

Correct answer: (C)

Step-by-step solution →
Q48·ChemistrySingle correct
Statement I: For colloidal particles, the values of colligative properties are of small order as compared to values shown by true solutions at same concentration. Statement II: For colloidal particles, the potential difference between the fixed layer and the diffused layer of same charges is called the electrokinetic potential or zeta potential. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)Statement I is false but Statement II is true
  2. (B)Statement I is true but Statement II is false
  3. (C)Both Statement I and Statement II are true
  4. (D)Both Statement I and Statement II are false

Correct answer: (B)

Step-by-step solution →
Q49·ChemistryAssertion & Reason
Assertion A: Hydrolysis of an alkyl chloride is a slow reaction but in the presence of NaI, the rate of the hydrolysis increases. Reason R: I−\text{I}^-I− is a good nucleophile as well as a good leaving group. In the light of the above statements, choose the correct answer from the options given below:
  1. (A)A is false but R is true
  2. (B)A is true but R is false
  3. (C)Both A and R are true but R is NOT the correct explanation of A
  4. (D)Both A and R are true and R is the correct explanation of A

Correct answer: (C)

Step-by-step solution →
Q50·ChemistrySingle correct
The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion is:
  1. (A)Cr2+\text{Cr}^{2+}Cr2+
  2. (B)Ti2+\text{Ti}^{2+}Ti2+
  3. (C)V2+\text{V}^{2+}V2+
  4. (D)Mn2+\text{Mn}^{2+}Mn2+

Correct answer: (C)

Step-by-step solution →
Q51·ChemistryNumerical
When Fe0.93O\text{Fe}_{0.93}\text{O}Fe0.93​O is heated in presence of oxygen, it converts to Fe2O3\text{Fe}_2\text{O}_3Fe2​O3​. The number of correct statement/s from the following is: A. The equivalent weight of Fe0.93O\text{Fe}_{0.93}\text{O}Fe0.93​O is Molecular weight0.79\tfrac{\text{Molecular weight}}{0.79}0.79Molecular weight​. B. The number of moles of Fe2+\text{Fe}^{2+}Fe2+ and Fe3+\text{Fe}^{3+}Fe3+ in 1 mole of Fe0.93O\text{Fe}_{0.93}\text{O}Fe0.93​O is 0.79 and 0.14 respectively. C. Fe0.93O\text{Fe}_{0.93}\text{O}Fe0.93​O is metal deficient with lattice comprising of cubic closed packed arrangement of O2−\text{O}^{2-}O2− ions. D. The % composition of Fe2+\text{Fe}^{2+}Fe2+ and Fe3+\text{Fe}^{3+}Fe3+ in Fe0.93O\text{Fe}_{0.93}\text{O}Fe0.93​O is 85% and 15% respectively.

Correct answer: 4

Step-by-step solution →
Q52·ChemistryNumerical
The number of correct statement/s from the following is: A. Larger the activation energy, smaller is the value of the rate constant. B. The higher is the activation energy, higher is the value of the temperature coefficient. C. At lower temperatures, increase in temperature causes more change in the value of k than at higher temperature. D. A plot of ln⁡k\ln klnk vs 1T\tfrac{1}{T}T1​ is a straight line with slope equal to −EaR-\tfrac{E_a}{R}−REa​​.

Correct answer: 4

Step-by-step solution →
Q53·ChemistryNumerical
For independent processes at 300 K: Process A (ΔH=−25\Delta H=-25ΔH=−25 kJ mol−1^{-1}−1, ΔS=−80\Delta S=-80ΔS=−80 J K−1^{-1}−1); Process B (ΔH=−22\Delta H=-22ΔH=−22 kJ mol−1^{-1}−1, ΔS=40\Delta S=40ΔS=40 J K−1^{-1}−1); Process C (ΔH=25\Delta H=25ΔH=25 kJ mol−1^{-1}−1, ΔS=−50\Delta S=-50ΔS=−50 J K−1^{-1}−1); Process D (ΔH=22\Delta H=22ΔH=22 kJ mol−1^{-1}−1, ΔS=20\Delta S=20ΔS=20 J K−1^{-1}−1). The number of non-spontaneous processes from these is _______ .

Correct answer: 2

Step-by-step solution →
Q54·ChemistryNumerical
5 g of NaOH was dissolved in deionized water to prepare a 450 mL stock solution. What volume (in mL) of this solution would be required to prepare 500 mL of 0.1 M solution? Given: Molar Mass of Na, O and H is 23, 16 and 1 g mol−1^{-1}−1 respectively.

Correct answer: 180

Step-by-step solution →
Q55·ChemistryNumerical
If wavelength of the first line of the Paschen series of hydrogen atom is 720 nm, then the wavelength of the second line of this series is _______ nm. (Nearest integer)

Correct answer: 492

Step-by-step solution →
Q56·ChemistryNumerical
Uracil is a base present in RNA. The percentage of nitrogen (by mass) in uracil is _______ .

Correct answer: 25

Step-by-step solution →
Q57·ChemistryNumerical
The dissociation constant of acetic acid is x×10−5x\times10^{-5}x×10−5. When 25 mL of 0.2 M CH3COONa\text{CH}_3\text{COONa}CH3​COONa solution is mixed with 25 mL of 0.02 M CH3COOH\text{CH}_3\text{COOH}CH3​COOH solution, the pH of the resultant solution is found to be equal to 5. The value of xxx is _______ .

Correct answer: 10

Step-by-step solution →
Q58·ChemistryNumerical
Number of moles of AgCl formed in the following reaction is _______ .

Correct answer: 2

Step-by-step solution →
Q59·ChemistryNumerical
The d-electronic configuration of [CoCl4]2−[\text{CoCl}_4]^{2-}[CoCl4​]2− in tetrahedral crystal field is emt2ne^m t_2^nemt2n​. Sum of 'm' and 'number of unpaired electrons' is _______ .

Correct answer: 7

Step-by-step solution →
Q60·ChemistryNumerical
At 298 K, a 1 litre solution containing 10 mmol of Cr2O72−\text{Cr}_2\text{O}_7^{2-}Cr2​O72−​ and 100 mmol of Cr3+\text{Cr}^{3+}Cr3+ shows a pH of 3.0. Given: Cr2O72−→Cr3+\text{Cr}_2\text{O}_7^{2-}\to\text{Cr}^{3+}Cr2​O72−​→Cr3+; E∘=1.330E^\circ=1.330E∘=1.330 V and 2.303RTF=0.059\tfrac{2.303RT}{F}=0.059F2.303RT​=0.059 V. The potential for the half cell reaction is x×10−3x\times10^{-3}x×10−3 V. The value of xxx is _______ .

Correct answer: 917

Step-by-step solution →

Mathematics — JEE Main 24 January 2023 Shift 1

Q61·MathematicsSingle correct
Let u⃗=i^−j^−2k^\vec{u}=\hat{i}-\hat{j}-2\hat{k}u=i^−j^​−2k^, v⃗=2i^+j^−k^\vec{v}=2\hat{i}+\hat{j}-\hat{k}v=2i^+j^​−k^, v⃗⋅w⃗=2\vec{v}\cdot\vec{w}=2v⋅w=2 and v⃗×w⃗=u⃗+λv⃗\vec{v}\times\vec{w}=\vec{u}+\lambda\vec{v}v×w=u+λv. Then u⃗⋅w⃗\vec{u}\cdot\vec{w}u⋅w is equal to
  1. (A)222
  2. (B)32\tfrac{3}{2}23​
  3. (C)111
  4. (D)−23-\tfrac{2}{3}−32​

Correct answer: (C)

Step-by-step solution →
Q62·MathematicsSingle correct
lim⁡t→0(11sin⁡2t+21sin⁡2t+⋯+n1sin⁡2t)sin⁡2t\lim\limits_{t\to 0}\left(1^{\frac{1}{\sin^2 t}}+2^{\frac{1}{\sin^2 t}}+\cdots+n^{\frac{1}{\sin^2 t}}\right)^{\sin^2 t}t→0lim​(1sin2t1​+2sin2t1​+⋯+nsin2t1​)sin2t is equal to
  1. (A)n2n^2n2
  2. (B)n(n+1)2\tfrac{n(n+1)}{2}2n(n+1)​
  3. (C)nnn
  4. (D)n2+nn^2+nn2+n

Correct answer: (C)

Step-by-step solution →
Q63·MathematicsSingle correct
Let α\alphaα be a root of the equation (a−c)x2+(b−a)x+(c−b)=0(a-c)x^2+(b-a)x+(c-b)=0(a−c)x2+(b−a)x+(c−b)=0 where a,b,ca,b,ca,b,c are distinct real numbers such that the matrix [α2α1111abc]\begin{bmatrix}\alpha^2 & \alpha & 1\\ 1 & 1 & 1\\ a & b & c\end{bmatrix}​α21a​α1b​11c​​ is singular. Then, the value of (a−c)2(b−a)(c−b)+(b−a)2(a−c)(c−b)+(c−b)2(a−c)(b−a)\dfrac{(a-c)^2}{(b-a)(c-b)}+\dfrac{(b-a)^2}{(a-c)(c-b)}+\dfrac{(c-b)^2}{(a-c)(b-a)}(b−a)(c−b)(a−c)2​+(a−c)(c−b)(b−a)2​+(a−c)(b−a)(c−b)2​ is
  1. (A)121212
  2. (B)999
  3. (C)333
  4. (D)666

Correct answer: (C)

Step-by-step solution →
Q64·MathematicsSingle correct
The area enclosed by the curves y2+4x=4y^2+4x=4y2+4x=4 and y−2x=2y-2x=2y−2x=2 is:
  1. (A)999
  2. (B)223\tfrac{22}{3}322​
  3. (C)233\tfrac{23}{3}323​
  4. (D)253\tfrac{25}{3}325​

Correct answer: (A)

Step-by-step solution →
Q65·MathematicsSingle correct
Let p,q∈Rp,q\in\mathbb{R}p,q∈R and (1−3 i)200=2199(p+iq)(1-\sqrt{3}\,i)^{200}=2^{199}(p+iq)(1−3​i)200=2199(p+iq), i=−1i=\sqrt{-1}i=−1​. Then p+q+q2p+q+q^2p+q+q2 and p−q+q2p-q+q^2p−q+q2 are roots of the equation
  1. (A)x2−4x−1=0x^2-4x-1=0x2−4x−1=0
  2. (B)x2−4x+1=0x^2-4x+1=0x2−4x+1=0
  3. (C)x2+4x−1=0x^2+4x-1=0x2+4x−1=0
  4. (D)x2+4x+1=0x^2+4x+1=0x2+4x+1=0

Correct answer: (B)

Step-by-step solution →
Q66·MathematicsSingle correct
Let NNN denote the number that turns up when a fair die is rolled. If the probability that the system of equations x+y+z=1x+y+z=1x+y+z=1, 2x+Ny+2z=22x+Ny+2z=22x+Ny+2z=2, 3x+3y+Nz=33x+3y+Nz=33x+3y+Nz=3 has unique solution is k6\dfrac{k}{6}6k​, then the sum of value of kkk and all possible values of NNN is
  1. (A)212121
  2. (B)181818
  3. (C)202020
  4. (D)191919

Correct answer: (C)

Step-by-step solution →
Q67·MathematicsSingle correct
For three positive integers p,q,rp,q,rp,q,r, xpq2=yqr=zp2rx^{pq^2}=y^{qr}=z^{p^2 r}xpq2=yqr=zp2r and r=pq+1r=pq+1r=pq+1 such that 3, 3log⁡yx, 3log⁡zy, 7log⁡xz3,\ 3\log_y x,\ 3\log_z y,\ 7\log_x z3, 3logy​x, 3logz​y, 7logx​z are in A.P. with common difference 12\tfrac{1}{2}21​. Then r−p−qr-p-qr−p−q is equal to
  1. (A)−6-6−6
  2. (B)121212
  3. (C)666
  4. (D)222

Correct answer: (D)

Step-by-step solution →
Q68·MathematicsSingle correct
The relation R={(a,b):gcd⁡(a,b)=1, 2a≠b, a,b∈Z}R=\{(a,b):\gcd(a,b)=1,\ 2a\ne b,\ a,b\in\mathbb{Z}\}R={(a,b):gcd(a,b)=1, 2a=b, a,b∈Z} is:
  1. (A)reflexive but not symmetric
  2. (B)transitive but not reflexive
  3. (C)symmetric but not transitive
  4. (D)neither symmetric nor transitive

Correct answer: (D)

Step-by-step solution →
Q69·MathematicsSingle correct
Let PQRPQRPQR be a triangle. The points AAA, BBB and CCC are on the sides QRQRQR, RPRPRP and PQPQPQ respectively such that QAAR=RBBP=PCCQ=12\dfrac{QA}{AR}=\dfrac{RB}{BP}=\dfrac{PC}{CQ}=\dfrac{1}{2}ARQA​=BPRB​=CQPC​=21​. Then Area(△PQR)Area(△ABC)\dfrac{\text{Area}(\triangle PQR)}{\text{Area}(\triangle ABC)}Area(△ABC)Area(△PQR)​ is equal to
  1. (A)444
  2. (B)333
  3. (C)52\tfrac{5}{2}25​
  4. (D)222

Correct answer: (B)

Step-by-step solution →
Q70·MathematicsSingle correct
Let y=y(x)y=y(x)y=y(x) be the solution of the differential equation x3 dy+(xy−1) dx=0x^3\,dy+(xy-1)\,dx=0x3dy+(xy−1)dx=0, x>0x>0x>0, y ⁣(12)=3−ey\!\left(\tfrac{1}{2}\right)=3-ey(21​)=3−e. Then y(1)y(1)y(1) is equal to
  1. (A)111
  2. (B)eee
  3. (C)333
  4. (D)2−e2-e2−e

Correct answer: (A)

Step-by-step solution →
Q71·MathematicsSingle correct
If AAA and BBB are two non-zero n×nn\times nn×n matrices such that A2+B=A2BA^2+B=A^2 BA2+B=A2B, then
  1. (A)A2=IA^2=IA2=I or B=IB=IB=I
  2. (B)A2B=IA^2 B=IA2B=I
  3. (C)AB=IAB=IAB=I
  4. (D)A2B=BA2A^2 B=BA^2A2B=BA2

Correct answer: (D)

Step-by-step solution →
Q72·MathematicsSingle correct
The equation x2−4x+[x]+3=x[x]x^2-4x+[x]+3=x[x]x2−4x+[x]+3=x[x], where [x][x][x] denotes the greatest integer function, has:
  1. (A)a unique solution in (−∞,1)(-\infty,1)(−∞,1)
  2. (B)no solution
  3. (C)exactly two solutions in (−∞,∞)(-\infty,\infty)(−∞,∞)
  4. (D)a unique solution in (−∞,∞)(-\infty,\infty)(−∞,∞)

Correct answer: (D)

Step-by-step solution →
Q73·MathematicsSingle correct
Let a tangent to the curve y2=24xy^2=24xy2=24x meet the curve xy=2xy=2xy=2 at the points AAA and BBB. Then the mid points of such line segments ABABAB lie on a parabola with the
  1. (A)Length of latus rectum 32\tfrac{3}{2}23​
  2. (B)directrix 4x=−34x=-34x=−3
  3. (C)length of latus rectum 222
  4. (D)directrix 4x=34x=34x=3

Correct answer: (D)

Step-by-step solution →
Q74·MathematicsSingle correct
Let Ω\OmegaΩ be the sample space and A⊆ΩA\subseteq\OmegaA⊆Ω be an event. Given below are two statements: (S1): If P(A)=0P(A)=0P(A)=0, then A=∅A=\varnothingA=∅. (S2): If P(A)=1P(A)=1P(A)=1, then A=ΩA=\OmegaA=Ω. Then
  1. (A)both (S1) and (S2) are true
  2. (B)only (S1) is true
  3. (C)only (S2) is true
  4. (D)both (S1) and (S2) are false

Correct answer: (D)

Step-by-step solution →
Q75·MathematicsSingle correct
The value of ∑r=02222Cr 23Cr\sum\limits_{r=0}^{22}{}^{22}C_r\,{}^{23}C_rr=0∑22​22Cr​23Cr​ is
  1. (A)44C23{}^{44}C_{23}44C23​
  2. (B)45C23{}^{45}C_{23}45C23​
  3. (C)44C22{}^{44}C_{22}44C22​
  4. (D)45C24{}^{45}C_{24}45C24​

Correct answer: (B)

Step-by-step solution →
Q76·MathematicsSingle correct
The distance of the point (−1,9,−16)(-1,9,-16)(−1,9,−16) from the plane 2x+3y−z=52x+3y-z=52x+3y−z=5 measured parallel to the line x+43=2−y4=z−312\dfrac{x+4}{3}=\dfrac{2-y}{4}=\dfrac{z-3}{12}3x+4​=42−y​=12z−3​ is
  1. (A)313131
  2. (B)13213\sqrt{2}132​
  3. (C)20220\sqrt{2}202​
  4. (D)262626

Correct answer: (D)

Step-by-step solution →
Q77·MathematicsSingle correct
tan⁡−1 ⁣(1+33+3)+sec⁡−1 ⁣(8+436+33)\tan^{-1}\!\left(\dfrac{1+\sqrt{3}}{3+\sqrt{3}}\right)+\sec^{-1}\!\left(\sqrt{\dfrac{8+4\sqrt{3}}{6+3\sqrt{3}}}\right)tan−1(3+3​1+3​​)+sec−1(6+33​8+43​​​) is equal to:
  1. (A)π3\tfrac{\pi}{3}3π​
  2. (B)π4\tfrac{\pi}{4}4π​
  3. (C)π6\tfrac{\pi}{6}6π​
  4. (D)π2\tfrac{\pi}{2}2π​

Correct answer: (A)

Step-by-step solution →
Q78·Mathematics·DifferentiabilitySingle correct
Let f(x)={x2sin⁡ ⁣(1x),x≠00,x=0f(x)=\begin{cases}x^2\sin\!\left(\tfrac{1}{x}\right), & x\ne 0\\ 0, & x=0\end{cases}f(x)={x2sin(x1​),0,​x=0x=0​. Then at x=0x=0x=0
  1. (A)fff is continuous but not differentiable
  2. (B)fff and f′f'f′ both are continuous
  3. (C)f′f'f′ is continuous but not differentiable
  4. (D)fff is continuous but f′f'f′ is not continuous

Correct answer: (D)

Step-by-step solution →
Q79·MathematicsSingle correct
The compound statement (∼(P∧Q))∨((∼P)∧Q)⇒((∼P)∧(∼Q))(\sim(P\wedge Q))\vee((\sim P)\wedge Q)\Rightarrow((\sim P)\wedge(\sim Q))(∼(P∧Q))∨((∼P)∧Q)⇒((∼P)∧(∼Q)) is equivalent to
  1. (A)(∼Q)∨P(\sim Q)\vee P(∼Q)∨P
  2. (B)((∼P)∨Q)∧(∼Q)((\sim P)\vee Q)\wedge(\sim Q)((∼P)∨Q)∧(∼Q)
  3. (C)(∼P)∨Q(\sim P)\vee Q(∼P)∨Q
  4. (D)((∼P)∨Q)∧((∼Q)∨P)((\sim P)\vee Q)\wedge((\sim Q)\vee P)((∼P)∨Q)∧((∼Q)∨P)

Correct answer: (D)

Step-by-step solution →
Q80·MathematicsSingle correct
The distance of the point (7,−3,−4)(7,-3,-4)(7,−3,−4) from the plane passing through the points (2,−3,1)(2,-3,1)(2,−3,1), (−1,1,−2)(-1,1,-2)(−1,1,−2) and (3,−4,2)(3,-4,2)(3,−4,2) is:
  1. (A)555
  2. (B)444
  3. (C)525\sqrt{2}52​
  4. (D)424\sqrt{2}42​

Correct answer: (C)

Step-by-step solution →
Q81·MathematicsNumerical
Let λ∈R\lambda\in\mathbb{R}λ∈R and let the equation EEE be ∣x∣2−2∣x∣+∣λ−3∣=0|x|^2-2|x|+|\lambda-3|=0∣x∣2−2∣x∣+∣λ−3∣=0. Then the largest element in the set S={x+λ:x is an integer solution of E}S=\{x+\lambda:x \text{ is an integer solution of } E\}S={x+λ:x is an integer solution of E} is _______ .

Correct answer: 5

Step-by-step solution →
Q82·MathematicsNumerical
Let a tangent to the curve 9x2+16y2=1449x^2+16y^2=1449x2+16y2=144 intersect the coordinate axes at the points AAA and BBB. Then, the minimum length of the line segment ABABAB is _______ .

Correct answer: 7

Step-by-step solution →
Q83·MathematicsNumerical
The shortest distance between the lines x−23=y+12=z−62\dfrac{x-2}{3}=\dfrac{y+1}{2}=\dfrac{z-6}{2}3x−2​=2y+1​=2z−6​ and x−63=1−y2=z+80\dfrac{x-6}{3}=\dfrac{1-y}{2}=\dfrac{z+8}{0}3x−6​=21−y​=0z+8​ is equal to _______ .

Correct answer: 14

Step-by-step solution →
Q84·MathematicsNumerical
Suppose ∑r=02023r2 2023Cr=2023×α×22022\sum\limits_{r=0}^{2023} r^2\,{}^{2023}C_r=2023\times\alpha\times2^{2022}r=0∑2023​r22023Cr​=2023×α×22022. Then the value of α\alphaα is _______ .

Correct answer: 1012

Step-by-step solution →
Q85·MathematicsNumerical
The value of 8π∫0π/2(cos⁡x)2023(sin⁡x)2023+(cos⁡x)2023 dx\dfrac{8}{\pi}\displaystyle\int_0^{\pi/2}\dfrac{(\cos x)^{2023}}{(\sin x)^{2023}+(\cos x)^{2023}}\,dxπ8​∫0π/2​(sinx)2023+(cosx)2023(cosx)2023​dx is _______ .

Correct answer: 2

Step-by-step solution →
Q86·MathematicsNumerical
The number of 999 digit numbers, that can be formed using all the digits of the number 123412341123412341123412341 so that the even digits occupy only even places, is _______ .

Correct answer: 60

Step-by-step solution →
Q87·MathematicsNumerical
A boy needs to select five courses from 121212 available courses, out of which 555 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is _______ .

Correct answer: 546

Step-by-step solution →
Q88·MathematicsNumerical
The 4th4^{\text{th}}4th term of GP is 500500500 and its common ratio is 1m\dfrac{1}{m}m1​, m∈Nm\in\mathbb{N}m∈N. Let SnS_nSn​ denote the sum of the first nnn terms of this GP. If S6>S5+1S_6>S_5+1S6​>S5​+1 and S7<S6+12S_7<S_6+\tfrac{1}{2}S7​<S6​+21​, then the number of possible values of mmm is _______ .

Correct answer: 12

Step-by-step solution →
Q89·MathematicsNumerical
Let CCC be the largest circle centred at (2,0)(2,0)(2,0) and inscribed in the ellipse x236+y216=1\dfrac{x^2}{36}+\dfrac{y^2}{16}=136x2​+16y2​=1. If (1,α)(1,\alpha)(1,α) lies on CCC, then 10α210\alpha^210α2 is equal to _______ .

Correct answer: 118

Step-by-step solution →
Q90·MathematicsNumerical
The value of 12∫03∣x2−3x+2∣ dx12\displaystyle\int_0^3 |x^2-3x+2|\,dx12∫03​∣x2−3x+2∣dx is _______ .

Correct answer: 22

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
  • p-Block Elements 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
  • d- and f-Block Elements 126/186
  • Thermodynamics 154/186
  • Aldehydes and Ketones 135/186
  • Equilibrium 163/186
  • Solutions 158/186
  • Laws of Motion 130/186
  • Chemical Thermodynamics 165/186
  • Units and Measurements 149/186
  • Complex Numbers 165/186
  • Biomolecules 162/186
  • Chemical Kinetics 169/186
  • Gravitation 152/186
  • Electric Field and Coulomb's Law 133/186
  • Atomic Structure 161/186
  • Electronic Devices 145/186
  • Dual Nature of Matter and Radiation 155/186
  • Quadratic Equations 148/186
  • 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
  • Parabola 101/186
  • Ellipse 103/186
  • 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
  • Electronic Effects and Stability 74/186
  • Solid State 63/186
  • Chemistry in Everyday Life 60/186
  • Reaction Mechanism 29/186
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