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JEE Main 24 February 2021 Shift 2 Question Paper with Answers

24 February 2021 · February session · 87 questions

87 of the 90 questions from the JEE Main 24 February 2021 Shift 2 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

3 questions are held back from this paper while we re-check the transcription or the answer key. We would rather show you nothing than show you an answer we are not confident is right.

Physics
28
Chemistry
30
Mathematics
29

Physics — JEE Main 24 February 2021 Shift 2

Q1·PhysicsSingle correct
Zener breakdown occurs in a p-n junction having p and n both :
  1. (A)lightly doped and have wide depletion layer.
  2. (B)heavily doped andhave narrow depletion layer.
  3. (C)heavily doped and have wide depletion layer.
  4. (D)lightly doped and have narrow depletion layer.

Correct answer: (B)

Step-by-step solution →
Q2·PhysicsSingle correct
According to Bohr atom model, in which of the following transitions will the frequency be maximum?
  1. (A)n=2 to n=1
  2. (B)n=4 to n =3
  3. (C)n=5 to n=4
  4. (D)n=3 to n=2

Correct answer: (A)

Step-by-step solution →
Q3·PhysicsSingle correct
An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be :
  1. (A)10−210^{-2}10−2 nm
  2. (B)10−310^{-3}10−3 nm
  3. (C)10−410^{-4}10−4 nm
  4. (D)10−110^{-1}10−1 nm

Correct answer: (B)

Step-by-step solution →
Q4·PhysicsSingle correct
On the basis of kinetic theory of gases, the gas exerts pressure because its molecules:
  1. (A)suffer change in momentum when impinge on the walls of container.
  2. (B)continuously stick to the walls of container.
  3. (C)continuously lose their energy till it reaches wall.
  4. (D)are attracted by the walls of container.

Correct answer: (A)

Step-by-step solution →
Q5·PhysicsSingle correct
A circular hole of radius (a2)\left(\frac{a}{2}\right)(2a​) is cut out of a circular disc of radius 'a' shown in figure. The centroid of the remaining circular portion with respect to point 'O' will be :
  1. (A)1011a\frac{10}{11}a1110​a
  2. (B)23a\frac{2}{3}a32​a
  3. (C)16a\frac{1}{6}a61​a
  4. (D)56a\frac{5}{6}a65​a

Correct answer: (D)

Step-by-step solution →
Q6·PhysicsSingle correct
Given below are two statements : Statement I : PN junction diodes can be used to function as transistor, simply by connecting two diodes, back to back, which acts as the base terminal. Statement II : In the study of transistor, the amplification factor β\betaβ indicates ratio of the collector current to the base current. 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 true
  3. (C)Statement I is true but Statement II is false.
  4. (D)Both Statement I and Statement II are false

Correct answer: (A)

Step-by-step solution →
Q7·PhysicsSingle correct
When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is :
  1. (A)elliptical
  2. (B)parabolic
  3. (C)straight line
  4. (D)circular

Correct answer: (A)

Step-by-step solution →
Q8·PhysicsSingle correct
Match List - I with List - II. List - I (a) Source of microwave frequency (b) Source of infrared frequency (c) Source of Gamma Rays (d) Source of X-rays List - II (i) Radioactive decay of nucleus (ii) Magnetron (iii) Inner shell electrons (iv) Vibration of atoms and molecules (v) LASER (vi) RC circuit Choose the correct answer from the options given below :
  1. (A)(a)-(ii),(b)-(iv),(c)-(i),(d)-(iii)
  2. (B)(a)-(vi),(b)-(iv),(c)-(i),(d)-(v)
  3. (C)(a)-(ii),(b)-(iv),(c)-(vi),(d)-(iii)
  4. (D)(a)-(vi),(b)-(v),(c)-(i),(d)-(iv)

Correct answer: (A)

Step-by-step solution →
Q9·PhysicsSingle correct
The logic circuit shown above is equivalent to :
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q10·PhysicsSingle correct
If the source of light used in a Young's double slit experiment is changed from red to violet:
  1. (A)the fringes will become brighter.
  2. (B)consecutive fringe lineswill come closer.
  3. (C)the central bright fringe will become a dark fringe.
  4. (D)the intensity of minima will increase.

Correct answer: (B)

Step-by-step solution →
Q11·PhysicsSingle correct
A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator? [Use g=GMR2=\frac{GM}{R^2}=R2GM​ = 9.8 ms−2ms^{-2}ms−2 and radius of earth, R = 6400 km.]
  1. (A)49 N
  2. (B)49.83 N
  3. (C)49.17 N
  4. (D)48.83 N

Correct answer: (D)

Step-by-step solution →
Q12·PhysicsSingle correct
If one mole of an ideal gas at (P1P_1P1​, V1V_1V1​) is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value (B→\rightarrow→C). Then it is restored to its initial state by a reversible adiabatic compression (C to A). The net workdone by the gas is equal to :
  1. (A)0
  2. (B)−RT2(γ−1)-\frac{RT}{2(\gamma-1)}−2(γ−1)RT​
  3. (C)RT[ln⁡2−12(γ−1)]RT\left[\ln 2-\frac{1}{2(\gamma-1)}\right]RT[ln2−2(γ−1)1​]
  4. (D)RTln⁡2RT\ln 2RTln2

Correct answer: (C)

Step-by-step solution →
Q13·PhysicsSingle correct
The period of oscillation of a simple pendulum is T=2πLgT=2\pi\sqrt{\frac{L}{g}}T=2πgL​​. Measured value of 'L' is 1.0 m from meter scale having a minimum division of 1 mm and time of one complete oscillation is 1.95 s measured from stopwatch of 0.01 s resolution. The percentage error in the determination of 'g' will be :
  1. (A)1.33 %
  2. (B)1.30 %
  3. (C)1.13 %
  4. (D)1.03 %

Correct answer: (C)

Step-by-step solution →
Q14·PhysicsSingle correct
Figure shows a circuit that contains four identical resistors with resistance R = 2.0 Ω\OmegaΩ. Two identical inductors with inductance L = 2.0 mH and an ideal battery with emf E = 9.V. The current 'i' just after the switch 's' is closed will be :
  1. (A)9A
  2. (B)3.0 A
  3. (C)2.25 A
  4. (D)3.37 A

Correct answer: (C)

Step-by-step solution →
Q15·PhysicsSingle correct
The de Broglie wavelength of a proton andα\alphaα-particle are equal. The ratio of their velocities is :
  1. (A)4:2
  2. (B)4:1
  3. (C)1:4
  4. (D)4:3

Correct answer: (B)

Step-by-step solution →
Q16·PhysicsSingle correct
Two electrons each are fixed at a distance ‘2d’. A third charge proton placed at the midpoint is displaced slightly by a distance x (x<<d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency: (m = mass of charged particle)
  1. (A)(q22πε0md3)12\left(\dfrac{q^{2}}{2\pi\varepsilon_{0}md^{3}}\right)^{\frac{1}{2}}(2πε0​md3q2​)21​
  2. (B)(πε0md32q2)12\left(\dfrac{\pi\varepsilon_{0}md^{3}}{2q^{2}}\right)^{\frac{1}{2}}(2q2πε0​md3​)21​
  3. (C)(2πε0md3q2)12\left(\dfrac{2\pi\varepsilon_{0}md^{3}}{q^{2}}\right)^{\frac{1}{2}}(q22πε0​md3​)21​
  4. (D)(2q2πε0md3)12\left(\dfrac{2q^{2}}{\pi\varepsilon_{0}md^{3}}\right)^{\frac{1}{2}}(πε0​md32q2​)21​

Correct answer: (A)

Step-by-step solution →
Q17·PhysicsSingle correct
A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains :
  1. (A)decrease in size and changes orientation.
  2. (B)may increase or decrease in size and change its orientation.
  3. (C)increase in size but no change in orientation.
  4. (D)have no relation with external magnetic field.

Correct answer: (B)

Step-by-step solution →
Q18·PhysicsSingle correct
Which of the following equations represents a travelling wave?
  1. (A)y=Ae−x2(vt+θ)y = Ae^{-x^{2}}(vt + \theta)y=Ae−x2(vt+θ)
  2. (B)y=Asin⁡(15x−2t)y = A\sin(15x - 2t)y=Asin(15x−2t)
  3. (C)y=Aexcos⁡(ωt−θ)y = Ae^{x}\cos(\omega t - \theta)y=Aexcos(ωt−θ)
  4. (D)y=Asin⁡xcos⁡ωty = A\sin x\cos\omega ty=Asinxcosωt

Correct answer: (B)

Step-by-step solution →
Q19·PhysicsNumerical
A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled andsubjected to the same force will be _________ cm.

Correct answer: 2

Step-by-step solution →
Q20·PhysicsNumerical
A cylindrical wire of radius 0.5 mm and conductivity 5×1075\times10^{7}5×107 S/m is subjected to an electric field of 10 mV/m. The expected value of current in the wire will be x3πx^{3}\pix3π mA. The value of x is _____.

Correct answer: 5

Step-by-step solution →
Q21·PhysicsNumerical
Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be _________ Hz. [Velocity of sound in air is 340 m/s.]

Correct answer: 8

Step-by-step solution →
Q22·PhysicsNumerical
A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is _______×10−1\times 10^{-1}×10−1 kg m2^{2}2.

Correct answer: 8

Step-by-step solution →
Q23·PhysicsNumerical
A point charge of +12 μ\muμC is at a distance 6 cm vertically above the centre of a square of side 12 cm as shown in figure. The magnitude of the electric flux through the square will be ______ ×103\times 10^{3}×103 Nm2^{2}2/C.

Correct answer: 226

Step-by-step solution →
Q24·PhysicsNumerical
Two solids A and B of mass 1 kg and 2 kg respectively are moving withequal linear momentum. The ratio of their kinetic energies (K.E.)A_{A}A​ : (K.E.)B_{B}B​ will be A1\dfrac{A}{1}1A​. So the value of A will be _________.

Correct answer: 2

Step-by-step solution →
Q25·PhysicsNumerical
The root mean square speed of molecules of a given mass of a gas at 27°C and 1 atmosphere pressure is 200 ms−1^{-1}−1. The root mean square speed of molecules of the gas at 127°C and 2 atmosphere pressure is x3\dfrac{x}{\sqrt{3}}3​x​ ms−1^{-1}−1. The value of x will be ____________.

Correct answer: 400

Step-by-step solution →
Q26·PhysicsNumerical
A series LCR circuit is designed to resonate at an angular frequency ω0=105 rad/s\omega_{0} = 10^{5}\,\mathrm{rad/s}ω0​=105rad/s. The circuit draws 16W power from 120 V source at resonance. The value of resistance ‘R’ in the circuit is ________ Ω\OmegaΩ.

Correct answer: 900

Step-by-step solution →
Q27·PhysicsNumerical
An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium wil be ________ ×10−2\times 10^{-2}×10−2 cm.

Correct answer: 667

Step-by-step solution →
Q28·PhysicsNumerical
A signal of 0.1 kW is transmitted in a cable. The attenuation of cable is -5 dB per km and cable length is 20 km. the power received at receiver is 10−x10^{-x}10−xW. The value of x is ________. [Gain in dB =10log⁡10(P0Pi)= 10\log_{10}\left(\dfrac{P_{0}}{P_{i}}\right)=10log10​(Pi​P0​​)]

Correct answer: 8

Step-by-step solution →

Chemistry — JEE Main 24 February 2021 Shift 2

Q29·ChemistrySingle correct
The correct order of the following compounds showing increasing tendency towards nucleophilic substitution reaction is :
  1. (A)(iv) < (i) < (iii) < (ii)
  2. (B)(iv) < (i) < (ii) < (iii)
  3. (C)(i) < (ii) < (iii) < (iv)
  4. (D)(iv) < (iii) < (ii) < (i)

Correct answer: (C)

Step-by-step solution →
Q30·ChemistrySingle correct
Match List-I with List-II List- I List-II (Metal) (Ores) (a) Aluminium (i) Siderite (b) Iron (ii) Calamine (c) Copper (iii) Kaolinite (d) Zinc (iv) Malachite Choose the correct answer from the options given below :
  1. (A)(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
  2. (B)(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
  3. (C)(a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)
  4. (D)(a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)

Correct answer: (C)

Step-by-step solution →
Q31·ChemistrySingle correct
Match List-I with List-II List- I List-II (Salt) (Flame colour wavelength) (a) LiCl (i) 455.5 nm (b) NaCl (ii) 970.8 nm (c) RbCl (iii) 780.0 nm (d) CsCl (iv) 589.2 nm Choose the correct answer from the options given below :
  1. (A)(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
  2. (B)(a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)
  3. (C)(a)-(iv), (b)-(ii), (c)-(iii), (d)-(i)
  4. (D)(a)-(i), (b)-(iv), (c)-(ii), (d)-(iii)

Correct answer: (B)

Step-by-step solution →
Q32·ChemistrySingle correct
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Hydrogen is the most abundant element in the Universe, but it is not the most abundant gas in the troposphere. Reason R : Hydrogen is the lightest element. In the light of the above statements, choose the correct answer from the 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)A is true but R is false
  4. (D)Both A and R are true but R is NOT the correct explanation of A

Correct answer: (B)

Step-by-step solution →
Q33·ChemistrySingle correct
Given below are two statements : Statement I : The value of the parameter "Biochemical Oxygen Demand (BOD)" is important for survival of aquatic life. Statement II : The optimum value of BOD is 6.5 ppm. 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 false
  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 true

Correct answer: (C)

Step-by-step solution →
Q34·ChemistrySingle correct
Wich one of the following carbonyl compounds cannot be prepared by addition of wate on an alkyne in the presence of HgSO4HgSO_{4}HgSO4​ and H2SO4H_{2}SO_{4}H2​SO4​ ?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (A)

Step-by-step solution →
Q35·Chemistry·AromaticitySingle correct
Which one of the following compounds is non-aromatic ?
  1. (A)(A)
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Correct answer: (B)

Step-by-step solution →
Q36·ChemistrySingle correct
The incorrect statement among the following is :
  1. (A)VOSO4VOSO_{4}VOSO4​ is a reducing agent
  2. (B)Red colour of ruby is due to the presence of CO3+CO^{3+}CO3+
  3. (C)Cr2O3Cr_{2}O_{3}Cr2​O3​ is an amphoteric oxide
  4. (D)RuO4RuO_{4}RuO4​ is an oxidizing agent

Correct answer: (B)

Step-by-step solution →
Q37·ChemistrySingle correct
According to Bohr's atomic theory : (A) Kinetic energy of electron is ∝Z2n2\propto \frac{Z^{2}}{n^{2}}∝n2Z2​ (B) The product of velocity (v) of electron and principal quantum number (n). 'vn' ∝Z2\propto Z^{2}∝Z2 . (C) Frequency of revolution of electron in an orbit is ∝Z3n3\propto \frac{Z^{3}}{n^{3}}∝n3Z3​ . (D) Coulombic force of attraction on the electron is ∝Z3n4\propto \frac{Z^{3}}{n^{4}}∝n4Z3​ . Choose the most appropriate answer from the options given below:
  1. (A)(C) only
  2. (B)(A) and (D) only
  3. (C)(A) only
  4. (D)(A), (C) and (D) only

Correct answer: (B)

Step-by-step solution →
Q38·ChemistrySingle correct
Match List-I with List-II List- I List-II (a) Valium (i) Antifertility drug (b) Morphine (ii) Pernicious anaemia (c) Norethindrone (iii) Analgesic (d) Vitamin B12B_{12}B12​ (iv) Tranquilizer
  1. (A)(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
  2. (B)(a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)
  3. (C)(a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)
  4. (D)(a)-(iv), (b)-(iii), (c)-(i), (d)-(ii)

Correct answer: (D)

Step-by-step solution →
Q39·ChemistrySingle correct
The Correct set from the following in which both pairs are in correct order of melting point is :
  1. (A)LiF > LiCl ; NaCl > MgO
  2. (B)LiF > LiCl ; MgO > NaCl
  3. (C)LiCl > LiF ; NaCl > MgO
  4. (D)LiCl > LiF ; MgO > NaCl

Correct answer: (B)

Step-by-step solution →
Q40·ChemistrySingle correct
The calculated magnetic moments (spin only value) for species [FeCl4]2−\left[FeCl_{4}\right]^{2-}[FeCl4​]2− , [Co(C2O4)3]3−\left[Co\left(C_{2}O_{4}\right)_{3}\right]^{3-}[Co(C2​O4​)3​]3− and MnO42−MnO_{4}^{2-}MnO42−​ respectively are :
  1. (A)5.92, 4.90 and 0 BM
  2. (B)5.82, O and 0 BM
  3. (C)4.90, 0 and 1.73 BM
  4. (D)4.90, 0 and 2.83 BM

Correct answer: (C)

Step-by-step solution →
Q41·ChemistrySingle correct
Which of the following reagent is suitable for the preparation of the product in the above reaction.
  1. (A)Red P + Cl2Cl_{2}Cl2​
  2. (B)NH2−NH2/C2H5O⊖Na⊕NH_{2}-NH_{2}/C_{2}H_{5}O^{\ominus}Na^{\oplus}NH2​−NH2​/C2​H5​O⊖Na⊕
  3. (C)Ni/H2Ni/H_{2}Ni/H2​
  4. (D)NaBH4NaBH_{4}NaBH4​

Correct answer: (B)

Step-by-step solution →
Q42·ChemistrySingle correct
The diazonium salt of which of the following compounds will form a coloured dye on reaction with β\betaβ-Naphthol in NaOH ?
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (C)

Step-by-step solution →
Q43·ChemistrySingle correct
What is the correct sequence of reagents used for converting nitrobenzene into m-dibromobenzene ?
  1. (A)→Sn/HCl\xrightarrow{Sn/HCl}Sn/HCl​ / →Br2\xrightarrow{Br_{2}}Br2​​ / →NaNO2\xrightarrow{NaNO_{2}}NaNO2​​ / →NaBr\xrightarrow{NaBr}NaBr​
  2. (B)→Sn/HCl\xrightarrow{Sn/HCl}Sn/HCl​ / →KBr\xrightarrow{KBr}KBr​ / →Br2\xrightarrow{Br_{2}}Br2​​ / →H+\xrightarrow{H^{+}}H+​
  3. (C)→NaNO2\xrightarrow{NaNO_{2}}NaNO2​​ / →HCl\xrightarrow{HCl}HCl​ / →KBr\xrightarrow{KBr}KBr​ / →H+\xrightarrow{H^{+}}H+​
  4. (D)→Br2/Fe\xrightarrow{Br_{2}/Fe}Br2​/Fe​ / →Sn/HCl\xrightarrow{Sn/HCl}Sn/HCl​ / →NaNO2/HCl\xrightarrow{NaNO_{2}/HCl}NaNO2​/HCl​ / →CuBr/HBr\xrightarrow{CuBr/HBr}CuBr/HBr​

Correct answer: (D)

Step-by-step solution →
Q44·ChemistrySingle correct
The correct shape and I-I-I bond angles respectively in I3−I_{3}^{-}I3−​ ion are :
  1. (A)Trigonal planar; 120º
  2. (B)Distorted trigonal planar; 135º and 90º
  3. (C)Linear; 180º
  4. (D)T-shaped; 180º and 90º

Correct answer: (C)

Step-by-step solution →
Q45·ChemistrySingle correct
What is the correct order of the following elements with respect to their density ?
  1. (A)Cr < Fe < Co < Cu < Zn
  2. (B)Cr < Zn < Co < Cu < Fe
  3. (C)Zn < Cu < Co < Fe < Cr
  4. (D)Zn < Cr < Fe < Co < Cu

Correct answer: (D)

Step-by-step solution →
Q46·ChemistrySingle correct
Match List-I and List-II. List – I (a) R−C∥O−Cl→R−CHOR-\overset{\overset{O}{\|}}{C}-Cl \rightarrow R-CHOR−C∥O​−Cl→R−CHO (b) R−CH2−COOH→R−CH∣Cl−COOHR-CH_{2}-COOH \rightarrow R-\underset{\underset{Cl}{|}}{CH}-COOHR−CH2​−COOH→R−Cl∣​CH​−COOH (c) R−C∥O−NH2→R−NH2R-\overset{\overset{O}{\|}}{C}-NH_{2} \rightarrow R-NH_{2}R−C∥O​−NH2​→R−NH2​ (d) R−C∥O−CH3→R−CH2−CH3R-\overset{\overset{O}{\|}}{C}-CH_{3} \rightarrow R-CH_{2}-CH_{3}R−C∥O​−CH3​→R−CH2​−CH3​ List-II (i) Br2Br_{2}Br2​/NaOH (ii) H2H_{2}H2​/Pd-BaSO4BaSO_{4}BaSO4​ (iii) Zn(Hg)/Conc. HCl (iv) Cl2Cl_{2}Cl2​/Red P, H2OH_{2}OH2​O Choose the correct answer from the options given below :
  1. (A)(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
  2. (B)(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
  3. (C)(a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)
  4. (D)(a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)

Correct answer: (D)

Step-by-step solution →
Q47·ChemistrySingle correct
In polymer Buna-S ; 'S' stands for :
  1. (A)Styrene
  2. (B)Sulphur
  3. (C)Strength
  4. (D)Sulphonation

Correct answer: (A)

Step-by-step solution →
Q48·ChemistrySingle correct
Most suitable salt which can be used for efficient clotting of blood will be :
  1. (A)Mg(HCO3)2Mg(HCO_{3})_{2}Mg(HCO3​)2​
  2. (B)FeSO4FeSO_{4}FeSO4​
  3. (C)NaHCO3NaHCO_{3}NaHCO3​
  4. (D)FeCl3FeCl_{3}FeCl3​

Correct answer: (D)

Step-by-step solution →
Q49·ChemistryNumerical
The magnitude of the change in oxidising power of the MnO4−MnO_{4}^{-}MnO4−​ / Mn2+Mn^{2+}Mn2+ couple is x × 10−410^{-4}10−4 V, if the H+H^{+}H+ concentration is decreased from 1M to 10−410^{-4}10−4 M at 25ºC. (Assume concentration of MnO4−MnO_{4}^{-}MnO4−​ and Mn2+Mn^{2+}Mn2+ to be same on change in H+H^{+}H+ concentration). The value of x is ______. (Rounded off to the nearest integer) [Given:2303RTF=0.059]\left[ Given : \frac{2303RT}{F} = 0.059 \right][Given:F2303RT​=0.059]

Correct answer: 3776

Step-by-step solution →
Q50·ChemistryNumerical
Among the following allotropic forms of sulphur, the number of allotropic forms, which will show paramagnetism is _______. (1) α\alphaα-sulphur (2) β\betaβ-sulphur (3) S2S_{2}S2​-form

Correct answer: 1

Step-by-step solution →
Q51·ChemistryNumerical
C6H6C_{6}H_{6}C6​H6​ freezes at 5.5ºC. The temperature at which a solution of 10 g of C4H10C_{4}H_{10}C4​H10​ in 200 g of C6H6C_{6}H_{6}C6​H6​ freeze is ________ºC. (The molal freezing point depression constant of C6H6C_{6}H_{6}C6​H6​ is) 5.12ºC/m)

Correct answer: 1

Step-by-step solution →
Q52·ChemistryNumerical
The volume occupied by 4.75 g of acetylene gas at 50ºC and 740 mmHg pressure is ________L. (Rounded off to the nearest integer) (Given R = 0.0826 L atm K−1K^{-1}K−1 mol−1mol^{-1}mol−1)

Correct answer: 5

Step-by-step solution →
Q53·ChemistryNumerical
The solubility product of PbI2PbI_{2}PbI2​ is 8.0 × 10−910^{-9}10−9 . The solubility of lead iodide in 0.1 molar solution of lead nitrate is x × 10−610^{-6}10−6 mol/L. The value of x is _________(Rounded off to the nearest integer) [Given 2=1.41\sqrt{2} = 1.412​=1.41]

Correct answer: 141

Step-by-step solution →
Q54·ChemistryNumerical
The total number of amines among the following which can be synthesized by Gabriel synthesis is _________.

Correct answer: 3

Step-by-step solution →
Q55·ChemistryNumerical
1.86 g of aniline completely reacts to form acetanilide. 10% of the product is lost during purificatiion. Amount of acetanilide obtained after purification (in g) is ____× 10−210^{-2}10−2 .

Correct answer: 243

Step-by-step solution →
Q56·ChemistryNumerical
The formula of a gaseous hydrocarbon which requires 6 times of its own volume of O2O_{2}O2​ for complete oxidation and produces 4 times its own volume of CO2CO_{2}CO2​ is CxHyC_{x}H_{y}Cx​Hy​. The value of y is …………

Correct answer: 8

Step-by-step solution →
Q57·ChemistryNumerical
Sucrose hydrolyses in acid solution into glucose and fructose following first order rate law with a half-life of 3.33 h at 25ºC. After 9h, the fraction of sucrose remaining is f. The value of log⁡10(1f)\log_{10}\left(\frac{1}{f}\right)log10​(f1​) is ___________× 10−210^{-2}10−2 (Rounded off to the nearest integer) [Assume: ln10 = 2.303, ln2 = 0.693]

Correct answer: 81

Step-by-step solution →
Q58·ChemistryNumerical
Assuming ideal behaviour, the magnitude of log K for the following reaction at 25ºC is x × 10−110^{-1}10−1 . The value of x is ____________.(Integer answer) 3HC≡CH(g)⇌C6H6(ℓ)3HC \equiv CH_{(g)} \rightleftharpoons C_{6}H_{6(\ell)}3HC≡CH(g)​⇌C6​H6(ℓ)​ [Given : ΔfG°(HC≡CH)\Delta_{f}G°(HC \equiv CH)Δf​G°(HC≡CH) = – 2.04 × 10510^{5}105] mol−1mol^{-1}mol−1; ΔfG°(C6H6)\Delta_{f}G°(C_{6}H_{6})Δf​G°(C6​H6​) = – 1.24 × 10510^{5}105 J mol−1mol^{-1}mol−1 ; R = 8.314 J K−1K^{-1}K−1 mol−1mol^{-1}mol−1 ]

Correct answer: 855

Step-by-step solution →

Mathematics — JEE Main 24 February 2021 Shift 2

Q59·MathematicsSingle correct
Let a,b∈Ra,b\in Ra,b∈R. If the mirror image of the point P(a,6,9)P(a,6,9)P(a,6,9) with respect to the line x−37=y−25=z−1−9\frac{x-3}{7}=\frac{y-2}{5}=\frac{z-1}{-9}7x−3​=5y−2​=−9z−1​ is (20,b,−a−9)(20,b,-a-9)(20,b,−a−9), then ∣a+b∣|a+b|∣a+b∣ is equal to :
  1. (A)86
  2. (B)88
  3. (C)84
  4. (D)90

Correct answer: (B)

Step-by-step solution →
Q60·MathematicsSingle correct
Let fff be a twice differentiable function defined on R such that f(0)=1, f′(0)=2f(0)=1,\ f'(0)=2f(0)=1, f′(0)=2 and f′(x)≠0f'(x)\neq 0f′(x)=0 for all x∈Rx\in Rx∈R. If ∣f(x)f′(x)f′(x)f′′(x)∣=0,\begin{vmatrix} f(x) & f'(x) \\ f'(x) & f''(x) \end{vmatrix}=0,​f(x)f′(x)​f′(x)f′′(x)​​=0, for all x∈Rx\in Rx∈R then the value of f(1)f(1)f(1) lies in the interval :
  1. (A)(9, 12)
  2. (B)(6, 9)
  3. (C)(3, 6)
  4. (D)(0, 3)

Correct answer: (B)

Step-by-step solution →
Q61·MathematicsSingle correct
A possible value of tan⁡(14sin⁡−1638)\tan\left(\frac{1}{4}\sin^{-1}\frac{\sqrt{63}}{8}\right)tan(41​sin−1863​​) is :
  1. (A)122\frac{1}{2\sqrt{2}}22​1​
  2. (B)17\frac{1}{\sqrt{7}}7​1​
  3. (C)7−1\sqrt{7}-17​−1
  4. (D)22−12\sqrt{2}-122​−1

Correct answer: (B)

Step-by-step solution →
Q62·MathematicsSingle correct
The probability that two randomly selected subsets of the set {1,2,3,4,5}\{1,2,3,4,5\}{1,2,3,4,5} have exactly two elements in their intersection, is:
  1. (A)6527\frac{65}{2^{7}}2765​
  2. (B)13529\frac{135}{2^{9}}29135​
  3. (C)6528\frac{65}{2^{8}}2865​
  4. (D)3527\frac{35}{2^{7}}2735​

Correct answer: (B)

Step-by-step solution →
Q63·MathematicsSingle correct
The vector equation of the plane passing through the intersection of the planes r⃗⋅(i^+j^+k^)=1\vec{r}\cdot(\hat{i}+\hat{j}+\hat{k})=1r⋅(i^+j^​+k^)=1 and r⃗⋅(i^−2j^)=−2,\vec{r}\cdot(\hat{i}-2\hat{j})=-2,r⋅(i^−2j^​)=−2, and the point (1,0,2) is :
  1. (A)r⃗⋅(i^−7j^+3k^)=73\vec{r}\cdot\left(\hat{i}-7\hat{j}+3\hat{k}\right)=\frac{7}{3}r⋅(i^−7j^​+3k^)=37​
  2. (B)r⃗⋅(i^+7j^+3k^)=7\vec{r}\cdot\left(\hat{i}+7\hat{j}+3\hat{k}\right)=7r⋅(i^+7j^​+3k^)=7
  3. (C)r⃗⋅(3i^+7j^+3k^)=7\vec{r}\cdot\left(3\hat{i}+7\hat{j}+3\hat{k}\right)=7r⋅(3i^+7j^​+3k^)=7
  4. (D)r⃗⋅(i^+7j^+3k^)=73\vec{r}\cdot\left(\hat{i}+7\hat{j}+3\hat{k}\right)=\frac{7}{3}r⋅(i^+7j^​+3k^)=37​

Correct answer: (B)

Step-by-step solution →
Q64·MathematicsSingle correct
If P is a point on the parabola y=x2+4y=x^{2}+4y=x2+4 which is closest to the straight line y=4x−1,y=4x-1,y=4x−1, then the co-ordinates of P are :
  1. (A)(−2,8)(-2, 8)(−2,8)
  2. (B)(1,5)(1, 5)(1,5)
  3. (C)(3,13)(3, 13)(3,13)
  4. (D)(2,8)(2, 8)(2,8)

Correct answer: (D)

Step-by-step solution →
Q65·MathematicsSingle correct
Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a,c),(2,b)(a,c),(2,b)(a,c),(2,b) and (a,b)(a,b)(a,b) be (103,73)\left(\frac{10}{3},\frac{7}{3}\right)(310​,37​). If α,β\alpha,\betaα,β are the roots of the equation ax2+bx+1=0ax^{2}+bx+1=0ax2+bx+1=0, then the value of α2+β2−αβ\alpha^{2}+\beta^{2}-\alpha\betaα2+β2−αβ is:
  1. (A)71256\frac{71}{256}25671​
  2. (B)−69256-\frac{69}{256}−25669​
  3. (C)69256\frac{69}{256}25669​
  4. (D)−71256-\frac{71}{256}−25671​

Correct answer: (D)

Step-by-step solution →
Q66·MathematicsSingle correct
The value of the integral, ∫13[x2−2x−2]dx,\int_{1}^{3}\left[x^{2}-2x-2\right]dx,∫13​[x2−2x−2]dx, where [x] denotes the greatest integer less than or equal to xxx, is:
  1. (A)−4-4−4
  2. (B)−5-5−5
  3. (C)−2−3−1-\sqrt{2}-\sqrt{3}-1−2​−3​−1
  4. (D)−2−3+1-\sqrt{2}-\sqrt{3}+1−2​−3​+1

Correct answer: (C)

Step-by-step solution →
Q67·MathematicsSingle correct
Let f:R→Rf:\mathbf{R}\to\mathbf{R}f:R→R be defined as f(x)={−55x,if x<−52x3−3x2−120x,if −5≤x≤42x3−3x2−36x−336,if x>4f(x)=\begin{cases} -55x, & \text{if } x<-5 \\ 2x^{3}-3x^{2}-120x, & \text{if } -5\le x\le 4 \\ 2x^{3}-3x^{2}-36x-336, & \text{if } x>4 \end{cases}f(x)=⎩⎨⎧​−55x,2x3−3x2−120x,2x3−3x2−36x−336,​if x<−5if −5≤x≤4if x>4​ Let A={x∈R:f is increasing}A=\{x\in R: f\ \text{is increasing}\}A={x∈R:f is increasing}. Then A is equal to :
  1. (A)(−5,−4)∪(4,∞)\left(-5,-4\right)\cup\left(4,\infty\right)(−5,−4)∪(4,∞)
  2. (B)(−5,∞)\left(-5,\infty\right)(−5,∞)
  3. (C)(−∞,−5)∪(4,∞)\left(-\infty,-5\right)\cup\left(4,\infty\right)(−∞,−5)∪(4,∞)
  4. (D)(−∞,−5)∪(−4,∞)\left(-\infty,-5\right)\cup\left(-4,\infty\right)(−∞,−5)∪(−4,∞)

Correct answer: (A)

Step-by-step solution →
Q68·MathematicsSingle correct
If the curve y=ax2+bx+c,x∈R,y=ax^{2}+bx+c, x\in R,y=ax2+bx+c,x∈R, passes through the point (1,2) and the tangent line to this curve at origin is y=xy=xy=x, then the possible values of a,b,ca,b,ca,b,c are :
  1. (A)a =1, b=1, c=0
  2. (B)a = −1-1−1, b=1, c =1
  3. (C)a =1, b=0, c =1
  4. (D)a=12,b=12,c=1a=\frac{1}{2}, b=\frac{1}{2}, c=1a=21​,b=21​,c=1

Correct answer: (A)

Step-by-step solution →
Q69·MathematicsSingle correct
The negation of the statement ∼p∧(p∨q)\sim p\wedge(p\vee q)∼p∧(p∨q) is :
  1. (A)∼p∧q\sim p\wedge q∼p∧q
  2. (B)p∧∼qp\wedge\sim qp∧∼q
  3. (C)∼p∨q\sim p\vee q∼p∨q
  4. (D)p∨∼qp\vee\sim qp∨∼q

Correct answer: (D)

Step-by-step solution →
Q70·MathematicsSingle correct
For the system of linear equations: x−2y=1, x−y+kz=−2, ky+4z=6, k∈Rx-2y=1,\ x-y+kz=-2,\ ky+4z=6,\ k\in \mathbf{R}x−2y=1, x−y+kz=−2, ky+4z=6, k∈R consider the following statements: (A) The system has unique solution if k≠2,k≠−2k\neq 2, k\neq -2k=2,k=−2. (B) The system has unique solution if k=−2k=-2k=−2. (C) The system has unique solution if k=2k=2k=2. (D) The system has no-solution if k=2k=2k=2. (E) The system has infinite number of solutions if k≠−2k\neq -2k=−2. Which of the following statements are correct?
  1. (A)(B) and (E) only
  2. (B)(C) and (D) only
  3. (C)(A) and (D) only
  4. (D)(A) and (E) only

Correct answer: (C)

Step-by-step solution →
Q71·MathematicsSingle correct
For which of the following curves, the line x+3y=23x+\sqrt{3}y=2\sqrt{3}x+3​y=23​ is the tangent at the point (332,12)\left(\frac{3\sqrt{3}}{2},\frac{1}{2}\right)(233​​,21​)?
  1. (A)x2+9y2=9x^{2}+9y^{2}=9x2+9y2=9
  2. (B)2x2−18y2=92x^{2}-18y^{2}=92x2−18y2=9
  3. (C)y2=163xy^{2}=\frac{1}{6\sqrt{3}}xy2=63​1​x
  4. (D)x2+y2=7x^{2}+y^{2}=7x2+y2=7

Correct answer: (A)

Step-by-step solution →
Q72·MathematicsSingle correct
The angle of elevation of a jet plane from a point AAA on the ground is 60°. After a flight of 20 seconds at the speed of 432 km/ hour, the angle of elevation changes to 30°. If the jet plane is flying at a constant height, then its height is:
  1. (A)120031200\sqrt{3}12003​m
  2. (B)180031800\sqrt{3}18003​m
  3. (C)360033600\sqrt{3}36003​m
  4. (D)240032400\sqrt{3}24003​m

Correct answer: (A)

Step-by-step solution →
Q73·MathematicsSingle correct
Let A and B be 3×33\times 33×3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A2B2−B2A2)X=O\left(\mathrm{A}^{2}\mathrm{B}^{2}-\mathrm{B}^{2}\mathrm{A}^{2}\right)\mathrm{X}=\mathrm{O}(A2B2−B2A2)X=O, where X is a 3×13\times 13×1 column matrix of unknown variables and O is a 3×13\times 13×1 null matrix, has :
  1. (A)a unique solution
  2. (B)exactly two solutions
  3. (C)infinitely many solutions
  4. (D)no solution

Correct answer: (C)

Step-by-step solution →
Q74·MathematicsSingle correct
If n≥2n\ge 2n≥2 is a positive integer, then the sum of the series n+1C2+2(2C2+3C2+4C2+....+nC2)^{n+1}C_{2}+2\left(^{2}C_{2}+^{3}C_{2}+^{4}C_{2}+....+^{n}C_{2}\right)n+1C2​+2(2C2​+3C2​+4C2​+....+nC2​) is :
  1. (A)n(n+1)2(n+2)12\frac{n(n+1)^{2}(n+2)}{12}12n(n+1)2(n+2)​
  2. (B)n(n−1)(2n+1)6\frac{n(n-1)(2n+1)}{6}6n(n−1)(2n+1)​
  3. (C)n(n+1)(2n+1)6\frac{n(n+1)(2n+1)}{6}6n(n+1)(2n+1)​
  4. (D)n(2n+1)(3n+1)6\frac{n(2n+1)(3n+1)}{6}6n(2n+1)(3n+1)​

Correct answer: (C)

Step-by-step solution →
Q75·MathematicsSingle correct
If a curve y=f(x)y=f(x)y=f(x) passes through the point (1,2) and satisfies xdydx+y=bx4x\frac{dy}{dx}+y=bx^{4}xdxdy​+y=bx4, then for what value of b, ∫12f(x)dx=625\int_{1}^{2}f(x)dx=\frac{62}{5}∫12​f(x)dx=562​ ?
  1. (A)5
  2. (B)625\frac{62}{5}562​
  3. (C)315\frac{31}{5}531​
  4. (D)10

Correct answer: (D)

Step-by-step solution →
Q76·MathematicsSingle correct
The area of the region : R={(x, y):5x2≤y≤2x2+9}R=\left\{(x,\,y):5x^{2}\le y\le 2x^{2}+9\right\}R={(x,y):5x2≤y≤2x2+9} is:
  1. (A)939\sqrt{3}93​ square units
  2. (B)12312\sqrt{3}123​ square units
  3. (C)11311\sqrt{3}113​ square units
  4. (D)636\sqrt{3}63​ square units

Correct answer: (B)

Step-by-step solution →
Q77·MathematicsSingle correct
Let f(x)f(x)f(x) be a differentiable function defined on [0,2] such that f′(x)=f′(2−x)f^{'}(x)=f^{'}(2-x)f′(x)=f′(2−x) for all x∈(0,2)x\in(0,2)x∈(0,2), f(0)=1f(0)=1f(0)=1 and f(2)=e2f(2)=\mathrm{e}^{2}f(2)=e2. Then the value of ∫02f(x)dx\int_{0}^{2}f(x)dx∫02​f(x)dx is:
  1. (A)1+e21+e^{2}1+e2
  2. (B)1−e21-e^{2}1−e2
  3. (C)2(1−e2)2(1-e^{2})2(1−e2)
  4. (D)2(1+e2)2(1+e^{2})2(1+e2)

Correct answer: (A)

Step-by-step solution →
Q78·MathematicsNumerical
The number of the real roots of the equation (x+1)2+∣x−5∣=274(x+1)^{2}+|x-5|=\frac{27}{4}(x+1)2+∣x−5∣=427​ is________.

Correct answer: 2

Step-by-step solution →
Q79·MathematicsNumerical
The students S1,S2,…,S10S_{1},S_{2},\ldots,S_{10}S1​,S2​,…,S10​ are to be divided into 3 groups A, B and CCC such that each group has at least one student and the group CCC has at most 3 students. Then the total number of possibilities of forming such groups is________.

Correct answer: 31650

Step-by-step solution →
Q80·MathematicsNumerical
If a+α=1,b+β=2a+\alpha=1, b+\beta=2a+α=1,b+β=2 and af(x)+αf(1x)=bx+βx,x≠0,af(x)+\alpha f\left(\frac{1}{x}\right)=bx+\frac{\beta}{x}, x\neq 0,af(x)+αf(x1​)=bx+xβ​,x=0, then the value of the expression f(x)+f(1x)x+1x\frac{f(x)+f\left(\frac{1}{x}\right)}{x+\frac{1}{x}}x+x1​f(x)+f(x1​)​ is__________.

Correct answer: 2

Step-by-step solution →
Q81·MathematicsNumerical
If the variance of 10 natural numbers 1,1,1,…,1,k1,1,1,\ldots,1,k1,1,1,…,1,k is less than 10, then the maximum possible value of kkk is__________.

Correct answer: 11

Step-by-step solution →
Q82·MathematicsNumerical
Let λ\lambdaλ be an integer. If the shortest distance between the lines x−λ=2y−1=−2zx-\lambda=2y-1=-2zx−λ=2y−1=−2z and x=y+2λ=z−λx=y+2\lambda=z-\lambdax=y+2λ=z−λ is 722\frac{\sqrt{7}}{2\sqrt{2}}22​7​​, then the value of ∣λ∣|\lambda|∣λ∣ is

Correct answer: 1

Step-by-step solution →
Q83·MathematicsNumerical
Let i=−1i=\sqrt{-1}i=−1​. If (−1+i3)21(1−i)24+(1+i3)21(1+i)24=k,\frac{(-1+i\sqrt{3})^{21}}{(1-i)^{24}}+\frac{(1+i\sqrt{3})^{21}}{(1+i)^{24}}=k,(1−i)24(−1+i3​)21​+(1+i)24(1+i3​)21​=k, and n=[∣k∣]\mathrm{n}=\left[\left|k\right|\right]n=[∣k∣] be the greatest integral part of ∣k∣|k|∣k∣. Then ∑j=0n+5(j+5)2−∑j=0n+5(j+5)\sum_{j=0}^{n+5}(j+5)^{2}-\sum_{j=0}^{n+5}(j+5)∑j=0n+5​(j+5)2−∑j=0n+5​(j+5) is equal to________.

Correct answer: 310

Step-by-step solution →
Q84·MathematicsNumerical
Let a point P be such that its distance from the point (5,0) is thrice the distance of P from the point (−5,0)(-5,0)(−5,0). If the locus of the point P is a circle of radius r, then 4r24r^{2}4r2 is equal to

Correct answer: 56.25

Step-by-step solution →
Q85·MathematicsNumerical
For integers n and r, let (nr)={nCr,if n≥r≥00,otherwise\binom{n}{r}=\begin{cases}{}^{n}C_{r}, & \text{if } n\ge r\ge 0 \\ 0, & \text{otherwise}\end{cases}(rn​)={nCr​,0,​if n≥r≥0otherwise​ The maximum value of k for which the sum ∑i=0k(10i)(15k−i)+∑i=0k+1(12i)(13k+1−i)\sum_{i=0}^{k}\binom{10}{i}\binom{15}{k-i}+\sum_{i=0}^{k+1}\binom{12}{i}\binom{13}{k+1-i}∑i=0k​(i10​)(k−i15​)+∑i=0k+1​(i12​)(k+1−i13​) exists, is equal to________.

Correct answer: 12

Step-by-step solution →
Q86·MathematicsNumerical
The sum of first four terms of a geometric progression (G.P.) is 6512\frac{65}{12}1265​ and the sum of their respective reciprocals is 6518\frac{65}{18}1865​. If the product of first three terms of the G.P. is 1, and the third term is α\alphaα, then 2α2\alpha2α is__________.

Correct answer: 3

Step-by-step solution →
Q87·MathematicsNumerical
If the area of the triangle formed by the positive x-axis, the normal and the tangent to the circle (x−2)2+(y−3)2=25(x-2)^{2}+(y-3)^{2}=25(x−2)2+(y−3)2=25 at the point (5,7) is A, then 24A is equal to________.

Correct answer: 1225

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
  • Differential Equations 167/186
  • Probability 176/186
  • Permutations and Combinations 162/186
  • Binomial Theorem and Its Simple Applications 158/186
  • Electromagnetic Waves 144/186
  • Chemical Bonding and Molecular Structure 151/186
  • Application of Derivatives 139/186
  • d- and f-Block Elements 126/186
  • Thermodynamics 154/186
  • Aldehydes and Ketones 135/186
  • Equilibrium 163/186
  • Solutions 158/186
  • Chemical Thermodynamics 165/186
  • Units and Measurements 149/186
  • Complex Numbers 165/186
  • Trigonometric Functions 144/186
  • Chemical Kinetics 169/186
  • Gravitation 152/186
  • Electric Field and Coulomb's Law 133/186
  • Atomic Structure 161/186
  • Electronic Devices 145/186
  • Circles 142/186
  • Dual Nature of Matter and Radiation 155/186
  • Amines 133/186
  • 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
  • Oscillations 117/186
  • Alternating Currents 108/186
  • Organic Compounds Containing Halogens 109/186
  • Waves 109/186
  • Atoms 112/186
  • Statistics 118/186
  • Ellipse 103/186
  • Isolation of Metals 106/186
  • s-Block Elements 88/186
  • Surface Chemistry 98/186
  • Inverse Trigonometric Functions 93/186
  • Environmental Chemistry 83/186
  • Hydrogen 81/186
  • Polymers 64/186
  • 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
  • Aromaticity 22/186
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