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JEE Main 24 January 2026 Shift 1 Question Paper with Answers

24 January 2026 · January session · 73 questions

73 of the 75 questions from the JEE Main 24 January 2026 Shift 1 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

2 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
24
Chemistry
24
Mathematics
25

Physics — JEE Main 24 January 2026 Shift 1

Q1·PhysicsSingle correct
Match the List-I with List-II Choose the correct answer from the options given below:
List-IList-II
A.Magnetic inductionI.M L T−2A−2\mathrm{M\,L\,T^{-2}A^{-2}}MLT−2A−2
B.Magnetic fluxII.M L2 T−2A−2\mathrm{M\,L^{2}\,T^{-2}A^{-2}}ML2T−2A−2
C.Magnetic permeabilityIII.M L0 T−2A−1\mathrm{M\,L^{0}\,T^{-2}A^{-1}}ML0T−2A−1
D.Self inductanceIV.M L2 T−2A−1\mathrm{M\,L^{2}\,T^{-2}A^{-1}}ML2T−2A−1
  1. (A)A-IV,B-III,C-I,D-II
  2. (B)A-III,B-IV,C-II,D-I
  3. (C)A-I,B-III,C-IV,D-II
  4. (D)A-III,B-IV,C-I,D-II

Correct answer: (D)

Step-by-step solution →
Q2·PhysicsSingle correct
Three charges +2q. +3q and –4q are situated at (0,–3a), (2a, 0) and (–2a,0) respectively in the xy plane. The resultant dipole moment about origin is____
  1. (A)2qa(3j^−i^)2qa\left(3\hat{j}-\hat{i}\right)2qa(3j^​−i^)
  2. (B)2qa(3i^−7j^)2qa\left(3\hat{i}-7\hat{j}\right)2qa(3i^−7j^​)
  3. (C)2qa(7i^−3j^)2qa\left(7\hat{i}-3\hat{j}\right)2qa(7i^−3j^​)
  4. (D)2qa(3j^−7i^)2qa\left(3\hat{j}-7\hat{i}\right)2qa(3j^​−7i^)

Correct answer: (C)

Step-by-step solution →
Q3·PhysicsSingle correct
A cylindrical block of mass M and area of cross section A is floating in a liquid of density ρ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is________.
  1. (A)2πMρAg2\pi\sqrt{\dfrac{M}{\rho Ag}}2πρAgM​​
  2. (B)π2MρAg\pi\sqrt{\dfrac{2M}{\rho Ag}}πρAg2M​​
  3. (C)πρAMg\pi\sqrt{\dfrac{\rho A}{Mg}}πMgρA​​
  4. (D)2πρAMg2\pi\sqrt{\dfrac{\rho A}{Mg}}2πMgρA​​

Correct answer: (A)

Step-by-step solution →
Q4·PhysicsSingle correct
Density of water at 4°C and 20°C are 1000 kg/m3\mathrm{kg/m^{3}}kg/m3 and respectively. The increase in internal energy of 4 kg water when it is heated from 4 °C to 20°C is____J. (Specific heat capacity of water = 4.2 J/kg. and 1 atmospheric pressure = 10510^{5}105 Pa)
  1. (A)315826.2
  2. (B)234699.2
  3. (C)258700.8
  4. (D)268799.2

Correct answer: (D)

Step-by-step solution →
Q5·PhysicsSingle correct
Two resistors of 100 Ω each are connected in series with a 9V battery. A voltmeter of 400Ω resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is____V.
  1. (A)3
  2. (B)4.5
  3. (C)4
  4. (D)2

Correct answer: (C)

Step-by-step solution →
Q6·PhysicsSingle correct
The exit surface of a prism with refractive index n is coated with a material having refractive index n2\dfrac{n}{2}2n​. When this prism is set for minimum angle of deviation it exactly meets the condition of critical angle. The prism angle is____
  1. (A)60°
  2. (B)15°
  3. (C)30°
  4. (D)45°

Correct answer: (A)

Step-by-step solution →
Q7·PhysicsSingle correct
Two electrons are moving in orbits of two hydrogen like atoms with speeds 3×1053 \times 10^{5}3×105 m/s and 2.5×1052.5 \times 10^{5}2.5×105 m/s respectively. If the radii of these orbits are nearly same then the possible order of energy states are______ respectively.
  1. (A)6 and 5
  2. (B)9 and 8
  3. (C)8 and 10
  4. (D)10 and 12

Correct answer: (A)

Step-by-step solution →
Q8·PhysicsSingle correct
In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and 5 cm. Total magnification obtained with this system for normal adjustment is (5)k(5)^{k}(5)k. The value of k is_____
  1. (A)2
  2. (B)5
  3. (C)3.5
  4. (D)4

Correct answer: (A)

Step-by-step solution →
Q9·PhysicsSingle correct
For the series LCR circuit connected with 220 V, 50 Hz a.c source as shown in the figure, the power factor is α10\dfrac{\alpha}{10}10α​. The value of α is_______
  1. (A)4
  2. (B)10
  3. (C)6
  4. (D)8

Correct answer: (C)

Step-by-step solution →
Q10·PhysicsSingle correct
Match the List-I with List-II Choose the correct answer from the options given below:
List-IList-II
A.Radio-waveI.is produced by Magnetron value
B.Micro-waveII.Due to change in the vibrational modes of atoms
C.Infrared-waveIII.Due to inner shell electrons moving from higher energy level to lower energy level
D.X-rayIV.Due to rapid acceleration of electrons
  1. (A)A-II,B-IV,C-III,D-I
  2. (B)A-IV,B-III,C-I,D-II
  3. (C)A-IV,B-I,C-II,D-III
  4. (D)A-IV,B-II,C-I,D-III

Correct answer: (C)

Step-by-step solution →
Q11·PhysicsSingle correct
A spring of force constant 15 N/m is cut into two pieces. If the ratio of their length is 1:3, then the force constant of smaller piece is____N/m
  1. (A)15
  2. (B)20
  3. (C)60
  4. (D)45

Correct answer: (C)

Step-by-step solution →
Q12·PhysicsSingle correct
Two resistors 2Ω and 3Ω are connected in the gaps of bridge as shown in figure. The null point is obtained with the contact of jockey at some point on wire XY. When an unknown resistor is connected in parallel with 3Ω resistor, the null point is shifted by 22.5 cm toward Y. The resistance of unknown resistor is____Ω.
  1. (A)3
  2. (B)2
  3. (C)4
  4. (D)1

Correct answer: (B)

Step-by-step solution →
Q13·PhysicsSingle correct
Given below are two statements: Statement I : For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon. Statement II : For all elements, nuclei with less binding energy per nucleon transforms to nuclei with greater binding energy per nucleon. 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 true but Statement II is false
  3. (C)Both Statement I and Statement II are false
  4. (D)Statement I is false but Statement II is true

Correct answer: (D)

Step-by-step solution →
Q14·PhysicsSingle correct
A brass wire of length 2m and radius 1mm at 27°C is held taut between two rigid supports. Initially it was cooled to a temperature of –43°C creating a tension T in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to 1.4T, is ____°C
  1. (A)–86
  2. (B)–71
  3. (C)–65
  4. (D)–80

Correct answer: (B)

Step-by-step solution →
Q15·PhysicsSingle correct
The electrostatic potential in a charged spherical region of radius r varies as V=ar3+bV = ar^{3} + bV=ar3+b, where a and b are constants. The total charge in the sphere of unit radius is α×πa∈0\alpha \times \pi a \in_{0}α×πa∈0​. The value of α\alphaα is ______. (permittivity of vacuum is ∈0\in_{0}∈0​)
  1. (A)–12
  2. (B)–6
  3. (C)–9
  4. (D)–8

Correct answer: (A)

Step-by-step solution →
Q16·PhysicsSingle correct
Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from rest the heavier mass is observed to fall 81 cm in 9 s. The rotational inertia of the pulley is ________ kg.m2^{2}2. (g=9.8(g = 9.8(g=9.8 m/s2)^{2})2)
  1. (A)9.5×10−39.5 \times 10^{-3}9.5×10−3
  2. (B)4.75×10−34.75 \times 10^{-3}4.75×10−3
  3. (C)1.86×10−21.86 \times 10^{-2}1.86×10−2
  4. (D)8.3×10−38.3 \times 10^{-3}8.3×10−3

Correct answer: (A)

Step-by-step solution →
Q17·PhysicsSingle correct
An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and 232\sqrt{3}23​ (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is ______.
  1. (A)60°
  2. (B)10°
  3. (C)30°
  4. (D)45°

Correct answer: (A)

Step-by-step solution →
Q18·PhysicsSingle correct
A boy thrown a ball into air at 45° from the horizontal to land it on a roof of a building of height H. If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of H is _________ m. (g=10(g = 10(g=10 m/s2)^{2})2)
  1. (A)20
  2. (B)10
  3. (C)25
  4. (D)15

Correct answer: (D)

Step-by-step solution →
Q19·PhysicsSingle correct
There are three co-centric conducting spherical shells A, B and C of radii a, b and c respectively. The potential of the spheres A, B and C respectively, are :
  1. (A)14π∈0(q1+q2+q3a),14π∈0(q1+q2+q3b),14π∈0(q1+q2+q3c)\frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}+q_{3}}{a}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}+q_{3}}{b}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}+q_{3}}{c}\right)4π∈0​1​(aq1​+q2​+q3​​),4π∈0​1​(bq1​+q2​+q3​​),4π∈0​1​(cq1​+q2​+q3​​)
  2. (B)14π∈0(q1+q2+q3a),14π∈0(q1+q2b+q3c),14π∈0(q1a+q2b+q3c)\frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}+q_{3}}{a}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}}{a}+\frac{q_{2}}{b}+\frac{q_{3}}{c}\right)4π∈0​1​(aq1​+q2​+q3​​),4π∈0​1​(bq1​+q2​​+cq3​​),4π∈0​1​(aq1​​+bq2​​+cq3​​)
  3. (C)14π∈0(q1a+q2b+q3c),14π∈0(q1+q2b+q3c),14π∈0(q1+q2+q3c)\frac{1}{4\pi \in_{0}}\left(\frac{q_{1}}{a}+\frac{q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}+q_{3}}{c}\right)4π∈0​1​(aq1​​+bq2​​+cq3​​),4π∈0​1​(bq1​+q2​​+cq3​​),4π∈0​1​(cq1​+q2​+q3​​)
  4. (D)14π∈0(q1a+q2b+q3c),14π∈0(q1+q2+q3b),14π∈0(q1+q2+q3c)\frac{1}{4\pi \in_{0}}\left(\frac{q_{1}}{a}+\frac{q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}+q_{3}}{b}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}+q_{3}}{c}\right)4π∈0​1​(aq1​​+bq2​​+cq3​​),4π∈0​1​(bq1​+q2​+q3​​),4π∈0​1​(cq1​+q2​+q3​​)

Correct answer: (C)

Step-by-step solution →
Q20·PhysicsSingle correct
Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process _________ J. (Gravitational constant G=6.7×10−11G = 6.7 \times 10^{-11}G=6.7×10−11 N m2^{2}2 / kg2^{2}2)
  1. (A)9.86×10−69.86 \times 10^{-6}9.86×10−6
  2. (B)2.85×10−72.85 \times 10^{-7}2.85×10−7
  3. (C)1.74×10−71.74 \times 10^{-7}1.74×10−7
  4. (D)4.77×10−74.77 \times 10^{-7}4.77×10−7

Correct answer: (C)

Step-by-step solution →
Q21·PhysicsNumerical
A short bar magnet placed with its axis at 30° with an external field of 800 Gauss, experiences a torque of 0.016 N.m. The work done in moving it from most stable to most unstable position is α×10−3\alpha \times 10^{-3}α×10−3 J. The value of α\alphaα is ________.

Correct answer: 64

Step-by-step solution →
Q22·PhysicsNumerical
A voltage regulating circuit consisting of Zener diode, having break-down voltage of 10 V and maximum power dissipation of 0.4 W, is operated at 15 V. The approximate value of protective resistance in this circuit is ________ Ω.

Correct answer: 125

Step-by-step solution →
Q23·PhysicsNumerical
In the given figure the blocks A, B and C weigh 4 kg, 6 kg and 8 kg respectively. The co-efficient of sliding friction between any two surfaces is 0.5. The force F⃗\vec{F}F required to slide the block C with constant speed is _________ N. (Used g=10g = 10g=10 m/s2^{2}2)

Correct answer: 210

Step-by-step solution →
Q24·PhysicsNumerical
Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 cm/s coalesce to form a bigger drop. The terminal velocity of bigger drop is ______ cm/s.

Correct answer: 160

Step-by-step solution →

Chemistry — JEE Main 24 January 2026 Shift 1

Q25·ChemistrySingle correct
Given below are two statements : Statement-I Hybridisation, shape and spin only magnetic moment of K3[Co(CO3)3]K_3[Co(CO_3)_3]K3​[Co(CO3​)3​] is sp3d2sp^3d^2sp3d2, octahedral and 4.9 BM respectively. Statement-II Geometry, hybridisation and spin only magnetic moment values (BM) of the ions [Ni(CN)4]2−[Ni(CN)_4]^{2-}[Ni(CN)4​]2−, [MnBr4]2−[MnBr_4]^{2-}[MnBr4​]2− and [CoF6]3−[CoF_6]^{3-}[CoF6​]3− respectively are square planar, tetrahedral, octahedral : dsp2dsp^2dsp2, sp3sp^3sp3, sp3d2sp^3d^2sp3d2 and 0, 5.9, 4.9. 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 false but statement-II is true
  3. (C)Both statement-I and statement-II are true
  4. (D)Statement-I is true but statement-II is false

Correct answer: (C)

Step-by-step solution →
Q26·ChemistrySingle correct
A → D is an endothermic reaction occurring in three steps (elementary). (i) A → B ΔHi\Delta H_iΔHi​ = +ve (ii) B → C ΔHii\Delta H_{ii}ΔHii​ = –ve (iii) C → D ΔHiii\Delta H_{iii}ΔHiii​ = –ve Which of the following graphs between potential energy (y-axis) vs reaction coordinate (x-axis) correctly represents the reaction profile of A → D ?
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (C)

Step-by-step solution →
Q27·Chemistry·Electronic Effects and StabilitySingle correct
Arrange the following alkenes in decreasing order of stability. Choose the correct answer from the options given below :
  1. (A)III > I > II > IV
  2. (B)III > II > I > IV
  3. (C)I > III > II > IV
  4. (D)I > III > IV > II

Correct answer: (C)

Step-by-step solution →
Q28·ChemistrySingle correct
Given below are statements about some molecules/ions. Identify the CORRECT statements. A. The dipole moment value of NF3NF_3NF3​ is higher than that of NH3NH_3NH3​. B. The dipole moment value of BeH2BeH_2BeH2​ is zero. C. The bond order of O22−O_2^{2-}O22−​ and F2F_2F2​ is same. D. The formal charge on the central oxygen atom of ozone is –1. E. In NO2NO_2NO2​, all the three atoms satisfy the octet rule, hence it is very stable. Choose the correct answer from the options given below :
  1. (A)A, B, C, D & E
  2. (B)B & C only
  3. (C)B, C & D only
  4. (D)A, C & D only

Correct answer: (B)

Step-by-step solution →
Q29·ChemistrySingle correct
A solution is prepared by dissolving 0.3 g of a non-volatile non-electrolyte solute 'A' of molar mass 60 g mol−1^{-1}−1 and 0.9 g of a non-volatile non-electrolyte solute 'B' of molar mass 180 g mol−1^{-1}−1 in 100 mL H2OH_2OH2​O at 27°C. Osmotic pressure of the solution will be [Given : R = 0.082 L atm K−1^{-1}−1 mol−1^{-1}−1]
  1. (A)1.23 atm
  2. (B)2.46 atm
  3. (C)0.82 atm
  4. (D)1.47 atm

Correct answer: (B)

Step-by-step solution →
Q30·ChemistrySingle correct
Among the following, the CORRECT combinations are : A. IF3IF_3IF3​ → T-shaped (sp3dsp^3dsp3d) B. IF5IF_5IF5​ → Square pyramidal (sp3d2sp^3d^2sp3d2) C. IF7IF_7IF7​ → Pentagonal bipyramidal (sp3d3sp^3d^3sp3d3) D. ClO4−ClO_4^-ClO4−​ → Square planar (sp2dsp^2dsp2d) Choose the correct answer from the options given below :
  1. (A)A, B and C only
  2. (B)A and B only
  3. (C)A, B, C and D
  4. (D)B, C and D Only

Correct answer: (A)

Step-by-step solution →
Q31·ChemistrySingle correct
The correct stability order of the following diazonium salts is
  1. (A)A > B > C > D
  2. (B)C > D > B > A
  3. (C)A > C > D > B
  4. (D)C > A > D > B

Correct answer: (C)

Step-by-step solution →
Q32·ChemistrySingle correct
Consider a mixture 'X' which is made by dissolving 0.4 mol of [Co(NH3)5SO4][Co(NH_3)_5SO_4][Co(NH3​)5​SO4​] Br and 0.4 mol of [Co(NH3)5Br]SO4[Co(NH_3)_5Br]SO_4[Co(NH3​)5​Br]SO4​ in water to make 4 L of solution. When 2 L of mixture 'X' is allowed to react with excess of AgNO3AgNO_3AgNO3​, it forms precipitate 'Y'. The rest 2 L of mixture 'X' reacts with excess BaCl2BaCl_2BaCl2​ to form precipitate 'Z'. Which of the following statements is CORRECT.
  1. (A)0.2 mol of 'Z' is formed
  2. (B)'Y' is BaSO4BaSO_4BaSO4​ and 'Z' is AgBr
  3. (C)0.4 mol of 'Z' is formed
  4. (D)0.1 mol of 'Y' is formed

Correct answer: (A)

Step-by-step solution →
Q33·ChemistrySingle correct
Given below are two statements Statements-I : The number of paramagnetic species among [CoF6]3−[CoF_6]^{3-}[CoF6​]3−, [TiF6]3−[TiF_6]^{3-}[TiF6​]3−, V2O5V_2O_5V2​O5​ and [Fe(CN)6]3−[Fe(CN)_6]^{3-}[Fe(CN)6​]3− is 3. Statement-II : K4[Fe(CN)6]<K3[Fe(CN)6]<[Fe(H2O)6]SO4.H2O<[Fe(H2O)6]Cl3K_4[Fe(CN)_6] < K_3[Fe(CN)_6] < [Fe(H_2O)_6] SO_4.H_2O < [Fe(H_2O)_6]Cl_3K4​[Fe(CN)6​]<K3​[Fe(CN)6​]<[Fe(H2​O)6​]SO4​.H2​O<[Fe(H2​O)6​]Cl3​ is the correct order in terms of number of unpaired electron(s) in the complexes. 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)Both statement-I and statement-II are false
  3. (C)Statement-I is true but statement-II is false
  4. (D)Statement-I is false but statement-II is true

Correct answer: (A)

Step-by-step solution →
Q34·ChemistrySingle correct
Consider three metal chlorides x, y and z, where x is water soluble at room temperature, y is sparingly soluble in water at room temperature and z is soluble in hot water. x, y and z are respectively
  1. (A)MgCl2MgCl_2MgCl2​, AgCl and AlCl3AlCl_3AlCl3​
  2. (B)AgCl, Hg2Cl2Hg_2Cl_2Hg2​Cl2​ and PbCl2PbCl_2PbCl2​
  3. (C)AlCl3AlCl_3AlCl3​, PbCl2PbCl_2PbCl2​ and BaCl2BaCl_2BaCl2​
  4. (D)CuCl2CuCl_2CuCl2​, AgCl and PbCl2PbCl_2PbCl2​

Correct answer: (D)

Step-by-step solution →
Q35·ChemistrySingle correct
'W' g of a non-volatile electrolyte solid solute of molar mass 'M' g mol−1^{-1}−1 when dissolved in 100 mL water, decreases vapour pressure of water from 640 mm Hg to 600 mm Hg. If aqueous solution of the electrolyte boils at 375 K and KbK_bKb​ for water is 0.52 K kg mol−1^{-1}−1, then the mole fraction of the electrolyte solute (x2)(x_2)(x2​) in the solution can be expressed as (Given : density of water = 1 g/mL and boiling point of water = 373 K)
  1. (A)1.38×WM\frac{1.3}{8} \times \frac{W}{M}81.3​×MW​
  2. (B)162.6×WM\frac{16}{2.6} \times \frac{W}{M}2.616​×MW​
  3. (C)2.616×MW\frac{2.6}{16} \times \frac{M}{W}162.6​×WM​
  4. (D)1.38×MW\frac{1.3}{8} \times \frac{M}{W}81.3​×WM​

Correct answer: (A)

Step-by-step solution →
Q36·ChemistrySingle correct
Match the List-I (Isothermal process for ideal gas system) with List-II Work done (Vf>ViV_f > V_iVf​>Vi​) Choose the correct answer from the options given below :
List-I (Isothermal process for ideal gas system)List-II Work done ($V_f > V_i$)
A.Reversible expansionI.w=0w = 0w=0
B.Free expansionII.w=−nRTln⁡VfViw = -nRT \ln \frac{V_f}{V_i}w=−nRTlnVi​Vf​​
C.Irreversible expansionIII.w=−pex(Vf−Vi)w = -p_{ex} (V_f - V_i)w=−pex​(Vf​−Vi​)
D.Irreversible compressionIV.w=−pex(Vi−Vf)w = -p_{ex} (V_i - V_f)w=−pex​(Vi​−Vf​)
  1. (A)A-IV, B-I, C-III, D-II
  2. (B)A-IV, B-II, C-III, D-I
  3. (C)A-I, B-III, C-II, D-IV
  4. (D)A-II, B-I, C-III, D-IV

Correct answer: (D)

Step-by-step solution →
Q37·ChemistrySingle correct
A student is given one compound among the following compounds that gives positive test with Tollen's reagent. The compound is :
  1. (A)D
  2. (B)A
  3. (C)B
  4. (D)C

Correct answer: (D)

Step-by-step solution →
Q38·ChemistrySingle correct
A hydroxy compound (X) with molar mass 122 g mol−1^{-1}−1 is acetylated with acetic anhydride, using a large excess of the reagent ensuring complete acetylation of all hydroxyl groups. The product obtained has a molar mass of 290 g mol−1^{-1}−1. The number of hydroxyl groups present in compound (X) is :
  1. (A)3
  2. (B)5
  3. (C)2
  4. (D)4

Correct answer: (D)

Step-by-step solution →
Q39·ChemistrySingle correct
At 27°C in presence of a catalyst, activation energy of a reaction is lowered by 10 kJ mol−1^{-1}−1. The logarithm ratio of k(catalysed)k(uncatalysed)\dfrac{\mathrm{k}\left(\text{catalysed}\right)}{\mathrm{k}\left(\text{uncatalysed}\right)}k(uncatalysed)k(catalysed)​ is .... (Consider that the frequency factor for both the reactions is same)
  1. (A)17.41
  2. (B)1.741
  3. (C)3.482
  4. (D)0.1741

Correct answer: (B)

Step-by-step solution →
Q40·ChemistrySingle correct
Given below are two statements : Statement I : 'C–Cl' bond is stronger in CH2=CH−Cl\mathrm{CH_2 = CH - Cl}CH2​=CH−Cl than CH3−CH2−Cl\mathrm{CH_3 - CH_2 - Cl}CH3​−CH2​−Cl Statement II : The given optically active molecule, on hydrolysis gives a solution that can rotate the plane polarized light. 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)Both Statement I and Statement II are false
  4. (D)Statement I is true but Statement II is false

Correct answer: (D)

Step-by-step solution →
Q41·ChemistrySingle correct
Consider the following two reactions A and B. Numerical value of [molar mass of x+ molar mass of y] is ____ .
  1. (A)4
  2. (B)88
  3. (C)46
  4. (D)160

Correct answer: (C)

Step-by-step solution →
Q42·Chemistry·Electronic Effects and StabilitySingle correct
Arrange the following carbanions in the decreasing order of stability I. p−Br−C6H4−C⊖H2p-\mathrm{Br}-\mathrm{C_6H_4}-\overset{\ominus}{\mathrm{C}}\mathrm{H_2}p−Br−C6​H4​−C⊖H2​ II. C6H5−C⊖H2\mathrm{C_6H_5}-\overset{\ominus}{\mathrm{C}}\mathrm{H_2}C6​H5​−C⊖H2​ III. p−CH3O−C6H4−C⊖H2p-\mathrm{CH_3O}-\mathrm{C_6H_4}-\overset{\ominus}{\mathrm{C}}\mathrm{H_2}p−CH3​O−C6​H4​−C⊖H2​ IV. p−CHO−C6H4−C⊖H2p-\mathrm{CHO}-\mathrm{C_6H_4}-\overset{\ominus}{\mathrm{C}}\mathrm{H_2}p−CHO−C6​H4​−C⊖H2​ V. p−CH3−C6H4−C⊖H2p-\mathrm{CH_3}-\mathrm{C_6H_4}-\overset{\ominus}{\mathrm{C}}\mathrm{H_2}p−CH3​−C6​H4​−C⊖H2​ Choose the correct answer from the options given below :
  1. (A)I > II > IV > V > III
  2. (B)I > IV > II > V > III
  3. (C)IV > I > II > V > III
  4. (D)IV > II > I > III > V

Correct answer: (C)

Step-by-step solution →
Q43·ChemistrySingle correct
Given below are two statements : Statement I : K > Mg > Al > B is the correct order in terms of metallic character. Statement II : Atomic radius is always greater than the ionic radius for any element. 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)Both Statement I and Statement II are false
  3. (C)Statement I is false but Statement II is true
  4. (D)Statement I is true but Statement II is false

Correct answer: (D)

Step-by-step solution →
Q44·ChemistryNumerical
Electricity is passed through an acidic solution of Cu2+\mathrm{Cu^{2+}}Cu2+ till all the cu2+\mathrm{cu^{2+}}cu2+ was exhausted, leading to the deposition of 300 mg of Cu metal. However, a current of 600 mA was continued to pass through the same solution for another 28 minutes by keeping the total volume of the solution fixed at 200 mL. The total volume of oxygen evolved at STP during the entire process is ______ mL. (Nearest integer) [Given : Cu2+(aq)+2e−→Cu(s)  Ered0=+0.34 V\mathrm{Cu^{2+}\left(aq\right)+2e^{-} \rightarrow Cu\left(s\right)\; E^{0}_{red} = +0.34\,V}Cu2+(aq)+2e−→Cu(s)Ered0​=+0.34V O2(g)+4H++4e−→2H2O  Ered0=+1.23 V\mathrm{O_2\left(g\right)+4H^{+}+4e^{-} \rightarrow 2H_2O\; E^{0}_{red} = +1.23\,V}O2​(g)+4H++4e−→2H2​OEred0​=+1.23V Molar mass of Cu = 63.54 g mol−1^{-1}−1 Molar mass of O2\mathrm{O_2}O2​ = 32 g mol−1^{-1}−1 Faraday Constant = 96500 C mol−1^{-1}−1 Molar volume at STP = 22.4 L ]

Correct answer: 111

Step-by-step solution →
Q45·ChemistryNumerical
Consider two Group IV metal ions X2+\mathrm{X^{2+}}X2+ and Y2+\mathrm{Y^{2+}}Y2+. A solution containing 0.01 MX2+\mathrm{MX^{2+}}MX2+ and 0.01 MY2+\mathrm{MY^{2+}}MY2+ is saturated with H2S\mathrm{H_2S}H2​S. The pH at which the metal sulphide YS will form as a precipitate is ______ (Nearest integer) (Given : Ksp(XS)=1×10−22\mathrm{K_{sp}\left(XS\right)=1\times10^{-22}}Ksp​(XS)=1×10−22 at 25°C, Ksp(YS)=4×10−16\mathrm{K_{sp}\left(YS\right)=4\times10^{-16}}Ksp​(YS)=4×10−16 at 25°C, [H2S]\mathrm{[H_2S]}[H2​S] = 0.1M in solution, Ka1×Ka2\mathrm{K_{a1} \times K_{a2}}Ka1​×Ka2​ (H2S\mathrm{H_2S}H2​S) = 1.0×10−211.0 \times 10^{-21}1.0×10−21, log 2 = 0.30, log 3 = 0.48, log 5 = 0.70)

Correct answer: 4

Step-by-step solution →
Q46·ChemistryNumerical
The hydrogen spectrum consists of several spectral lines in Lyman series (L1\mathrm{L_1}L1​, L2\mathrm{L_2}L2​, L3\mathrm{L_3}L3​ ....; L1\mathrm{L_1}L1​ has lowest energy among Lyman series). Similarly it consists of several spectral lines in Balmer series (B1\mathrm{B_1}B1​, B2\mathrm{B_2}B2​, B3\mathrm{B_3}B3​....... ; B1\mathrm{B_1}B1​ has lowest energy among Balmer lines). The energy of L1\mathrm{L_1}L1​ is x times the energy of B1\mathrm{B_1}B1​. The value of x is ______ ×10−1\times 10^{-1}×10−1 (Nearest inteter)

Correct answer: 54

Step-by-step solution →
Q47·ChemistryNumerical
In Dumas method for estimation of nitrogen, 0.50 g of an organic compound gave 70 mL of nitrogen collected at 300 K and 715 mm pressure. The percentage of nitrogen in the organic compound is ______% (Aqueous tension at 300 K is 15 mm).

Correct answer: 15

Step-by-step solution →
Q48·ChemistryNumerical
X and Y are the number of electrons involved, respectively during the oxidation of I−\mathrm{I^{-}}I− to I2\mathrm{I_2}I2​ and S2−\mathrm{S^{2-}}S2− to S by acidified K2Cr2O7\mathrm{K_2Cr_2O_7}K2​Cr2​O7​. The value of X + Y is ______.

Correct answer: 12

Step-by-step solution →

Mathematics — JEE Main 24 January 2026 Shift 1

Q49·Mathematics·Limits and ContinuitySingle correct
If the function f(x) =ex(etan⁡x−x−1)+log⁡e(sec⁡x+tan⁡x)−xtan⁡x−x= \frac{e^{x}\left(e^{\tan x-x}-1\right)+\log_{e}(\sec x+\tan x)-x}{\tan x-x}=tanx−xex(etanx−x−1)+loge​(secx+tanx)−x​ is Continuous at x = 0, then the value of f(0) is equal to
  1. (A)222
  2. (B)23\frac{2}{3}32​
  3. (C)12\frac{1}{2}21​
  4. (D)32\frac{3}{2}23​

Correct answer: (D)

Step-by-step solution →
Q50·MathematicsSingle correct
Let a circle of radius 4 pass through the origin O, the points A (−3a,0)\left(-\sqrt{3}a,0\right)(−3​a,0) and B(0,−2 b)\left(0,-\sqrt{2}\,b\right)(0,−2​b), where a and b are real parameters and ab ≠ 0. Then the locus of the centroid of ΔOAB is a circle of radius
  1. (A)53\frac{5}{3}35​
  2. (B)73\frac{7}{3}37​
  3. (C)83\frac{8}{3}38​
  4. (D)113\frac{11}{3}311​

Correct answer: (C)

Step-by-step solution →
Q51·MathematicsSingle correct
Let the lines L1L_{1}L1​: r⃗=i^+2j^+3k^+λ(2i^+3j^+4k^)\vec{r}=\hat{i}+2\hat{j}+3\hat{k}+\lambda\left(2\hat{i}+3\hat{j}+4\hat{k}\right)r=i^+2j^​+3k^+λ(2i^+3j^​+4k^), λ∈ℝ and L2L_{2}L2​ : r⃗=(4i^+j^)+μ(5i^+2j^+k^)\vec{r}=\left(4\hat{i}+\hat{j}\right)+\mu\left(5\hat{i}+2\hat{j}+\hat{k}\right)r=(4i^+j^​)+μ(5i^+2j^​+k^), μ∈ℝ, intersect at the point R. Let P and Q be the points lying on lines L1L_{1}L1​ and L2L_{2}L2​, respectively, such that ∣PR→∣=29\left|\overrightarrow{PR}\right|=\sqrt{29}​PR​=29​ and ∣PQ→∣=473\left|\overrightarrow{PQ}\right|=\sqrt{\frac{47}{3}}​PQ​​=347​​ . If the point P lies in the first octant, then 27(QR)227(QR)^{2}27(QR)2 is equal to
  1. (A)340340340
  2. (B)360360360
  3. (C)320320320
  4. (D)348348348

Correct answer: (B)

Step-by-step solution →
Q52·MathematicsSingle correct
Let 729, 81, 9, 1, …. be a sequence and PnP_{n}Pn​ denote the product of the first n terms of this sequence. If 2∑n=140(Pn)1n=3α−13β2\sum_{n=1}^{40}\left(P_{n}\right)^{\frac{1}{n}}=\frac{3^{\alpha}-1}{3^{\beta}}2∑n=140​(Pn​)n1​=3β3α−1​ and gcd (α, β) = 1, then α + β is equal to
  1. (A)737373
  2. (B)747474
  3. (C)757575
  4. (D)767676

Correct answer: (A)

Step-by-step solution →
Q53·MathematicsSingle correct
Let a⃗=2i^+j^−2k^\vec{a}=2\hat{i}+\hat{j}-2\hat{k}a=2i^+j^​−2k^ , b⃗=i^+j^\vec{b}=\hat{i}+\hat{j}b=i^+j^​ and c⃗=a⃗×b⃗\vec{c}=\vec{a}\times\vec{b}c=a×b . Let d⃗\vec{d}d be a vector such that ∣d⃗−a⃗∣=11,∣c⃗×d⃗∣=3\left|\vec{d}-\vec{a}\right|=\sqrt{11},\left|\vec{c}\times\vec{d}\right|=3​d−a​=11​,​c×d​=3 and the angle between c⃗\vec{c}c and d⃗\vec{d}d is π4\frac{\pi}{4}4π​ . Then a⃗⋅d⃗\vec{a}\cdot\vec{d}a⋅d is equal to
  1. (A)111111
  2. (B)333
  3. (C)000
  4. (D)111

Correct answer: (C)

Step-by-step solution →
Q54·MathematicsSingle correct
If the domain of the function f(x)=log⁡(10x2−17x+7)(18x2−11x+1)f(x)=\log_{(10x^{2}-17x+7)}\left(18x^{2}-11x+1\right)f(x)=log(10x2−17x+7)​(18x2−11x+1) is (−∞, a)∪(b, c)∪(d, ∞)−{e}(-\infty,\ a)\cup(b,\ c)\cup(d,\ \infty)-\{e\}(−∞, a)∪(b, c)∪(d, ∞)−{e}, then 90(a+b+c+d+e)90(a+b+c+d+e)90(a+b+c+d+e) equals:
  1. (A)170170170
  2. (B)177177177
  3. (C)307307307
  4. (D)316316316

Correct answer: (D)

Step-by-step solution →
Q55·MathematicsSingle correct
Let each of the two ellipses E1:x2a2+y2b2=1,(a>b)E_{1}:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1,(a>b)E1​:a2x2​+b2y2​=1,(a>b) and E2:x2A2+y2B2=1E_{2}:\frac{x^{2}}{A^{2}}+\frac{y^{2}}{B^{2}}=1E2​:A2x2​+B2y2​=1 , (A<B)(A<B)(A<B) have eccentricity 45\frac{4}{5}54​ . Let the lengths of the latus recta of E1E_{1}E1​ and E2E_{2}E2​ be ℓ1\ell_{1}ℓ1​ and ℓ2\ell_{2}ℓ2​, respectively, such that 2ℓ12=9ℓ22\ell_{1}^{2}=9\ell_{2}2ℓ12​=9ℓ2​ . If the distance between the foci of E1E_{1}E1​ is 8, then the distance between the foci of E2E_{2}E2​ is
  1. (A)965\frac{96}{5}596​
  2. (B)325\frac{32}{5}532​
  3. (C)165\frac{16}{5}516​
  4. (D)85\frac{8}{5}58​

Correct answer: (B)

Step-by-step solution →
Q56·MathematicsSingle correct
The value of 3csc⁡20∘−sec⁡20∘cos⁡20∘cos⁡40∘cos⁡60∘cos⁡80∘\frac{\sqrt{3}\csc 20^\circ - \sec 20^\circ}{\cos 20^\circ \cos 40^\circ \cos 60^\circ \cos 80^\circ}cos20∘cos40∘cos60∘cos80∘3​csc20∘−sec20∘​ is equal to
  1. (A)32
  2. (B)16
  3. (C)64
  4. (D)12

Correct answer: (C)

Step-by-step solution →
Q57·MathematicsSingle correct
Let S={z∈C:∣z−6iz−2i∣=1 and ∣z−8+2iz+2i∣=35}S=\left\{z\in\mathbb{C}:\left|\frac{z-6i}{z-2i}\right|=1\ \text{and}\ \left|\frac{z-8+2i}{z+2i}\right|=\frac{3}{5}\right\}S={z∈C:​z−2iz−6i​​=1 and ​z+2iz−8+2i​​=53​} . Then ∑z∈s∣z∣2\sum_{z\in s}|z|^{2}∑z∈s​∣z∣2 is equal to
  1. (A)398398398
  2. (B)413413413
  3. (C)423423423
  4. (D)385385385

Correct answer: (D)

Step-by-step solution →
Q58·MathematicsSingle correct
If cot⁡x=512\cot x=\frac{5}{12}cotx=125​ for some x∈(π,3π2)x\in\left(\pi,\frac{3\pi}{2}\right)x∈(π,23π​), then sin⁡7x(cos⁡13x2+sin⁡13x2)+cos⁡7x(cos⁡13x2−sin⁡13x2)\sin 7x\left(\cos\frac{13x}{2}+\sin\frac{13x}{2}\right)+\cos 7x\left(\cos\frac{13x}{2}-\sin\frac{13x}{2}\right)sin7x(cos213x​+sin213x​)+cos7x(cos213x​−sin213x​) is equal to
  1. (A)426\frac{4}{\sqrt{26}}26​4​
  2. (B)626\frac{6}{\sqrt{26}}26​6​
  3. (C)113\frac{1}{\sqrt{13}}13​1​
  4. (D)513\frac{5}{\sqrt{13}}13​5​

Correct answer: (C)

Step-by-step solution →
Q59·MathematicsSingle correct
Let f(t)=∫(1−sin⁡(log⁡et)1−cos⁡(log⁡et))dt, t>1f(t)=\int\left(\frac{1-\sin(\log_{e}t)}{1-\cos\left(\log_{e}t\right)}\right)dt,\ t>1f(t)=∫(1−cos(loge​t)1−sin(loge​t)​)dt, t>1. If f(eπ/2)=−eπ/2f(e^{\pi/2})=-e^{\pi/2}f(eπ/2)=−eπ/2 and f(eπ/4)=α eπ/4f(e^{\pi/4})=\alpha\ e^{\pi/4}f(eπ/4)=α eπ/4, then α equals
  1. (A)−1−2-1-\sqrt{2}−1−2​
  2. (B)−1−22-1-2\sqrt{2}−1−22​
  3. (C)1+21+\sqrt{2}1+2​
  4. (D)−1+2-1+\sqrt{2}−1+2​

Correct answer: (A)

Step-by-step solution →
Q60·MathematicsSingle correct
Let R be a relation defined on the set {1,2,3,4}×{1,2,3,4}\{1,2,3,4\}\times\{1,2,3,4\}{1,2,3,4}×{1,2,3,4} by R={((a,b),(c,d)):2a+3b=3c+4d}R=\{((a,b),(c,d)):2a+3b=3c+4d\}R={((a,b),(c,d)):2a+3b=3c+4d}. Then the number of elements in R is
  1. (A)666
  2. (B)181818
  3. (C)121212
  4. (D)151515

Correct answer: (C)

Step-by-step solution →
Q61·MathematicsSingle correct
Let A(1, 0), B(2, −1) and C(73,43)C\left(\frac{7}{3},\frac{4}{3}\right)C(37​,34​) be three points. If the equation of the bisector of the angle ABC is αx+βy=5\alpha x+\beta y=5αx+βy=5, then the value of α2+β2\alpha^{2}+\beta^{2}α2+β2 is
  1. (A)888
  2. (B)555
  3. (C)131313
  4. (D)101010

Correct answer: (D)

Step-by-step solution →
Q62·MathematicsSingle correct
Let S =125!+13!23!+15!21!+...= \frac{1}{25!} + \frac{1}{3!23!} + \frac{1}{5!21!} + ...=25!1​+3!23!1​+5!21!1​+... up to 13 terms. If 13S=2kn!13\mathrm{S} = \frac{2^{k}}{n!}13S=n!2k​, k∈N, then n + k is equal to
  1. (A)51
  2. (B)52
  3. (C)49
  4. (D)50

Correct answer: (C)

Step-by-step solution →
Q63·MathematicsSingle correct
Consider an A.P.: a1,a2,....,ana_{1}, a_{2},....,a_{n}a1​,a2​,....,an​; a1>0a_{1} > 0a1​>0. If a2−a1=−34a_{2} - a_{1} = \frac{-3}{4}a2​−a1​=4−3​, an=14a1a_{n} = \frac{1}{4} a_{1}an​=41​a1​, and ∑i=1nai=5252\sum\limits_{i=1}^{n} a_{i} = \frac{525}{2}i=1∑n​ai​=2525​, then ∑i=117ai\sum\limits_{i=1}^{17} a_{i}i=1∑17​ai​ is equal to
  1. (A)476
  2. (B)952
  3. (C)238
  4. (D)136

Correct answer: (C)

Step-by-step solution →
Q64·Mathematics·DifferentiabilitySingle correct
Let α, β ∈ R\mathbb{R}R be such that the function f(x)={2α(x2−2)+2βx,x<1(α+3)x+(α−β),x≥1f(\mathrm{x}) = \begin{cases} 2\alpha(\mathrm{x}^{2} - 2) + 2\beta \mathrm{x} & ,\mathrm{x} < 1 \\ (\alpha + 3)\mathrm{x} + (\alpha - \beta) & ,\mathrm{x} \geq 1 \end{cases}f(x)={2α(x2−2)+2βx(α+3)x+(α−β)​,x<1,x≥1​ be differentiable at all x∈R\mathbb{R}R. Then 34(α + β) is equal to
  1. (A)84
  2. (B)48
  3. (C)36
  4. (D)24

Correct answer: (B)

Step-by-step solution →
Q65·MathematicsSingle correct
From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is :-
  1. (A)7107\frac{7}{10^{7}}1077​
  2. (B)81108\frac{81}{10^{8}}10881​
  3. (C)67108\frac{67}{10^{8}}10867​
  4. (D)73108\frac{73}{10^{8}}10873​

Correct answer: (D)

Step-by-step solution →
Q66·MathematicsSingle correct
The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observations α in this data is replaced by β, then the mean and variance become 10.1 and 1.99, respectively. Then α + β equals.
  1. (A)10
  2. (B)15
  3. (C)5
  4. (D)20

Correct answer: (D)

Step-by-step solution →
Q67·MathematicsSingle correct
Let A1\mathrm{A}_{1}A1​ be the bounded area enclosed by the curves y=x2+2y = x^{2} + 2y=x2+2, x+y=8x + y = 8x+y=8 and y-axis that lies in the first quadrant. Let A2\mathrm{A}_{2}A2​ be the bounded area enclosed by the curves y=x2+2y = x^{2} + 2y=x2+2, y2=xy^{2} = xy2=x, x=2x = 2x=2, and y-axis that lies in the first quadrant. Then A1−A2\mathrm{A}_{1} - \mathrm{A}_{2}A1​−A2​ is equal to
  1. (A)23(22+1)\frac{2}{3}\left(2\sqrt{2} + 1\right)32​(22​+1)
  2. (B)23(42+1)\frac{2}{3}\left(4\sqrt{2} + 1\right)32​(42​+1)
  3. (C)23(2+1)\frac{2}{3}\left(\sqrt{2} + 1\right)32​(2​+1)
  4. (D)23(32+1)\frac{2}{3}\left(3\sqrt{2} + 1\right)32​(32​+1)

Correct answer: (A)

Step-by-step solution →
Q68·MathematicsSingle correct
The number of the real solutions of the equation : x∣x+3∣+∣x−1∣−2=0\mathrm{x}\left|\mathrm{x} + 3\right| + \left|\mathrm{x} - 1\right| - 2 = 0x∣x+3∣+∣x−1∣−2=0 is
  1. (A)3
  2. (B)2
  3. (C)5
  4. (D)4

Correct answer: (A)

Step-by-step solution →
Q69·MathematicsNumerical
Let a differentiable function fff satisfy the equation ∫036f(tx36)dt=4αf(x).\int\limits_{0}^{36} f\left(\frac{\mathrm{tx}}{36}\right) \mathrm{dt} = 4\alpha f(\mathrm{x}).0∫36​f(36tx​)dt=4αf(x). If y = fff(x) is a standard parabola passing through the points (2, 1) and (–4, β), Then βα\beta^{\alpha}βα is equal to ______.

Correct answer: 64

Step-by-step solution →
Q70·MathematicsNumerical
Let a line L passing through the point P(1, 1, 1) be perpendicular to the lines x−44=y−11=z−11\frac{\mathrm{x} - 4}{4} = \frac{\mathrm{y} - 1}{1} = \frac{\mathrm{z} - 1}{1}4x−4​=1y−1​=1z−1​ and x−171=y−711=z0\frac{\mathrm{x} - 17}{1} = \frac{\mathrm{y} - 71}{1} = \frac{\mathrm{z}}{0}1x−17​=1y−71​=0z​. Let the line L intersect the yz-plane at the point Q. Another line parallel to L and passing through the point S(1,0, –1) intersects the yz-plane at the point R. Then the square of the area of the parallelogram PQRS is equal to ______.

Correct answer: 6

Step-by-step solution →
Q71·MathematicsNumerical
The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0, 1, 2, 5, 9, if the repetition of the digits is allowed, is ________

Correct answer: 42

Step-by-step solution →
Q72·MathematicsNumerical
Let (2α, α) be the largest interval in which the function f(t)=∣t+1∣t2f(\mathrm{t}) = \frac{|\mathrm{t} + 1|}{\mathrm{t}^{2}}f(t)=t2∣t+1∣​, t < 0, is strictly decreasing. Then the local maximum value of the function g(x)=2log⁡e(x−2)+αx2+4x−αg(\mathrm{x}) = 2 \log_{e}(\mathrm{x} - 2) + \alpha \mathrm{x}^{2} + 4\mathrm{x} - \alphag(x)=2loge​(x−2)+αx2+4x−α, x > 2, is _____

Correct answer: 4

Step-by-step solution →
Q73·MathematicsNumerical
The number of 3 × 2 matrices A, which can be formed using the elements of the set {−2, −1, 0, 1, 2}\{-2,\ -1,\ 0,\ 1,\ 2\}{−2, −1, 0, 1, 2} such that the sum of all the diagonal elements of ATA\mathrm{A}^{\mathrm{T}}\mathrm{A}ATA is 5, is ______

Correct answer: 312

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
  • 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
  • Limits and Continuity 149/186
  • 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
  • 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
  • Quadratic Equations 148/186
  • Wave Optics 130/186
  • Area Under Curves 139/186
  • Alcohols and Ethers 106/186
  • Purification and Characterisation of Organic Compounds 116/186
  • Oscillations 117/186
  • Alternating Currents 108/186
  • Nuclei 116/186
  • Organic Compounds Containing Halogens 109/186
  • Straight Lines 114/186
  • Atoms 112/186
  • Classification of Elements and Periodicity in Properties 113/186
  • Statistics 118/186
  • Ellipse 103/186
  • Differentiability 91/186
  • Electronic Effects and Stability 74/186
  • Electric Potential 63/186
  • Indefinite Integration 66/186
  • Principles of Qualitative Analysis 58/186
  • Diazonium Salts and Reactions 53/186
  • Magnetism and Matter 50/186
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