Jarvis OS
PYQ papersPricingSign inGet started
  1. Home
  2. /JEE Main PYQs
  3. /2026
  4. /28 Jan Shift 1

JEE Main 28 January 2026 Shift 1 Question Paper with Answers

28 January 2026 · January session · 71 questions

71 of the 75 questions from the JEE Main 28 January 2026 Shift 1 paper, each with its correct answer and tagged to the chapter it tests. Free to read, no account needed.

4 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
25
Mathematics
22

Physics — JEE Main 28 January 2026 Shift 1

Q1·PhysicsSingle correct
10 kg of ice at −10°C is added to 100 kg of water to lower its temperature from 25°C. Consider no heat exchange to surroundings. The decrement to the temperature of water is _________ °C. (specific heat of ice = 2100 J/Kg.°C, specific heat of water = 4200 J/Kg.°C, latent heat of fusion of ice = 3.36×1053.36 \times 10^{5}3.36×105 J/Kg)
  1. (A)10
  2. (B)15
  3. (C)6.67
  4. (D)11.6

Correct answer: (A)

Step-by-step solution →
Q2·PhysicsSingle correct
The electric current in the circuit is given as i=i0(t/T)i = i_{0}(t/T)i=i0​(t/T). The r.m.s current for the period t=0t = 0t=0 to t=Tt = Tt=T is __________
  1. (A)i02\frac{i_{0}}{\sqrt{2}}2​i0​​
  2. (B)i0i_{0}i0​
  3. (C)i06\frac{i_{0}}{\sqrt{6}}6​i0​​
  4. (D)i03\frac{i_{0}}{\sqrt{3}}3​i0​​

Correct answer: (D)

Step-by-step solution →
Q3·PhysicsSingle correct
In the potentiometer, when the cell in the secondary circuit is shunted with 4 Ω resistance, the balance is obtained at the length 120 cm of wire. Now when the same cell in shunted with 12 Ω resistance, the balance is shifted to a length of 180 cm. The internal resistance of cell is ___ Ω.
  1. (A)3
  2. (B)4
  3. (C)12
  4. (D)6

Correct answer: (B)

Step-by-step solution →
Q4·PhysicsSingle correct
Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure. If the mass of each disc is 600 gm and applied torque between two discs is 43×10543 \times 10^{5}43×105 dyne cm, the angular acceleration of the discs about the given axis ABABAB is _______ rad/s2^{2}2.
  1. (A)22
  2. (B)11
  3. (C)100
  4. (D)27

Correct answer: (B)

Step-by-step solution →
Q5·PhysicsSingle correct
Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is _______ m. (g=10g = 10g=10 m/s2^{2}2)
  1. (A)2.5
  2. (B)4.0
  3. (C)4.2
  4. (D)3.8

Correct answer: (C)

Step-by-step solution →
Q6·PhysicsSingle correct
The electric field of an electromagnetic wave travelling through a medium is given by E⃗(x,t)=25sin⁡(2.0×1015t−107x)n^\vec{E}(x,t) = 25\sin(2.0 \times 10^{15} t - 10^{7} x)\hat{n}E(x,t)=25sin(2.0×1015t−107x)n^ then the refractive index of the medium is ______ . (All given measurement are in SI units)
  1. (A)1.2
  2. (B)2
  3. (C)1.5
  4. (D)1.7

Correct answer: (C)

Step-by-step solution →
Q7·PhysicsSingle correct
Which of the following best represents the temperature versus heat supplied graph for water, in the range of −20°C to 120°C ?
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (B)

Step-by-step solution →
Q8·PhysicsSingle correct
Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15 cm length of wire QQQ is ______ . (μ0=4π×10−7\mu_{0} = 4\pi \times 10^{-7}μ0​=4π×10−7 T.m/A)
  1. (A)6×10−76 \times 10^{-7}6×10−7 N towards PPP
  2. (B)6×10−66 \times 10^{-6}6×10−6 N towards RRR
  3. (C)6×10−76 \times 10^{-7}6×10−7 N towards RRR
  4. (D)6×10−66 \times 10^{-6}6×10−6 N towards PPP

Correct answer: (B)

Step-by-step solution →
Q9·PhysicsSingle correct
Assuming in forward bias condition there is a voltage drop of 0.7 V across a silicon diode, the current through diode D1D_{1}D1​ in the circuit is ______ mA. (Assume all diodes in the given circuit are identical)
  1. (A)20.15
  2. (B)11.7
  3. (C)17.6
  4. (D)18.8

Correct answer: (D)

Step-by-step solution →
Q10·PhysicsSingle correct
The magnitudes of power of a biconvex lens (refractive index 1.5) and that of a plano-concave lens (refractive index = 1.7) are same. If the curvature of plano-concave lens exactly matches with the curvature of back surface of the biconvex lens, then ratio of radius of curvature of front and back surface of the biconvex lens is ________ .
  1. (A)5 : 2
  2. (B)5 : 12
  3. (C)12 : 5
  4. (D)2 : 5

Correct answer: (A)

Step-by-step solution →
Q11·PhysicsSingle correct
In the following ppp-VVV diagram the equation of state along the curved path is given by (V−2)2=4ap(V - 2)^{2} = 4ap(V−2)2=4ap where aaa is a constant. The total work done in the closed path is
  1. (A)−1a-\frac{1}{a}−a1​
  2. (B)+13a+\frac{1}{3a}+3a1​
  3. (C)12a\frac{1}{2a}2a1​
  4. (D)−13a-\frac{1}{3a}−3a1​

Correct answer: (D)

Step-by-step solution →
Q12·PhysicsSingle correct
For the two cells having same EMF E and internal resistance rrr, the current passing through the external resistor 6 Ω is same when both the cells are connected either in parallel or in series. The value of internal resistance rrr is __________ Ω.
  1. (A)3
  2. (B)4
  3. (C)9
  4. (D)6

Correct answer: (D)

Step-by-step solution →
Q13·PhysicsSingle correct
Two wires AAA and BBB made of different materials of length 6.0 cm and 5.4 cm, respectively and area of cross sections 3.0×10−53.0 \times 10^{-5}3.0×10−5 m2^{2}2 and 4.5×10−54.5 \times 10^{-5}4.5×10−5 m2^{2}2, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of AAA to that of BBB is x : 3. The value of x is ______ .
  1. (A)1
  2. (B)4
  3. (C)2
  4. (D)5

Correct answer: (D)

Step-by-step solution →
Q14·PhysicsSingle correct
A block of mass 5 kg is moving on an inclined plane which makes an angle of 30° with the horizontal. Friction coefficient between the block and inclined plane surface is 32\frac{\sqrt{3}}{2}23​​. The force to be applied on the block so that the block will move down without acceleration is _____ N.
  1. (A)25
  2. (B)12.5
  3. (C)7.5
  4. (D)15

Correct answer: (B)

Step-by-step solution →
Q15·PhysicsSingle correct
Given below are two statements : Statement-I : A plane wave after passing through prism remains as plane wave but passing through small pin hole may become spherical wave. Statement-II : The curvature of a spherical wave emerging from a slit will increase for increasing slit width. 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)Both Statement-I and Statement-II are true.
  3. (C)Statement-I is true but Statement-II is false.
  4. (D)Statement-I is false but Statement-II is true.

Correct answer: (C)

Step-by-step solution →
Q16·PhysicsSingle correct
When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, 4th4^{\text{th}}4th mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and 5th5^{\text{th}}5th division of vernier scale coincides with a min scale division. Measured length of cylinder is ________ mm. (Least count of Vernier calliper = 0.1 mm)
  1. (A)15.4
  2. (B)15.1
  3. (C)15.5
  4. (D)15.9

Correct answer: (B)

Step-by-step solution →
Q17·PhysicsSingle correct
The magnetic field at the centre of a current carrying circular loop of radius RRR is 16 μT. The magnetic field at a distance x=3Rx = \sqrt{3}Rx=3​R on its axis from the centre is ________ μT.
  1. (A)222\sqrt{2}22​
  2. (B)4
  3. (C)2
  4. (D)8

Correct answer: (C)

Step-by-step solution →
Q18·PhysicsSingle correct
Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is _______ μJ. 14π∈0=9×109 N.m2/C2\frac{1}{4\pi \in_{0}} = 9 \times 10^{9}\,\text{N.m}^{2} / \text{C}^{2}4π∈0​1​=9×109N.m2/C2
  1. (A)2.7
  2. (B)5.4
  3. (C)3.3
  4. (D)27

Correct answer: (A)

Step-by-step solution →
Q19·PhysicsSingle correct
A particle of mass m falls from rest through a resistive medium having resistive force, F = –kv, where v is the velocity of the particle and k is a constant. Which of the following graphs represents velocity (v) versus time(t) ?
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (B)

Step-by-step solution →
Q20·PhysicsNumerical
The displacement of a particle, executing simple harmonic motion with time period TTT, is expressed as x(t)x(t)x(t) = A sin ωt, where AAA is the amplitude. The maximum value of potential energy of this oscillator is found at ttt = TTT/2β. The value of β is __________.

Correct answer: 2

Step-by-step solution →
Q21·PhysicsNumerical
The ratio of de Broglie wavelength of a deutron with kinetic energy EEE to that of an alpha particle with kinetic energy 2E2E2E, is nnn : 1. The value of nnn is _________. (Assume mass of proton = mass of neutron) :

Correct answer: 2

Step-by-step solution →
Q22·PhysicsNumerical
A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is n\sqrt{n}n​ cm. The value of nnn is

Correct answer: 265

Step-by-step solution →
Q23·PhysicsNumerical
A convex lens of refractive index 1.5 and focal length fff = 18 cm is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is α × f . The value of α is _________. (refractive index of water = 4/3)

Correct answer: 3

Step-by-step solution →
Q24·PhysicsNumerical
The equivalent resistance between the points AAA and BBB in the following circuit is x5Ω\frac{x}{5}\Omega5x​Ω . The value of xxx is __________.

Correct answer: 21

Step-by-step solution →

Chemistry — JEE Main 28 January 2026 Shift 1

Q25·ChemistrySingle correct
20.0 dm3^{3}3 of an ideal gas 'X' at 600 K and 0.5 MPa undergoes isothermal reversible expansion until pressure of the gas is 0.2 MPa. Which of the following option is correct ? (Given: log 2 = 0.3010 and log 5 = 0.6989)
  1. (A)w = – 9.1 kJ, ΔU = 0, ΔH = 0, q = 9.1 kJ
  2. (B)w = 9.1 J, ΔU = 9.1 J, ΔH = 0; q = 0
  3. (C)w = + 4.1 kJ, ΔU = 0, ΔH = 0; q = – 4.1 kJ
  4. (D)w = – 3.9 kJ, ΔU = 0, ΔH = 0; q = 3.9 kJ

Correct answer: (A)

Step-by-step solution →
Q26·Chemistry·Electronic Effects and StabilitySingle correct
CORRECT order of stability for the following is CH2_{2}2​ = CH−^{-}−, CH3_{3}3​ – CH2−_{2}^{-}2−​, CH ≡ C−^{-}−
  1. (A)CH3_{3}3​ – CH2−_{2}^{-}2−​ > CH2_{2}2​ = CH−^{-}− > CH ≡ C−^{-}−
  2. (B)CH2_{2}2​ = CH−^{-}− > CH ≡ C−^{-}− > CH3_{3}3​ – CH2−_{2}^{-}2−​
  3. (C)CH ≡ C−^{-}− > CH2_{2}2​ = CH−^{-}− > CH3_{3}3​ – CH2−_{2}^{-}2−​
  4. (D)CH ≡ C−^{-}− > CH3_{3}3​ – CH2−_{2}^{-}2−​ > CH2_{2}2​ = CH−^{-}−

Correct answer: (C)

Step-by-step solution →
Q27·ChemistrySingle correct
At T(K), 2 moles of liquid A and 3 moles of liquid B are mixed. The vapour pressure of ideal solution formed is 320 mm Hg. At this stage, one mole of A and one mole of B are added to the solution. The vapour pressure is now measured as 328.6 mm Hg. The vapour pressure (in mm Hg) of A and B are respectively:
  1. (A)300, 200
  2. (B)600, 400
  3. (C)400, 300
  4. (D)500, 200

Correct answer: (D)

Step-by-step solution →
Q28·ChemistrySingle correct
Consider the following reaction sequence Compound (x) [76.6%C, 6.38%H, vapour density 47] →(ii) H3O+(i) CO2, NaOH, 120∘C, high pressure\xrightarrow[\text{(ii) H}_{3}\text{O}^{+}]{\text{(i) CO}_{2}\text{, NaOH, 120}^{\circ}\text{C, high pressure}}(i) CO2​, NaOH, 120∘C, high pressure(ii) H3​O+​ Compound (y) (Major Product) Compound (y) develops characteristic colour with neutral FeCl3_{3}3​ solution. Identify the INCORRECT statement from the following for the above sequence.
  1. (A)Both compounds x and y will dissolve in NaOH.
  2. (B)Compound y will dissolve in NaHCO3_{3}3​ and evolve a gas.
  3. (C)Compound x is more acidic than compound y.
  4. (D)Both compounds x and y will burn with sooty flame.

Correct answer: (C)

Step-by-step solution →
Q29·ChemistrySingle correct
Method used for separation of mixture of products (B and C) obtained in the following reaction is:
  1. (A)Simple distillation
  2. (B)sublimation
  3. (C)steam distillation
  4. (D)fractional distillation

Correct answer: (D)

Step-by-step solution →
Q30·ChemistrySingle correct
Consider a weak base 'B' of pKb_{b}b​ = 5.699. 'x' mL of 0.02 M HCl and 'y' mL of 0.02 M weak base 'B' are mixed to make 100 mL of a buffer of pH 9 at 25ºC. The values of 'x' and 'y' respectively are: [Given: log 2 = 0.3010, log 3 = 0.4771, log 5 = 0.699]
  1. (A)x | y 11.1 | 88.9
  2. (B)x | y 42.7 | 57.3
  3. (C)x | y 14.3 | 85.7
  4. (D)x | y 85.7 | 14.3

Correct answer: (C)

Step-by-step solution →
Q31·ChemistrySingle correct
An organic compound undergoes first order decomposition. The time taken for decomposition to (18)th\left(\dfrac{1}{8}\right)^{th}(81​)th and (110)th\left(\dfrac{1}{10}\right)^{th}(101​)th of its initial concentration are t1/8_{1/8}1/8​ and t1/10_{1/10}1/10​ respectively. What is the value of t1/8t1/10×10\dfrac{\text{t}_{1/8}}{\text{t}_{1/10}} \times 10t1/10​t1/8​​×10 ? (log 2 = 0.3)
  1. (A)9
  2. (B)0.9
  3. (C)3
  4. (D)30

Correct answer: (A)

Step-by-step solution →
Q32·ChemistrySingle correct
Given below are two statements for the following reaction sequence. Statement I: Compound 'Z' will give yellow precipitate with NaOI. Statement II: Compound 'Q' has two different types of 'H' atoms (aromatic : aliphatic) in the ratio 1 : 3. In the light of the above statements, choose the correct answer from the option given below:
  1. (A)Statement I is true but Statement II is false
  2. (B)Both Statement I and Statement II are true
  3. (C)Statement I is false but Statement II is true
  4. (D)Both Statement I and Statement II are false

Correct answer: (B)

Step-by-step solution →
Q33·ChemistrySingle correct
Given below are the four isomeric compounds (P, Q, R, S) Identify correct statements from below. A. Q, R and S will give precipitate with 2, 4 - DNP. B. P and Q will give positive Bayer's test. C. Q and R will give sooty flame. D. R and S will give yellow precipitate with I2_{2}2​/NaOH. E. Q alone will deposit silver with Tollen's reagent Choose the correct option.
  1. (A)A, C and E only
  2. (B)A and E only
  3. (C)C and E only
  4. (D)A, B, D and E only

Correct answer: (A)

Step-by-step solution →
Q34·ChemistrySingle correct
Given below are two statements: Statement I: The number of species among BF4−_{4}^{-}4−​, SiF4_{4}4​, XeF4_{4}4​ and SF4_{4}4​, that have unequal E–F bond lengths is two. Here, E is the central atom. Statement II: Among O2−_{2}^{-}2−​, O22−_{2}^{2-}22−​, F2_{2}2​ and O2+_{2}^{+}2+​, O2−_{2}^{-}2−​ has the highest bond order. 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)Both Statement I and Statement II are true
  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 →
Q35·ChemistrySingle correct
Regarding the hydrides of group 15 elements EH3_{3}3​ (E = N, P, As, Sb), select the correct statement from the following: A. The stability of hydrides decreases down the group. B. The basicity of hydrides decreases down the group. C. The reducing character increases down the group. D. The boiling point increases down the group. Choose the correct answer from the options given below:
  1. (A)A, B & C only
  2. (B)A & D only
  3. (C)A, B, C & D
  4. (D)B & C only

Correct answer: (A)

Step-by-step solution →
Q36·ChemistrySingle correct
Given below are two statements: Statement I: Griss–Ilosvay test is used for the detection of nitrite ion, which involves the use of sulphanilic acid and α–naphthylamine reagent. Statement II: In the above test, sulphanilic acid is diazotized by the acidified nitrite ion, which on further coupling with α–naphthylamine forms an azo-dye. 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: (B)

Step-by-step solution →
Q37·ChemistrySingle correct
Consider the following reactions giving major product. Identify the correct reaction.
  1. (A)(1)
  2. (B)(2)
  3. (C)(3)
  4. (D)(4)

Correct answer: (D)

Step-by-step solution →
Q38·ChemistrySingle correct
In the given pentapeptide, find out an essential amino acid (Y) and the sequence present in the pentapeptide: Choose the correct answer from the options given below:
  1. (A)Threonine | Ser – Thr – Asp – Gly – Ala
  2. (B)Serine | Thr – Ser – Asp – Ala – Gly
  3. (C)Threonine | Thr – Ser – Asp – Gly – Ala
  4. (D)Serine | Ser – Asp – Thr – Ala – Gly

Correct answer: (C)

Step-by-step solution →
Q39·ChemistrySingle correct
Ph−-−CH===CH2_{2}2​ →HBr(PhCOO)2\xrightarrow[\mathrm{HBr}]{(\mathrm{PhCOO})_{2}}(PhCOO)2​HBr​ Product Consider the above reaction A. The reaction proceeds through a more stable radical intermediate. B. The role of peroxide is to generate H∙\overset{\bullet}{\mathrm{H}}H∙ (Hydrogen radical). C. During this reaction, benzene is formed as a biproduct. D. 1-Bromo-2-phenylethane is fanned as the minor product. E. The same reaction in absence of peroxide proceeds via carbocation intermediate. Identify the correct statements. Choose the correct answer from the options given below:
  1. (A)A & E Only
  2. (B)A, B & D Only
  3. (C)C, D & E Only
  4. (D)A, C & E Only

Correct answer: (D)

Step-by-step solution →
Q40·ChemistrySingle correct
The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series. (R = Rydberg constant)
  1. (A)5R36,3R16,21R100\frac{5R}{36}, \frac{3R}{16}, \frac{21R}{100}365R​,163R​,10021R​
  2. (B)5R36,8R9,15R16\frac{5R}{36}, \frac{8R}{9}, \frac{15R}{16}365R​,98R​,1615R​
  3. (C)7R144,3R16,16R255\frac{7R}{144}, \frac{3R}{16}, \frac{16R}{255}1447R​,163R​,25516R​
  4. (D)3R4,3R16,7R144\frac{3R}{4}, \frac{3R}{16}, \frac{7R}{144}43R​,163R​,1447R​

Correct answer: (A)

Step-by-step solution →
Q41·ChemistrySingle correct
Figure 1. electron probability density for 2s orbital Figure 2. wave function for 2s orbital Which of the following point in Figure 2 most accurately represents the nodal surface as shown in Figure 1 ?
  1. (A)B
  2. (B)D
  3. (C)C
  4. (D)A

Correct answer: (A)

Step-by-step solution →
Q42·ChemistrySingle correct
Given below are two statements : Statement I : The number of pairs, from the following, in which both the ions are coloured in aqueous solution is 3. [Sc3+^{3+}3+, Ti3+^{3+}3+], [Mn2+^{2+}2+, Cr2+^{2+}2+], [Cu2+^{2+}2+, Zn2+^{2+}2+] and [Ni2+^{2+}2+, Ti4+^{4+}4+] Statement II : Th4+^{4+}4+ is the strongest reducing agent among Th4+^{4+}4+, Ce4+^{4+}4+, Gd3+^{3+}3+ and Eu2+^{2+}2+. In the light of the above statements, choose the correct answer from the options given below
  1. (A)Statement I is true but Statement II is false
  2. (B)Statement I is false but Statement II is true
  3. (C)Both Statement I and Statement II are false
  4. (D)Both Statement I and Statement II are true

Correct answer: (C)

Step-by-step solution →
Q43·ChemistrySingle correct
In period 4 of the periodic table, the elements with highest and lowest atomic radii are respectively.
  1. (A)Na & Cl
  2. (B)K & Se
  3. (C)K & Br
  4. (D)Rb & Br

Correct answer: (C)

Step-by-step solution →
Q44·ChemistrySingle correct
The correct statement among the following is :
  1. (A)[Ni(CN)4_{4}4​]2−^{2-}2− and [NiCl4_{4}4​]2−^{2-}2− are diamagnetic and Ni(CO)4_{4}4​ is paramagnetic.
  2. (B)Ni(CO)4_{4}4​ and [NiCl4_{4}4​]2−^{2-}2− are diamagnetic and [Ni(CN)4_{4}4​]2−^{2-}2− is paramagnetic.
  3. (C)Ni(CO)4_{4}4​ and [Ni(CN)4_{4}4​]2−^{2-}2− are diamagnetic and [NiCl4_{4}4​]2−^{2-}2− is paramagnetic.
  4. (D)Ni(CO)4_{4}4​ is diamagnetic and [NiCl4_{4}4​]2−^{2-}2− and [Ni(CN)4_{4}4​]2−^{2-}2− are paramagnetic.

Correct answer: (C)

Step-by-step solution →
Q45·ChemistryNumerical
500 mL of 1.2 M KI solution is mixed with 500 mL of 0.2 M KMnO4_{4}4​ solution in basic medium. The liberated iodine was titrated with standard 0.1 M Na2_{2}2​S2_{2}2​O3_{3}3​ solution in the presence of starch indicator till the blue color disappeared. The volume (in L) of Na2_{2}2​S2_{2}2​O3_{3}3​ consumed is________. (Nearest integer)

Correct answer: 3

Step-by-step solution →
Q46·ChemistryNumerical
Consider the following redox reaction taking place in acidic medium BH4−_{4}^{-}4−​(aq) +++ ClO3−_{3}^{-}3−​(aq) →\rightarrow→ H2_{2}2​BO3−_{3}^{-}3−​(aq) +++ Cl−^{-}−(aq) If the Nernst equation for the above balanced reaction is Ecell_{\mathrm{cell}}cell​ = Ecello_{\mathrm{cell}}^{\mathrm{o}}cello​ −-− R TnF\frac{\mathrm{R\,T}}{\mathrm{nF}}nFRT​ ℓ\ellℓn Q, Then the value of n is _________. (Nearest integer)

Correct answer: 24

Step-by-step solution →
Q47·ChemistryNumerical
X is the number of geometrical isomers exhibited by [Pt(NH3_{3}3​)(H2_{2}2​O)BrCl]. Y is the number of optically inactive isomer(s) exhibited by [CrCl2_{2}2​(ox)2_{2}2​]3−^{3-}3− Z is the number of geometrical isomers exhibited by [Co(NH3_{3}3​)3_{3}3​(NO2_{2}2​)3_{3}3​] The value of X + Y + Z is _________ .

Correct answer: 6

Step-by-step solution →
Q48·ChemistryNumerical
0.53 g of an organic compound (x) when heated with excess of nitric acid (concentrated) and then with silver nitrate gave 0.75 g of silver bromide precipitate. 1.0 g of (x) gave 1.32 g of CO2_{2}2​ gas on combustion. The percentage of hydrogen in the compound (x) is ________ %. [Nearest Integer] [Given : Molar mass in g mol−1^{-1}−1 H : 1, C : 12, Br : 80, Ag : 108, O : 16; Compound (x) : Cx_{x}x​Hy_{y}y​Brz_{z}z​]

Correct answer: 4

Step-by-step solution →
Q49·ChemistryNumerical
Consider the dissociation equilibrium of the following weak acid HA ⇌\rightleftharpoons⇌ H+^{+}+(aq) +++ A−^{-}−(aq) If the pKa of the acid is 4, then the pH of 10 mM HA solution is ________. (Nearest integer) [Given : The degree of dissociation can be neglected with respect to unity]

Correct answer: 3

Step-by-step solution →

Mathematics — JEE Main 28 January 2026 Shift 1

Q50·MathematicsSingle correct
If g(x)=3x2+2x−3g(x) = 3x^2 + 2x - 3g(x)=3x2+2x−3, f(0)=−3f(0) = -3f(0)=−3 and 4g(f(x))=3x2−32x+724g(f(x)) = 3x^2 - 32x + 724g(f(x))=3x2−32x+72, then f(g(2))f(g(2))f(g(2)) is equal to:
  1. (A)256\dfrac{25}{6}625​
  2. (B)−256-\dfrac{25}{6}−625​
  3. (C)72\dfrac{7}{2}27​
  4. (D)−72-\dfrac{7}{2}−27​

Correct answer: (C)

Step-by-step solution →
Q51·MathematicsSingle correct
The value of ∑k=1∞(−1)k+1(k(k+1)k!)\sum\limits_{k=1}^{\infty} (-1)^{k+1}\left(\dfrac{k(k+1)}{k!}\right)k=1∑∞​(−1)k+1(k!k(k+1)​) is :
  1. (A)2/e2/e2/e
  2. (B)1/e1/e1/e
  3. (C)e\sqrt{e}e​
  4. (D)e/2e/2e/2

Correct answer: (B)

Step-by-step solution →
Q52·MathematicsSingle correct
Let y=xy = xy=x be the equation of a chord of the circle C1C_1C1​ (in the closed half-plane x≥0x \ge 0x≥0) of diameter 10 passing through the origin. Let C2C_2C2​ be another circle described on the given chord as its diameter. If the equation of the chord of the circle C2C_2C2​, which passes through the point (2,3)(2, 3)(2,3) and is farthest from the center of C2C_2C2​, is x+ay+b=0x + ay + b = 0x+ay+b=0, then a−ba - ba−b is equal to :
  1. (A)10
  2. (B)−6
  3. (C)−2
  4. (D)6

Correct answer: (C)

Step-by-step solution →
Q53·MathematicsSingle correct
If tan⁡(A−B)tan⁡A+sin⁡2Csin⁡2A=1\dfrac{\tan(A-B)}{\tan A} + \dfrac{\sin^2 C}{\sin^2 A} = 1tanAtan(A−B)​+sin2Asin2C​=1, AAA, BBB, C∈(0,π2)C \in \left(0, \dfrac{\pi}{2}\right)C∈(0,2π​), then
  1. (A)tan⁡A\tan AtanA, tan⁡C\tan CtanC, tan⁡B\tan BtanB are in G.P.
  2. (B)tan⁡A\tan AtanA, tan⁡B\tan BtanB, tan⁡C\tan CtanC are in G.P.
  3. (C)tan⁡A\tan AtanA, tan⁡C\tan CtanC, tan⁡B\tan BtanB are in A.P.
  4. (D)tan⁡A\tan AtanA, tan⁡B\tan BtanB, tan⁡C\tan CtanC are in A.P.

Correct answer: (A)

Step-by-step solution →
Q54·MathematicsSingle correct
Let zzz be a complex number such that ∣z−6∣=5|z - 6| = 5∣z−6∣=5 and ∣z+2−6i∣=5|z + 2 - 6i| = 5∣z+2−6i∣=5. Then the value of z3+3z2−15z+141z^3 + 3z^2 - 15z + 141z3+3z2−15z+141 is equal to
  1. (A)42
  2. (B)37
  3. (C)50
  4. (D)61

Correct answer: (C)

Step-by-step solution →
Q55·MathematicsSingle correct
Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line x+22 y=4x + 2\sqrt{2}\,y = 4x+22​y=4. If the co-ordinates of the vertex A are (α,β)(\alpha, \beta)(α,β), then the greatest integer less than or equal to ∣α+2 β∣\left|\alpha + \sqrt{2}\,\beta\right|​α+2​β​ is
  1. (A)2
  2. (B)3
  3. (C)5
  4. (D)4

Correct answer: (D)

Step-by-step solution →
Q56·MathematicsSingle correct
Let S={1,2,3,4,5,6,7,8,9}S = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}S={1,2,3,4,5,6,7,8,9} . Let xxx be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let yyy be the number of 9-digit numbers formed using the digits of the set S such that only two digits are repeated and each of these is repeated exactly twice. Then,
  1. (A)29x=5y29x = 5y29x=5y
  2. (B)45x=7y45x = 7y45x=7y
  3. (C)21x=4y21x = 4y21x=4y
  4. (D)56x=9y56x = 9y56x=9y

Correct answer: (C)

Step-by-step solution →
Q57·MathematicsSingle correct
Let S={x3+ax2+bx+c:a,b,c∈NS = \{x^3 + ax^2 + bx + c : a, b, c \in NS={x3+ax2+bx+c:a,b,c∈N and a,b,c≤20}a, b, c \le 20\}a,b,c≤20} be a set of polynomials. Then the number of polynomials in S, which are divisible by x2+2x^2 + 2x2+2, is
  1. (A)20
  2. (B)6
  3. (C)120
  4. (D)10

Correct answer: (D)

Step-by-step solution →
Q58·MathematicsSingle correct
If α\alphaα, β\betaβ, where α<β\alpha < \betaα<β, are the roots of the equation λx2−(λ+3)x+3=0\lambda x^2 - (\lambda + 3)x + 3 = 0λx2−(λ+3)x+3=0 such that 1α−1β=13\dfrac{1}{\alpha} - \dfrac{1}{\beta} = \dfrac{1}{3}α1​−β1​=31​, then the sum of all possible values of λ\lambdaλ is :
  1. (A)6
  2. (B)2
  3. (C)4
  4. (D)8

Correct answer: (A)

Step-by-step solution →
Q59·MathematicsSingle correct
If ∫(1−5cos⁡2xsin⁡5xcos⁡2x)dx=f(x)+C\int\left(\dfrac{1 - 5\cos^2 x}{\sin^5 x \cos^2 x}\right)dx = f(x) + C∫(sin5xcos2x1−5cos2x​)dx=f(x)+C where C is the constant of integration, then f(π6)−f(π4)f\left(\dfrac{\pi}{6}\right) - f\left(\dfrac{\pi}{4}\right)f(6π​)−f(4π​) is equal to
  1. (A)13(26+3)\dfrac{1}{\sqrt{3}}\left(26 + \sqrt{3}\right)3​1​(26+3​)
  2. (B)43(8−6)\dfrac{4}{\sqrt{3}}\left(8 - \sqrt{6}\right)3​4​(8−6​)
  3. (C)13(26−3)\dfrac{1}{\sqrt{3}}\left(26 - \sqrt{3}\right)3​1​(26−3​)
  4. (D)23(4+6)\dfrac{2}{\sqrt{3}}\left(4 + \sqrt{6}\right)3​2​(4+6​)

Correct answer: (B)

Step-by-step solution →
Q60·MathematicsSingle correct
Let fff be a polynomial function such that f(x2+1)=x4+5x2+2f(x^2 + 1) = x^4 + 5x^2 + 2f(x2+1)=x4+5x2+2, for all x∈Rx \in \mathbb{R}x∈R. Then ∫03f(x) dx\int\limits_{0}^{3} f(x)\,dx0∫3​f(x)dx is equal to
  1. (A)413\dfrac{41}{3}341​
  2. (B)332\dfrac{33}{2}233​
  3. (C)272\dfrac{27}{2}227​
  4. (D)53\dfrac{5}{3}35​

Correct answer: (B)

Step-by-step solution →
Q61·MathematicsSingle correct
The area of the region R={(x,y):xy≤8,1≤y≤x2,x≥0}R = \{(x, y) : xy \le 8, 1 \le y \le x^2, x \ge 0\}R={(x,y):xy≤8,1≤y≤x2,x≥0} is
  1. (A)13(49log⁡e(2)−15)\dfrac{1}{3}\left(49\log_e(2) - 15\right)31​(49loge​(2)−15)
  2. (B)23(20log⁡e(2)+9)\dfrac{2}{3}\left(20\log_e(2) + 9\right)32​(20loge​(2)+9)
  3. (C)23(24log⁡e(2)−7)\dfrac{2}{3}\left(24\log_e(2) - 7\right)32​(24loge​(2)−7)
  4. (D)13(40log⁡e(2)+27)\dfrac{1}{3}\left(40\log_e(2) + 27\right)31​(40loge​(2)+27)

Correct answer: (C)

Step-by-step solution →
Q62·MathematicsSingle correct
The value of lim⁡x→0log⁡e(sec⁡(ex).sec⁡(e2x)⋅...⋅sec⁡(e10x))e2−e2cos⁡x\lim_{x \to 0} \dfrac{\log_e\left(\sec(ex).\sec\left(e^{2}x\right)\cdot ... \cdot \sec\left(e^{10}x\right)\right)}{e^{2} - e^{2\cos x}}limx→0​e2−e2cosxloge​(sec(ex).sec(e2x)⋅...⋅sec(e10x))​ is equal to
  1. (A)(e10−1)2e2(e2−1)\dfrac{(e^{10}-1)}{2e^{2}(e^{2}-1)}2e2(e2−1)(e10−1)​
  2. (B)(e20−1)2e2(e2−1)\dfrac{(e^{20}-1)}{2e^{2}(e^{2}-1)}2e2(e2−1)(e20−1)​
  3. (C)(e20−1)2(e2−1)\dfrac{(e^{20}-1)}{2(e^{2}-1)}2(e2−1)(e20−1)​
  4. (D)(e10−1)2(e2−1)\dfrac{(e^{10}-1)}{2(e^{2}-1)}2(e2−1)(e10−1)​

Correct answer: (C)

Step-by-step solution →
Q63·MathematicsSingle correct
The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2, 3, 5, 10, 11, 13, 15, 21, then the mean deviation about the median of all the 10 observations is
  1. (A)5
  2. (B)4
  3. (C)6
  4. (D)7

Correct answer: (A)

Step-by-step solution →
Q64·MathematicsSingle correct
Let A, B and C be three 2×22\times22×2 matrices with real entries such that B=(I+A)−1B = (I + A)^{-1}B=(I+A)−1 and A+C=IA + C = IA+C=I. If BC=[1−5−12]BC = \begin{bmatrix} 1 & -5 \\ -1 & 2 \end{bmatrix}BC=[1−1​−52​] and CB[x1x2]=[12−6]CB\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} 12 \\ -6 \end{bmatrix}CB[x1​x2​​]=[12−6​], then x1+x2x_1 + x_2x1​+x2​ is
  1. (A)2
  2. (B)0
  3. (C)–2
  4. (D)4

Correct answer: (B)

Step-by-step solution →
Q65·MathematicsSingle correct
The common difference of the A.P.: a1a_1a1​, a2a_2a2​, …., ama_mam​ is 13 more than the common difference of the A.P.: b1b_1b1​, b2b_2b2​, …., bnb_nbn​. If b31b_{31}b31​ = –277, b43b_{43}b43​ = –385 and a78a_{78}a78​ = 327, then a1a_1a1​ is equal to
  1. (A)21
  2. (B)24
  3. (C)19
  4. (D)16

Correct answer: (C)

Step-by-step solution →
Q66·MathematicsSingle correct
If the distances of the point (1, 2, a) from the line x−11=y2=z−11\dfrac{x-1}{1} = \dfrac{y}{2} = \dfrac{z-1}{1}1x−1​=2y​=1z−1​ along the lines L1:x−13=y−24=z−abL_1 : \dfrac{x-1}{3} = \dfrac{y-2}{4} = \dfrac{z-a}{b}L1​:3x−1​=4y−2​=bz−a​ and L2:x−11=y−24=z−acL_2 : \dfrac{x-1}{1} = \dfrac{y-2}{4} = \dfrac{z-a}{c}L2​:1x−1​=4y−2​=cz−a​ are equal, then a + b + c is equal to
  1. (A)7
  2. (B)5
  3. (C)6
  4. (D)4

Correct answer: (A)

Step-by-step solution →
Q67·MathematicsSingle correct
For three unit vectors a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c}a,b,c satisfying ∣a⃗−b⃗∣2+∣b⃗−c⃗∣2+∣c⃗−a⃗∣2=9\left|\vec{a}-\vec{b}\right|^{2} + \left|\vec{b}-\vec{c}\right|^{2} + \left|\vec{c}-\vec{a}\right|^{2} = 9​a−b​2+​b−c​2+∣c−a∣2=9 and ∣2a⃗+kb⃗+kc⃗∣=3\left|2\vec{a} + k\vec{b} + k\vec{c}\right| = 3​2a+kb+kc​=3, the positive value of k is :
  1. (A)3
  2. (B)6
  3. (C)4
  4. (D)5

Correct answer: (D)

Step-by-step solution →
Q68·MathematicsNumerical
In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms is R\mathbb{R}R – (a, b ), then a2+b2a^{2} + b^{2}a2+b2 is equal to ____.

Correct answer: 90

Step-by-step solution →
Q69·MathematicsNumerical
For some θ∈(0,π2)\theta \in \left(0, \dfrac{\pi}{2}\right)θ∈(0,2π​), let the eccentricity and the length of the latus rectum of the hyperbola x2−y2sec⁡2θ=8x^{2} - y^{2}\sec^{2}\theta = 8x2−y2sec2θ=8 be e1e_1e1​ and ℓ1\ell_1ℓ1​, respectively, and let the eccentricity and the length of the latus rectum of the ellipse x2sec⁡2θ+y2=6x^{2}\sec^{2}\theta + y^{2} = 6x2sec2θ+y2=6 be e2e_2e2​ and ℓ2\ell_2ℓ2​, respectively. If e12=e22(sec⁡2θ+1)e_1^{2} = e_2^{2}\left(\sec^{2}\theta + 1\right)e12​=e22​(sec2θ+1), then (ℓ1ℓ2e1e2)tan⁡2θ\left(\dfrac{\ell_1\ell_2}{e_1e_2}\right)\tan^{2}\theta(e1​e2​ℓ1​ℓ2​​)tan2θ is equal to _____.

Correct answer: 8

Step-by-step solution →
Q70·MathematicsNumerical
If k=tan⁡(π4+12cos⁡−1(23))+tan⁡(12sin⁡−1(23))k = \tan\left(\dfrac{\pi}{4} + \dfrac{1}{2}\cos^{-1}\left(\dfrac{2}{3}\right)\right) + \tan\left(\dfrac{1}{2}\sin^{-1}\left(\dfrac{2}{3}\right)\right)k=tan(4π​+21​cos−1(32​))+tan(21​sin−1(32​)) then the number of solutions of the equation sin⁡−1(kx−1)=sin⁡−1x−cos⁡−1x\sin^{-1}(kx - 1) = \sin^{-1}x - \cos^{-1}xsin−1(kx−1)=sin−1x−cos−1x is ______.

Correct answer: 1

Step-by-step solution →
Q71·MathematicsNumerical
The value of ∑r=120(∣π(∫0rx ∣sin⁡πx ∣dx)∣)\sum_{r=1}^{20}\left(\left|\sqrt{\pi\left(\int_{0}^{r} x\,|\sin \pi x\,|dx\right)}\right|\right)∑r=120​(​π(∫0r​x∣sinπx∣dx)​​) is ____.

Correct answer: 210

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
  • Permutations and Combinations 162/186
  • Magnetic Field of Current 147/186
  • 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
  • Hydrocarbons 126/186
  • Complex Numbers 165/186
  • Trigonometric Functions 144/186
  • Biomolecules 162/186
  • Chemical Kinetics 169/186
  • 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
  • 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
  • Straight Lines 114/186
  • Classification of Elements and Periodicity in Properties 113/186
  • Statistics 118/186
  • Inverse Trigonometric Functions 93/186
  • Electronic Effects and Stability 74/186
  • Hyperbola 77/186
  • Experimental Skills 68/186
  • Electric Potential 63/186
  • Indefinite Integration 66/186
  • Principles of Qualitative Analysis 58/186
← 24 Jan Shift 2 2026All papers28 Jan Shift 2 2026 →

Attempt this paper under exam timing.

Take the 28 January 2026 Shift 1 paper as a timed mock and Jarvis marks it, then tells you which errors were conceptual gaps, which were silly mistakes, and which pattern you have now repeated. Step-by-step solutions for every question included.

Attempt this paper freeSee pricing

Free plan, no time limit · No credit card needed

Jarvis OS

AI-powered JEE preparation.

Question papers

JEE Main PYQsJEE Advanced PYQsPhysics PYQsChemistry PYQsMaths PYQs

Product

TourPricingSign inCreate account

Legal

Privacy PolicyTerms of ServiceRefund & CancellationShipping & DeliveryContact Us

Operated by

Venyou Craft Private Limited

info@jarvisos.net

© 2026 Jarvis OS