The magnetic field of an E.M. wave is given by B = ( √(3) 2 i + (1)/(2)j ) 30 (ω t - (z)/(c) ) (S.I. Units). The corresponding electric field in S.I. units is:

E = ((1)/(2)i - √(3) 2 j ) 30c (ω t - (z)/(c) )

JEE Main 2025 January 28, Shift 2 Question Paper with Solutions

Q: How many questions are in the JEE Main 2025 January 28, Shift 2 paper?

The JEE Main 2025 January 28, Shift 2 paper has 75 questions — Physics (25), Chemistry (25) and Mathematics (25). Every question is on this page with its correct answer and a step-by-step solution.

Q: What is the marking scheme for JEE Main?

JEE Main awards +4 marks for each correct answer and −1 for a wrong answer, with 0 for questions left unattempted. The paper covers Physics, Chemistry and Mathematics.

Q: Are the answer key and step-by-step solutions provided for the 2025 January 28, Shift 2 paper?

Yes — every question shows the correct answer (answer key) and a detailed step-by-step solution, free to read online.

Q: Can I take the JEE Main 2025 January 28, Shift 2 paper as a timed mock test?

Yes. With a free JEEnify account you can attempt this exact paper as a timed test in the real exam interface, then see your score and weak-area analysis.

All 75 questions from the JEE Main 2025 (January 28, Shift 2) shift — Physics (25), Chemistry (25) and Mathematics (25) — each with the correct answer (answer key) and a step-by-step solution. Read it free online, or attempt the full paper as a timed mock test.

Physics PYQs 2025 Chemistry PYQs 2025 Mathematics PYQs 2025

Physics25 questions

Q26Single correctElectromagnetic Induction and Alternating Currents

A uniform magnetic field of

0.4

T acts perpendicular to a circular copper disc

20

cm in radius. The disc is having a uniform angular velocity of

10 π

rad

s^{- 1}

about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim? (

π = 3.14

)

(A)

0.0628

(B)

0.5024

(C)

0.2512

(D)

0.1256

Q27Single correctElectrostatics

A parallel plate capacitor of capacitance

1

μF is charged to a potential difference of

20

V. The distance between plates is

1

m. The energy density between plates of capacitor is:

(A)

1.8 \times 1 0^{3}

m^{3}

(B)

2 \times 1 0^{- 4}

m^{3}

(C)

2 \times 1 0^{2}

m^{3}

(D)

1.8 \times 1 0^{5}

m^{3}

Q28Single correctUnits and Measurements

Match List-I with List-II

List-I (Physical Quantity)	List-II (Dimensional Formula)
(A) Angular Impulse	(I) $[M^{0} L^{2} T^{- 2}]$
(B) Latent Heat	(II) $[M L^{2} T^{- 3} A^{- 1}]$
(C) Electrical resistivity	(III) $[M L^{2} T^{- 1}]$
(D) Electromotive force	(IV) $[M L^{3} T^{- 3} A^{- 2}]$

Choose the correct answer from the options given below:

(A)

(A)-(III), (B)-(I), (C)-(IV), (D)-(II)

(B)

(A)-(I), (B)-(III), (C)-(IV), (D)-(II)

(C)

(A)-(III), (B)-(I), (C)-(II), (D)-(IV)

(D)

(A)-(II), (B)-(I), (C)-(IV), (D)-(III)

Q29Single correctKinetic Theory of Gases

The ratio of vapour densities of two gases at the same temperature is

\frac{4}{25}

, then the ratio of r.m.s. velocities will be:

(A)

\frac{25}{4}

(B)

\frac{2}{5}

(C)

\frac{5}{2}

(D)

\frac{4}{25}

Q30Single correctKinetic Theory of Gases

The kinetic energy of translation of the molecules in

50

g of C

O_{2}

gas at

17°

C is:

(A)

3986.3

(B)

4102.8

(C)

4205.5

(D)

3582.7

Q31Single correctOptics

In a long glass tube, mixture of two liquids A and B with refractive indices

1.3

and

1.4

respectively, forms a convex refractive meniscus towards A. If an object placed at

13

cm from the vertex of the meniscus in A forms an image with a magnification of '

- 2

' then the radius of curvature of meniscus is:

(A)

1

(B)

\frac{1}{3}

(C)

\frac{2}{3}

(D)

\frac{4}{3}

Q32Single correctAtoms and Nuclei

The frequency of revolution of the electron in Bohr's orbit varies with

n

, the principal quantum number as

(A)

\frac{1}{n}

(B)

\frac{1}{n ^{3}}

(C)

\frac{1}{n ^{4}}

(D)

\frac{1}{n ^{2}}

Q33Single correctDual Nature of Matter and Radiation

Which of the following phenomena can not be explained by wave theory of light?

(A)

Reflection of light

(B)

Diffraction of light

(C)

Refraction of light

(D)

Compton effect

Q34Single correctKinematics

The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between

t = 0

t = 4 s

(A)

30 m

(B)

10 m

(C)

13 m

(D)

11 m

Q35Single correctMagnetic Effects of Current and Magnetism

A bar magnet has total length

2 l = 20

units and the field point P is at a distance

d = 10

units from the centre of the magnet. If the relative uncertainty of length measurement is 1%, then uncertainty of the magnetic field at point P is:

(A)

10%

(B)

4%

(C)

3%

(D)

5%

Q36Single correctGravitation

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:

(A)

11.2

(B)

5.6

(C)

2.8

(D)

8.4

Q37Single correctOscillations and Waves

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). **Assertion (A):** Knowing initial position

x_{0}

and initial momentum

p_{0}

is enough to determine the position and momentum at any time t for a simple harmonic motion with a given angular frequency

ω

. **Reason (R):** The amplitude and phase can be expressed in terms of

x_{0}

and

p_{0}

. In the light of the above statements, choose the correct answer from the options given below:

(A)

Both (A) and (R) are true but (R) is NOT the correct explanation of (A).

(B)

(A) is false but (R) is true.

(C)

(A) is true but (R) is false.

(D)

Both (A) and (R) are true and (R) is the correct explanation of (A).

Q38Single correctOptics

A concave mirror produces an image of an object such that the distance between the object and image is 20 cm. If the magnification of the image is '−3', then the magnitude of the radius of curvature of the mirror is:

(A)

3.75 cm

(B)

30 cm

(C)

7.5 cm

(D)

15 cm

Q39Single correctWork, Energy and Power

A body of mass 4 kg is placed on a plane at a point P having coordinate (3, 4) m. Under the action of force

F = (2 \hat{i} + 3 \hat{j})

N, it moves to a new point Q having coordinates (6, 10)m in 4 sec. The average power and instantaneous power at the end of 4 sec are in the ratio of:

(A)

13 : 6

(B)

6 : 13

(C)

1 : 2

(D)

4 : 3

Q40Single correctElectronic Devices

In the circuit shown here, assuming threshold voltage of diode is negligibly small, then voltage

V_{A B}

is correctly represented by:

(A)

V_{A B}

would be zero at all times

(B)

(C)

(D)

Q41Single correctMagnetic Effects of Current and Magnetism

An infinite wire has a circular bend of radius

a

, and carrying a current

I

as shown in figure. The magnitude of magnetic field at the origin O of the arc is given by:

(A)

\frac{μ _{0} I}{4 πa} (\frac{π}{2} + 1)

(B)

\frac{μ _{0} I}{4 πa} (\frac{3 π}{2} + 1)

(C)

\frac{μ _{0} I}{2 πa} (\frac{π}{2} + 2)

(D)

\frac{μ _{0} I}{4 πa} (\frac{3 π}{2} + 2)

Q42Single correctRotational Motion

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is

(A)

300

g

(B)

190

g

(C)

200

g

(D)

290

g

Q43Single correctProperties of Solids and Liquids

A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water? (Given: density of water = 1000 kg

m^{- 3}

)

(A)

1400

cm

(B)

4000

cm

(C)

400

cm

(D)

600

cm

Q44Single correctElectromagnetic Waves

The magnetic field of an E.M. wave is given by

B = (\frac{3}{2} \hat{i} + \frac{1}{2} \hat{j}) 30 sin (ω t - \frac{z}{c})

(S.I. Units). The corresponding electric field in S.I. units is:

(A)

E = (\frac{1}{2} \hat{i} - \frac{3}{2} \hat{j}) 30 c sin (ω t - \frac{z}{c})

(B)

E = (\frac{3}{4} \hat{i} + \frac{1}{4} \hat{j}) 30 c cos (ω t - \frac{z}{c})

(C)

E = (\frac{1}{2} \hat{i} + \frac{3}{2} \hat{j}) 30 c sin (ω t + \frac{z}{c})

(D)

E = (\frac{3}{2} \hat{i} - \frac{1}{2} \hat{j}) 30 c sin (ω t + \frac{z}{c})

Q45Single correctLaws of Motion

A balloon and its content having mass M is moving up with an acceleration 'a'. The mass that must be released from the content so that the balloon starts moving up with an acceleration '3a' will be: (Take 'g' as acceleration due to gravity)

(A)

\frac{3 M a}{2 a + g}

(B)

\frac{3 M a}{2 a - g}

(C)

\frac{2 M a}{3 a + g}

(D)

\frac{2 M a}{3 a - g}

Q46NumericalElectromagnetic Induction and Alternating Currents

A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time t = 0 with a constant velocity. If the induced

EMF i s E \propto

t^{n}

, then value of n is ___.

Q47NumericalElectrostatics

An electric dipole of dipole moment

6 \times

1 0^{- 6}

C-m

is placed in uniform electric field of magnitude

1 0^{6}

V/m

. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be _____ J.

Q48NumericalProperties of Solids and Liquids

The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure

o f 7 \times

1 0^{6}

Pa

, would be _____

m m^{3}

. (Given bulk modulus of copper

= 1.4 \times

1 0^{11}

N m

^{- 2})

Q49NumericalCurrent Electricity

The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be __________ A.

Q50NumericalOptics

A thin transparent film with refractive index 1.4, is held on circular ring of radius 1.8 cm. The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the rate of evaporation is _______

\times 1 0^{- 13} m^{3} / s

Chemistry25 questions

Q51Single correctChemical Kinetics

Consider the elementary reaction

A (g) + B (g) \to C (g) + D (g)

. If the volume of reaction mixture is suddenly reduced to

\frac{1}{3}

of its initial volume, the reaction rate will become 'x' times of the original reaction rate. The value of x is:

(A)

\frac{1}{9}

(B)

9

(C)

\frac{1}{3}

(D)

3

Q52Single correctd- and f-Block Elements

The amphoteric oxide among

V_{2} O_{3}

V_{2} O_{4}

and

V_{2} O_{5}

upon reaction with alkali leads to formation of an oxide anion. The oxidation state of V in the oxide anion is:

(A)

+ 3

(B)

+ 7

(C)

+ 5

(D)

+ 4

Q53Single correctBiomolecules

Match List-I with List-II

List-I (Saccharides)	List-II (Glycosidic linkages found)
(A) Sucrose	(I) $α$ 1-4
(B) Maltose	(II) $α$ 1-4 and $α$ 1-6
(C) Lactose	(III) $α$ 1- $β$ 2
(D) Amylopectin	(IV) $β$ 1-4

Choose the correct answer from the options given below:

(A)

(A)-(III), (B)-(I), (C)-(IV), (D)-(II)

(B)

(A)-(IV), (B)-(II), (C)-(I), (D)-(III)

(C)

(A)-(II), (B)-(IV), (C)-(III), (D)-(I)

(D)

(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

Q54Single correctHydrocarbons

Identify product [A], [B] and [C] in the following reaction sequence:

C H_{3} - C \equiv C H H_{2}, P d / C [A] (i) O_{3}, (ii) Z n, H_{2} O [B] + [C]

(A)

[A]:

C H_{3} - C H = C H_{2}

, [B]:

C H_{3} CHO

, [C]: HCHO

(B)

[A]:

C H_{2} = C H_{2}

, [B]:

H_{3} C - C (= O) - C H_{3}

, [C]: HCHO

(C)

[A]:

C H_{3} - C H = C H_{2}

, [B]:

C H_{3} CHO

, [C]:

C H_{3} C H_{2} O H

(D)

[A]:

C H_{3} C H_{2} C H_{3}

, [B]:

C H_{3} CHO

, [C]: HCHO

Q55Single correctEquilibrium

Arrange the following in increasing order of solubility product:

C a (O H)_{2}

, AgBr, PbS, HgS

(A)

PbS < HgS < C a (O H)_{2} < AgBr

(B)

HgS < PbS < AgBr < C a (O H)_{2}

(C)

C a (O H)_{2} < AgBr < HgS < PbS

(D)

HgS < AgBr < PbS < C a (O H)_{2}

Q56Single correctPurification and Characterisation of Organic Compounds

The purification method based on the following physical transformation is:

Solid (X) Heat Vapour (X) Cool Solid (X)

(A)

Sublimation

(B)

Distillation

(C)

Crystallization

(D)

Extraction

Q57Single correctBiomolecules

Identify correct conversion during acidic hydrolysis from the following:

(A) starch gives galactose
(B) cane sugar gives equal amount of glucose and fructose
(C) milk sugar gives glucose and galactose
(D) amylopectin gives glucose and fructose
(E) amylose gives only glucose

Choose the correct answer from the options given below:

(A)

(C), (D) and (E) only

(B)

(A), (B) and (C) only

(C)

(B), (C) and (E) only

(D)

(B), (C) and (D) only

Q58Single correctChemical Thermodynamics

An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path A

\to

B \to C \to D \to A a s

shown in the three cases. Choose the correct option regarding

Δ U

(A)

Δ U

(Case-III) >

Δ U

(Case-II) >

Δ U

(Case-I)

(B)

Δ U

(Case-I) >

Δ U

(Case-II) >

Δ U

(Case-III)

(C)

Δ U

(Case-I) >

Δ U

(Case-III) >

Δ U

(Case-II)

(D)

Δ U

(Case-I) =

Δ U

(Case-II) =

Δ U

(Case-III)

Q59Single correctOrganic Compounds Containing Nitrogen

The product B formed in the following reaction sequence is:

Styrene (Ph-CH=CH_{2}) HCl (A) Major AgCN (B) Major

(A)

(B)

(C)

(D)

Q60Single correctSolutions

Concentrated nitric acid is labelled as 75% by mass. The volume in mL of the solution which contains 30 g of nitric acid is ___________. Given: Density of nitric acid solution is 1.25 g/mL

(A)

(B)

(C)

(D)

Q61Single correctCoordination Compounds

Match List-I with List-II:

List-I (Complex)	List-II (Hybridization)
(A) $[CoF_{6}]^{3 -}$	(I) $d^{2} sp^{3}$
(B) $[NiCl_{4}]^{2 -}$	(II) $sp^{3}$
(C) $[Co(NH_{3})_{6}]^{3 +}$	(III) $sp^{3} d^{2}$
(D) $[Ni(CN)_{4}]^{2 -}$	(IV) $dsp^{2}$

Choose the correct answer from the options given below:

(A)

(A)-(I), (B)-(IV), (C)-(III), (D)-(II)

(B)

(A)-(III), (B)-(II), (C)-(I), (D)-(IV)

(C)

(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

(D)

(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

Q62Single correctHydrocarbons

The total number of compounds from below when treated with hot KMn

O_{4}

giving benzoic acid is:

Toluene, Ethylbenzene, Isopropylbenzene, tert-Butylbenzene, Benzyl alcohol, Styrene

(A)

(B)

(C)

(D)

Q63Single correctOrganic Compounds Containing Halogens

The major product of the following reaction is:

Ph-CH(Br)-CH_{2} -CH_{2} -CH(Br)-CH_{3} KOH/EtOH (excess) /Δ Major product

(A)

6-Phenylhepta-2,4-diene

(B)

2-Phenylhepta-2,5-diene

(C)

6-Phenylhepta-3,5-diene

(D)

2-Phenylhepta-2,4-diene

Q64Single correctClassification of Elements and Periodicity in Properties

Given below are two statements:

**Statement (I):** According to the Law of Octaves, the elements were arranged in the increasing order of their atomic number.

**Statement (II):** Meyer observed a periodically repeated pattern upon plotting physical properties of certain elements against their respective atomic numbers.

(A)

Statement I is false but Statement II is true

(B)

Both Statement I and Statement II are true

(C)

Statement I is true but Statement II is false

(D)

Both Statement I and Statement II are false

Q65Single correctChemical Kinetics

For bacterial growth in a cell culture, growth law is very similar to the law of radioactive decay. Which of the following graphs is most suitable to represent bacterial colony growth?

(A)

(B)

(C)

(D)

Q66Single correctAtomic Structure

Which of the following is/are not correct with respect to energy of atomic orbitals of hydrogen atom?

(A) 1s < 2p < 3d < 4s
(B) 1s < 2s = 2p < 3s = 3p
(C) 1s < 2s < 2p < 3s < 3p
(D) 1s < 2s < 4s < 3d

(A)

(B) and (D) only

(B)

(A) and (C) only

(C)

(D)

(A) and (B) only

Q67Single correctSolutions

Assume a living cell with

0.9

% (

ω

ω

) of glucose solution (aqueous). This cell is immersed in another solution having equal mole fraction of glucose and water. (Consider the data upto first decimal place only). The cell will:

(A)

shrink since solution is

0.5%

(

ω

ω

)

(B)

shrink since solution is

0.45%

(

ω

ω

) as a result of association of glucose molecules (due to hydrogen bonding)

(C)

swell up since solution is

1%

(

ω

ω

)

(D)

Show no change in volume since solution is

0.9%

(

ω

ω

)

Q68Single correctOrganic Compounds Containing Nitrogen

Identify correct statements:
(A) Primary amines do not give diazonium salts when treated with

N a N O_{2}

in acidic condition.
(B) Aliphatic and aromatic primary amines on heating with

C H C l_{3}

and ethanolic KOH form carbylamines.
(C) Secondary and tertiary amines also give carbylamine test.
(D) Benzenesulfonyl chloride is known as Hinsberg's reagent.
(E) Tertiary amines react with benzenesulfonyl chloride very easily.
Choose the correct answer from the options given below:

(A)

(B)

and

(D)

only

(B)

(A)

and

(B)

only

(C)

(D)

and

(E)

only

(D)

(B)

and

(C)

only

Q69Single correctSome Basic Principles of Organic Chemistry

Given below are two statements: In the light of the these statements, choose the correct answer from the options given below:

(A)

Both Statement I and Statement II are false

(B)

Both Statement I and Statement II are true

(C)

Statement I is true but Statement II is false

(D)

Statement I is false but Statement II is true

Q70Single correctPrinciples Related to Practical Chemistry

Identify the inorganic sulphides that are yellow in colour:

(A)

(NH_{4})_{2} S

(B)

PbS

(C)

CuS

(D)

As_{2} S_{3}

(E)

As_{2} S_{5}

Choose the correct answer from the options given below:

(A)

and

(C)

only

(B)

(A), (D)

and

(E)

only

(C)

(A)

and

(B)

only

(D)

and

(E)

only

Q71Numericald- and f-Block Elements

The spin only magnetic moment (

μ

) value (B.M.) of the compound with strongest oxidising power among

Mn_{2} O_{3}

TiO

and

VO

is _____ B.M. (Nearest integer).

Q72NumericalChemical Thermodynamics

Consider the following data:

Heat of formation of

C O_{2}

(g) = -393.5

kJ mol

^{- 1}

Heat of formation of

H_{2}

O(l) = -286.0

kJ mol

^{- 1}

Heat of combustion of benzene

= -3267.0

kJ mol

^{- 1}

The heat of formation of benzene is _____

kJ mol

^{- 1}

(Nearest integer)

Q73NumericalRedox Reactions and Electrochemistry

Electrolysis of 600 mL aqueous solution of NaCl for 5 min changes the pH of the solution to 12. The current in Amperes used for the given electrolysis is ____. (Nearest integer).

Q74Numericalp-Block Elements

A group 15 element forms d

π

-d

π

bond with transition metals. It also forms hydride, which is a strongest base among the hydrides of other group members that form d

π

-d

π

bond. The atomic number of the element is _____.

Q75NumericalChemical Bonding and Molecular Structure

Total number of molecules/species from following which will be paramagnetic is ______.

O_{2}

O_{2}

^+,

O_{2}

^-, NO,

N O_{2}

, CO,

K_{2}

[

N i C l_{4}

], [Co

(

NH_3

)_{6}

]

C l_{3}

K_{2}

[Ni

(CN)_{4}

]

More JEE Main 2025 papers

Frequently Asked Questions

How many questions are in the JEE Main 2025 January 28, Shift 2 paper?

The JEE Main 2025 January 28, Shift 2 paper has 75 questions — Physics (25), Chemistry (25) and Mathematics (25). Every question is on this page with its correct answer and a step-by-step solution.

What is the marking scheme for JEE Main?

JEE Main awards +4 marks for each correct answer and −1 for a wrong answer, with 0 for questions left unattempted. The paper covers Physics, Chemistry and Mathematics.

Are the answer key and step-by-step solutions provided for the 2025 January 28, Shift 2 paper?

Yes — every question shows the correct answer (answer key) and a detailed step-by-step solution, free to read online.

Can I take the JEE Main 2025 January 28, Shift 2 paper as a timed mock test?

Yes. With a free JEEnify account you can attempt this exact paper as a timed test in the real exam interface, then see your score and weak-area analysis.

Solved this paper? Calculate your JEE Main score · most important chapters · formula sheets · all free tools.

Physics25 questions

Chemistry25 questions

Mathematics25 questions

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