JEE Main 2025 January 29, Shift 1 Question Paper with Solutions

All 75 questions from the JEE Main 2025 (January 29, Shift 1) 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

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

**Assertion (A):** Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.

**Reason (R):** By using the choke coil, the voltage across the tube is reduced by a factor

\frac{R}{R ^{2} + ω ^{2} L ^{2}}

, where

ω

is frequency of the supply across resistor R and inductor L. If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.

In the light of the above statements, choose the most appropriate 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)

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

(D)

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

Q27Single correctKinematics

Two projectiles are fired with same initial speed from same point on ground at angles of

(4 5^{\circ} - α)

and

(4 5^{\circ} + α)

, respectively, with the horizontal direction. The ratio of their maximum heights attained is:

(A)

\frac{1 - tan α}{1 + tan α}

(B)

\frac{1 + sin α}{1 - sin α}

(C)

\frac{1 - sin 2 α}{1 + sin 2 α}

(D)

\frac{1 + sin 2 α}{1 - sin 2 α}

Q28Single correctElectrostatics

An electric dipole of mass m, charge q, and length

ℓ

is placed in a uniform electric field

E = E_{0} \hat{i}

. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:

(A)

\frac{1}{2 π} \frac{2 m}{q E _{0} ℓ}

(B)

2 π \frac{m}{q E _{0} ℓ}

(C)

\frac{1}{2 π} \frac{m}{2 q E _{0} ℓ}

(D)

2 π \frac{m}{2 q E _{0} ℓ}

Q29Single correctUnits and Measurements

The pair of physical quantities not having same dimensions is:

(A)

Torque and energy

(B)

Surface tension and impulse

(C)

Angular momentum and Planck's constant

(D)

Pressure and Young's modulus

Q30Single correctOscillations and Waves

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

**Assertion (A):** Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.

**Reason (R):** Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.

In the light of the above statements, choose the most appropriate answer from the options given below:

(A)

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

(B)

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

(C)

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

(D)

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

Q31Single correctUnits and Measurements

The expression given below shows the variation of velocity (v) with time (t),

v = A t^{2} + \frac{Bt}{C + t}

. The dimension of ABC is:

(A)

[M^{0} L^{2} T^{- 3}]

(B)

[M^{0} L^{1} T^{- 3}]

(C)

[M^{0} L^{1} T^{- 2}]

(D)

[M^{0} L^{2} T^{- 2}]

Q32Single correctElectromagnetic Induction and Alternating Currents

Consider

I_{1}

and

I_{2}

are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If

L_{1}

= self inductance of coil 1,

M_{12}

= mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be

(A)

ε_{1} = - L_{1} \frac{d I _{1}}{d t} + M_{12} \frac{d I _{2}}{d t}

(B)

ε_{1} = - L_{1} \frac{d I _{1}}{d t} - M_{12} \frac{d I _{1}}{d t}

(C)

ε_{1} = - L_{1} \frac{d I _{1}}{d t} - M_{12} \frac{d I _{2}}{d t}

(D)

ε_{1} = - L_{1} \frac{d I _{2}}{d t} - M_{12} \frac{d I _{1}}{d t}

Q33Single correctOptics

At the interface between two materials having refractive indices

n_{1}

and

n_{2}

, the critical angle for reflection of an em wave is

θ_{1 C}

. The

n_{2}

material is replaced by another material having refractive index

n_{3}

, such that the critical angle at the interface between

n_{1}

and

n_{3}

materials is

θ_{2 C}

. If

n_{3} > n_{2} > n_{1}

;

\frac{n _{2}}{n _{3}} = \frac{2}{5}

and

sin θ_{2 C} - sin θ_{1 C} = \frac{1}{2}

, then

θ_{1 C}

(A)

sin^{- 1} (\frac{1}{6 n _{1}})

(B)

sin^{- 1} (\frac{2}{3 n _{1}})

(C)

sin^{- 1} (\frac{5}{6 n _{1}})

(D)

sin^{- 1} (\frac{1}{3 n _{1}})

Q34Single correctMagnetic Effects of Current and Magnetism

Consider a long straight wire of a circular cross-section (radius

a

) carrying a steady current

I

. The current is uniformly distributed across this cross-section. The distances from the centre of the wire's cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be

(A)

[\frac{a}{4}, \frac{3 a}{2}]

(B)

[\frac{a}{2}, 2 a]

(C)

[\frac{a}{2}, 3 a]

(D)

[\frac{a}{4}, 2 a]

Q35Single correctWork, Energy and Power

As shown below, bob A of a pendulum having massless string of length 'R' is released from

6 0^{\circ}

to the vertical. It hits another bob B of half the mass that is at rest on a friction less table in the centre. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity)

(A)

\frac{1}{3} R g

(B)

R g

(C)

\frac{4}{3} R g

(D)

\frac{2}{3} R g

Q36Single correctDual Nature of Matter and Radiation

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): Emission of electrons in photoelectric effect can be suppressed by applying a sufficiently negative electron potential to the photoemissive substance.

Reason (R): A negative electric potential, which stops the emission of electrons from the surface of a photoemissive substance, varies linearly with frequency of incident radiation.

In the light of the above statements, choose the most appropriate answer from the options given below:

(A)

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

(B)

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

(C)

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

(D)

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

Q37Single correctElectromagnetic Induction and Alternating Currents

A coil of area A and N turns is rotating with angular velocity

ω

in a uniform magnetic field

B

about an axis perpendicular to

B

. Magnetic flux

ϕ

and induced emf

ε

across it, at an instant when

B

is parallel to the plane of coil, are:

(A)

ϕ = A B, ε = 0

(B)

ϕ = 0, ε = NAB ω

(C)

ϕ = 0, ε = 0

(D)

ϕ = A B, ε = NAB ω

Q38Single correctProperties of Solids and Liquids

The fractional compression

(\frac{Δ V}{V})

of water at the depth of 2.5 km below the sea level is ________ %. Given, the Bulk modulus of water =

2 \times 1 0^{9}

m^{- 2}

, density of water =

1 0^{3}

m^{- 3}

, acceleration due to gravity =

g = 10

s^{- 2}

(A)

1.75

(B)

1.0

(C)

1.5

(D)

1.25

Q39Single correctDual Nature of Matter and Radiation

λ

and K are de Broglie wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be:

(A)

(B)

(C)

(D)

Q40Single correctElectronic Devices

For the circuit shown above, equivalent GATE is:

(A)

OR gate

(B)

NOT gate

(C)

AND gate

(D)

NAND gate

Q41Single correctWork, Energy and Power

A body of mass 'm' connected to a massless and unstretchable string goes in vertical circle of radius 'R' under gravity g. The other end of the string is fixed at the center of circle. If velocity at top of circular path is

n g R

, where

n \geq 1

, then ratio of kinetic energy of the body at bottom to that at top of the circle is:

(A)

\frac{n}{n + 4}

(B)

\frac{n + 4}{n}

(C)

\frac{n ^{2}}{n ^{2} + 4}

(D)

\frac{n ^{2} + 4}{n ^{2}}

Q42Single correctOptics

Let

u

and

v

be the distances of the object and the image from a lens of focal length

f

. The correct graphical representation of

u

and

v

for a convex lens when

∣ u ∣ > f

, is:

(A)

(B)

(C)

(D)

Q43Single correctElectrostatics

Match List-I with List-II.

List-I	List-II
A. Electric field inside (distance $r > 0$ from center) of a uniformly charged spherical shell with surface charge density $σ$ , and radius R.	I. $σ / ε_{0}$
B. Electric field at distance $r > 0$ from a uniformly charged infinite plane sheet with surface charge density $σ$	II. $σ /2 ε_{0}$
C. Electric field outside (distance $r > 0$ from center) of a uniformly charged spherical shell with surface charge density $σ$ , and radius R	III. $0$
D. Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density $σ$ .	IV. $\frac{σ R ^{2}}{ε _{0} r ^{2}}$

Choose the correct answer from the options given below:

(A)

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

(B)

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

(C)

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

(D)

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

Q44Single correctThermodynamics

The work done in an adiabatic change in an ideal gas depends upon only:

(A)

change in its pressure

(B)

change in its specific heat

(C)

change in its volume

(D)

change in its temperature

Q45Single correctElectromagnetic Waves

Given below are two statements: one is labelled as Assertion (A) and other is labelled as Reason (R).

Assertion (A): Electromagnetic waves carry energy but not momentum.

Reason (R): Mass of a photon is zero.

In the light of the above statements, choose the most appropriate answer from the options given below:

(A)

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

(B)

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

(C)

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

(D)

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

Q46NumericalRotational Motion

The coordinates of a particle with respect to origin in a given reference frame is

(1, 1, 1)

meters. If a force of

F = \hat{i} + \hat{j} + \hat{k}

acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is _________.

Q47NumericalKinetic Theory of Gases

A container of fixed volume contains a gas at

2 7^{\circ}

C. To double the pressure of the gas, the temperature of gas should be raised to _______

^{\circ}

Q48NumericalOptics

Two light beams fall on a transparent material block at point 1 and 2 with angle

θ_{1}

and

θ_{2}

, respectively, as shown in figure. After refraction, the beams intersect at point 3 which is exactly on the interface at other end of the block. Given: the distance between 1 and 2,

d = 43

cm and

θ_{1} = θ_{2} = cos^{- 1} (\frac{n _{2}}{2 n _{1}})

, where refractive index of the block

n_{2} >

refractive index of the outside medium

n_{1}

, then the thickness of the block is ________ cm.

Q49NumericalProperties of Solids and Liquids

In a hydraulic lift, the surface area of the input piston is

6

m^{2}

and that of the output piston is

1500

m^{2}

. If

100

N force is applied to the input piston to raise the output piston by

20

cm, then the work done is _________ kJ.

Q50NumericalKinematics

The maximum speed of a boat in still water is

27

km/h. Now this boat is moving downstream in a river flowing at

9

km/h. A man in the boat throws a ball vertically upwards with speed of

10

m/s. Range of the ball as observed by an observer at rest on the river bank, is _________ cm. (Take

g = 10

s^{2}

)

Chemistry25 questions

Q51Single correctSome Basic Principles of Organic Chemistry

Total number of nucleophiles from the following is:-

N H_{3}

, PhSH,

(H_{3} C)_{2} S

H_{2} C = C H_{2}

\overline{O H}

H_{3} O^{\oplus}

(C H_{3})_{2} CO

⋗ NCH_{3}

(A)

5

(B)

4

(C)

7

(D)

6

Q52Single correctRedox Reactions and Electrochemistry

The standard reduction potential values of some of the p-block ions are given below. Predict the one with the strongest oxidising capacity.

(A)

E_{S n^{4 +} / S n^{2 +}}^{⊝} = + 1.15 V

(B)

E_{T l^{3 +} / T l^{+}}^{⊝} = + 1.26 V

(C)

E_{A l^{3 +} / A l}^{⊝} = - 1.66 V

(D)

E_{P b^{4 +} / P b^{2 +}}^{⊝} = + 1.67 V

Q53Single correctRedox Reactions and Electrochemistry

The molar conductivity of a weak electrolyte when plotted against the square root of its concentration, which of the following is expected to be observed?

(A)

A small decrease in molar conductivity is observed at infinite dilution.

(B)

A small increase in molar conductivity is observed at infinite dilution.

(C)

Molar conductivity increases sharply with increase in concentration.

(D)

Molar conductivity decreases sharply with increase in concentration.

Q54Single correctEquilibrium

At temperature T, compound

A B_{2 (g)}

dissociates as

A B_{2} (g) ⇌ A B (g) + \frac{1}{2} B_{2} (g)

having degree of dissociation x (small compared to unity). The correct expression for x in terms of

K_{p}

and p is

(A)

3 \frac{2 K _{p}}{p}

(B)

4 \frac{2 K _{p}}{p}

(C)

3 \frac{2 K _{p}^{2}}{p}

(D)

K_{p}

Q55Single correctHydrocarbons

Match List-I with List-II.
Choose the correct answer from the options given below:

(A)

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

(B)

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

(C)

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

(D)

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

Q56Single correctSome Basic Concepts in Chemistry

Choose the correct statements.

(A) Weight of a substance is the amount of matter present in it.

(B) Mass is the force exerted by gravity on an object.

(C) Volume is the amount of space occupied by a substance.

(D) Temperatures below 0°C are possible in Celsius scale, but in Kelvin scale negative temperature is not possible.

(E) Precision refers to the closeness of various measurements for the same quantity.

(A)

(B), (C) and (D) Only

(B)

(A), (B) and (C) Only

(C)

(A), (D) and (E) Only

(D)

(C), (D) and (E) Only

Q57Single correctCoordination Compounds

The correct increasing order of stability of the complexes based on

Δ_{o}

value is:

(I)

[M n (CN)_{6}]^{3 -}

(II)

[C o (CN)_{6}]^{4 -}

(III)

[F e (CN)_{6}]^{4 -}

(IV)

[F e (CN)_{6}]^{3 -}

(A)

<

III

<

<

(B)

<

III

<

<

(C)

<

<

<

III

(D)

III

<

<

<

Q58Single correctCoordination Compounds

Match List-I with List-II.

List-I (Complex)	List-II (Hybridisation & Magnetic character)
(A) $[MnBr_{4}]^{2 -}$	(I) $d^{2} s p^{3}$ & diamagnetic
(B) $[FeF_{6}]^{3 -}$	(II) $s p^{3} d^{2}$ & paramagnetic
(C) $[C o (C_{2} O_{4})_{3}]^{3 -}$	(III) $s p^{3}$ & diamagnetic
(D) $[N i (CO)_{4}]$	(IV) $s p^{3}$ & paramagnetic

Choose the correct answer from the options given below:

(A)

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

(B)

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

(C)

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

(D)

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

Q59Single correctOrganic Compounds Containing Halogens

In the following substitution reaction:
Product 'P' formed is:

(A)

(B)

(C)

(D)

Q60Single correctRedox Reactions and Electrochemistry

For a

M g ∣ M g^{2 +} (a q) ∣∣ A g^{+} (a q) ∣ A g

the correct Nernst Equation is:

(A)

E_{ce ll} = E_{ce ll}^{o} - \frac{RT}{2 F} ln \frac{[ A g ^{+} ]}{[ M g ^{2 +} ]}

(B)

E_{ce ll} = E_{ce ll}^{o} - \frac{RT}{2 F} ln \frac{[ A g ^{+} ] ^{2}}{[ M g ^{2 +} ]}

(C)

E_{ce ll} = E_{ce ll}^{o} - \frac{RT}{2 F} ln \frac{[ M g ^{2 +} ]}{[ A g ^{+} ] ^{2}}

(D)

E_{ce ll} = E_{ce ll}^{o} - \frac{RT}{2 F} ln \frac{[ A g ^{+} ] ^{2}}{[ M g ^{2 +} ]}

Q61Single correctd- and f-Block Elements

The correct option with order of melting points of the pairs (Mn, Fe), (Tc, Ru) and (Re, Os) is:

(A)

<

Mn, Ru

<

Tc and Re

<

(B)

<

Fe, Tc

<

Ru and Re

<

(C)

<

Fe, Tc

<

Ru and Os

<

(D)

<

Mn, Ru

<

Tc and Os

<

Q62Single correctSolutions

1.24 g of

A X_{2}

(molar mass 124 g mo

l^{- 1}

) is dissolved in 1 kg of water to form a solution with boiling point of 100.0156°C, while 25.4 g of

A Y_{2}

(molar mass 250 g mo

l^{- 1}

) in 2 kg of water constitutes a solution with a boiling point of 100.0260°C.

K_{b} (H_{2} O) = 0.52

K kg mo

l^{- 1}

Which of the following is correct?

(A)

A X_{2}

and

A Y_{2}

(both) are completely unionised.

(B)

A X_{2}

and

A Y_{2}

(both) are fully ionised.

(C)

A X_{2}

is completely unionised while

A Y_{2}

is fully ionised.

(D)

A X_{2}

is fully ionised while

A Y_{2}

is completely unionised.

Q63Single correctChemical Thermodynamics

500 J of energy is transferred as heat to 0.5 mol of Argon gas at 298 K and 1.00 atm. The final temperature and the change in internal energy respectively are:

Given:

R = 8.3 J K^{- 1} mol^{- 1}

(A)

348 K and 300 J

(B)

378 K and 300 J

(C)

368 K and 500 J

(D)

378 K and 500 J

Q64Single correctChemical Kinetics

The reaction

A_{2} + B_{2} \to 2 AB

follows the mechanism:

A_{2} k_{1} k_{- 1} A + A

(fast)

A + B_{2} k_{2} AB + B

(slow)

A + B \to AB

(fast)

The overall order of the reaction is:

(A)

1.5

(B)

(C)

2.5

(D)

Q65Single correctAtomic Structure

a_{0}

is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength (

λ

) of the electron present in the second orbit of hydrogen atom? [n : any integer]

(A)

\frac{2 a _{0}}{n}

(B)

\frac{8 π a _{0}}{n}

(C)

\frac{4 π a _{0}}{n}

(D)

\frac{4 n}{π a _{0}}

Q66Single correctOrganic Compounds Containing Oxygen

The product (P) formed in the following reaction is:

(A)

(B)

(C)

(D)

Q67Single correctChemical Bonding and Molecular Structure

An element 'E' has the ionisation enthalpy value of 374 kJ mo

l^{- 1}

. 'E' reacts with elements A, B, C and D with electron gain enthalpy values of

- 328

- 349

- 325

and

- 295

kJ mo

l^{- 1}

, respectively.
The correct order of the products EA, EB, EC and ED in terms of ionic character is:

(A)

EB > EA > EC > ED

(B)

ED > EC > EA > EB

(C)

EA > EB > EC > ED

(D)

ED > EC > EB > EA

Q68Single correctBiomolecules

Match List-I with List-II.

List-I (Carbohydrate)	List-II (Linkage, Source)
(A) Amylose	(I) $β$ - $C_{1}$ - $C_{4}$ , plant
(B) Cellulose	(II) $α$ - $C_{1}$ - $C_{4}$ , animal
(C) Glycogen	(III) $α$ - $C_{1}$ - $C_{4}$ , $α$ - $C_{1}$ - $C_{6}$ , plant
(D) Amylopectin	(IV) $α$ - $C_{1}$ - $C_{4}$ , plant

Choose the correct answer from the options given below:

(A)

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

(B)

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

(C)

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

(D)

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

Q69Single correctPurification and Characterisation of Organic Compounds

The steam volatile compounds among the following are:

(A) o-Nitrophenol
(B) o-Nitroaniline
(C) o-Aminophenol
(D) p-Aminophenol

Choose the correct answer from the options given below:

(A)

(B)

(C)

(D)

Q70Single correctClassification of Elements and Periodicity in Properties

Given below are two statements:

**Statement (I):** The radii of isoelectronic species increases in the order: M

g^{2 +}

< Na

^{+}

< F

^{-}

O^{2 -}

**Statement (II):** The magnitude of electron gain enthalpy of halogen decreases in the order: Cl > F > Br > I

In the light of the above statements, choose the most appropriate answer from the options given below:

(A)

Statement I is incorrect but Statement II is correct

(B)

Both Statement I and Statement II are incorrect

(C)

Statement I is correct but Statement II is incorrect

(D)

Both Statement I and Statement II are correct

Q71NumericalOrganic Compounds Containing Nitrogen

Given below are some nitrogen containing compounds.

Each of them is treated with HCl separately. 1.0 g of the most basic compound will consume ______ mg of HCl.

(Given molar mass in g mo

l^{- 1}

C:12, H:1, O:16, Cl:35.5)

Q72Numericald- and f-Block Elements

The molar mass of the water insoluble product formed from the fusion of chromite ore (FeC

r_{2} O_{4}

) with N

a_{2} C O_{3}

in presence of

O_{2}

is ______ g mo

l^{- 1}

Q73NumericalChemical Bonding and Molecular Structure

The sum of sigma (

σ

) and pi (

π

) bonds in Hex-1,3-dien-5-yne is _______.

Q74NumericalSolutions

A_{2}

B is 30% ionised in an aqueous solution, then the value of van't Hoff factor (i) is _____

\times 1 0^{- 1}

Q75NumericalOrganic Compounds Containing Oxygen

A cyclic compound with OH group undergoes the following reactions:

0.1 mole of compound 'S' will weigh _____ g.

(Given molar mass in g mo

l^{- 1}

C:12, H:1, O:16)

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