CUET UG 2025 Physics Previous Year Solved Paper

Step 1. Recall the basic charges
• Charge of 1 proton = +e
• Charge of 1 electron = –e
Step 2. Calculate total charge
If the object has:
• x electrons → total charge = –x·e
• y protons → total charge = +y·e
Step 3. Find the net charge
Net charge = (Charge due to protons) + (Charge due to electrons)
= (+y·e) + (–x·e)
= (y – x)·e
Final Answer: (y – x)e
Correct Option: 4)

Step 1. Given data

Step 2. Formula for work done
Work done (W) = Potential energy =

Step 3. Substitute the values

Step 4. Simplify step by step

Final Answer: 6×10-5 J
Correct Option: 3)

Step 1. Recall the rule for capacitors in series
When capacitors are connected in series, the same charge (Q) flows through
each capacitor because the charge has only one path to move through.
This is similar to how in a series circuit of resistors, the same current flows
through all components.
Step 2. Relation between charge, voltage, and capacitance
For a capacitor,
Q = C × V
In series combination:
• The total voltage (V) is divided among capacitors.
• But the charge (Q) on each capacitor remains the same, regardless of
their capacitance.
Step 3. Conclusion
Therefore, in a series combination, each capacitor carries an equal charge
for any value of its capacitance.
Final Answer: each capacitor has equal charge for any value of its
capacitance
Correct Option: 3)

Step 1. Use potential energy of two point charges:

Step 2. Compute initial potential energy:

Step 3. At infinite separation, potential energy, 𝑈𝑓 = 0.
Step 4. Work required by an external agent to separate them:

Final Answer: 0.9 J
Correct Option: 1)

Step 1. Recall the basic formula from Gauss's Law.
Gauss's Law in electrostatics provides the relationship between the net
electric flux (Φ) through a closed surface and the net charge enclosed (ԛ
inside) by it.

(Where ϵ0 is the permittivity of free space.)
Step 2. Identify the given values from the question.

Step 3. Rearrange the formula to find the net charge (qinside).
To solve for the charge, we multiply both sides of the formula by ϵ0.

Step 4. Substitute the given values and calculate.
Now, we plug the values from Step 2 into the rearranged formula from Step
3.
• Calculation:

Final Answer: 9.29 × 10-12 C
Correct Option: 4)

Step 1. List the given data and convert to SI units.
First, we write down all the values from the problem and convert them into
standard SI units for calculation.

Step 2. Calculate the capacitance (C) of the capacitor.
The basic definition of capacitance is the ratio of the charge stored to the
potential difference across it.

Step 3. Recall the formula for a parallel plate capacitor with a dielectric.
The capacitance of a parallel plate capacitor also depends on its physical
dimensions and the dielectric material between its plates.

(Here, K is the dielectric constant we need to find.)
Step 4. Rearrange the formula and solve for K.
Now we rearrange the formula from Step 3 to solve for K and substitute all
the known values.

Final Answer: 11.3
Correct Option: 3)

Step 1. Recall the formula for potential due to an electric dipole

The electric potential at a point due to a dipole is given by:

Where:

Step 2. Analyze each statement

(B) Depends on the angle between the position vector and dipole moment
vector:

(D) Does not depend on the distance separating the charges: ❌
The dipole moment 𝑝 = 𝑞 × 2𝑎, so potential does depend indirectly on the
separation (through 𝑝).
Step 3. Correct statements
(A), (B), and (C) are correct.
Final Answer: (A), (B), and (C) only
Correct Option: 2)

Step 1. Write the original force using Coulomb’s law

where

Step 2. One of the charges is doubled

Step 3. Force remains the same

Step 4. Simplify the equation

Final Answer: √2 d
Correct Option: 3)

Step 1. Recall the concept of current in conductors

Electric current is the flow of free electrons through a conductor.
For electrons to move, there must be a force acting on them - this force is
provided by an electric field.
Step 2. When does a conductor develop current?
• When an electric field is applied, electrons experience a force and
start moving in the opposite direction of the field.
• This movement of electrons constitutes electric current.
Step 3. Analyze other options
• Magnetic field alone → does not produce current in a stationary
conductor.
• Gravitational field → effect is negligible on electrons due to their very
small mass.
• Both magnetic and gravitational fields together → still do not produce
current without an electric field.
Final Answer: On applying electric field
Correct Option: 1)

Step 1. Recall the concept of resistivity
Resistivity (ρ) is an intrinsic property of a material that determines how
strongly it resists the flow of electric current.
It is independent of the conductor’s shape or size — it depends only on the
nature of the material and temperature.
Step 2. Key relation
The resistance 𝑅 of a conductor is given by:

where:
• R = resistance
• ρ = resistivity

• L = length
• A = cross-sectional area
Here, 𝑅 depends on L and A, but resistivity (ρ) does not — it depends on:
1. Material of the conductor (different materials have different ρ)
2. Temperature (resistivity increases with temperature for metals)
Final Answer: Its material and temperature of the conductor
Correct Option: 2)

Step 1. Recall the behavior of electrons in a conductor
Electrons in a metal move freely but continuously collide with positive ions
(the metal lattice).
Their motion between collisions depends on whether an electric field is
applied or not.
Step 2. Case (i): Absence of electric field
• Without an electric field, electrons move randomly due to thermal
energy.
• Between collisions, no external force acts on them.
• So, each electron moves in a straight line between collisions.
Step 3. Case (ii): Presence of electric field
• When an electric field is applied, electrons experience a force
opposite to the field direction.
• Due to this force, their paths are slightly curved between collisions
(not straight), as they accelerate under the field.

Step 4. Conclusion
(i) In the absence of electric field → Straight line
(ii) In the presence of electric field → Curved in general

Final Answer: (i) Straight line, (ii) Curved in general
Correct Option: 4)

Step 1. Given data

We need to find R (resistance).
Step 2. Use Joule’s law of heating
The heat (energy) developed in a resistor is given by:

Step 3. Rearrange to find R

Substitute values:

Final Answer: 10 Ω
Correct Option: 2)

Step 1. Given data
𝑅 = 4Ω, 𝑟 = 7cm = 0.07 m, 𝜌 = 2 × 10-7 Ω𝑚, 𝑑 = 1.4 mm = 1.4 × 10-3 m
We have to find the number of turns (n).
Step 2. Formula for resistance

Where
• L = total length of the wire
• A = cross-sectional area of the wire
Step 3. Find the cross-sectional area

Step 4. Find the total length of the wire

Step 5. Find length of one turn
Each turn forms a circle of radius 𝑟 = 0.07 m
Length of one turn = 2𝜋𝑟 = 2𝜋 × 0.07 = 0.44 m
Step 6. Find the number of turns

Final Answer: 70
Correct Option: 1)

Step 1. Given data

We need to find the voltage across the external resistor (V).
Step 2. Concept used
When a battery of emf E and internal resistance 𝑟 is connected in a circuit
where
• V = potential difference across the external resistor
• I𝑟 = voltage drop across internal resistance
Step 3. Substitute values

Final Answer: 10.2 V
Correct Option: 1)

Step 1. Given data
• Total resistance of the wire 𝑅 = 12 Ω
• It is cut into three parts in the ratio 1 : 2 : 3
• Hence, total length ratio sum = 1 + 2 + 3 = 6
Step 2. Calculate individual resistances
Resistance is proportional to length.

Step 3. Forming a triangle
When the three resistors are connected to form a triangle (Δ), and the cell
is connected across the highest resistor (6 Ω), the other two resistors (2 Ω
and 4 Ω) are connected in series, and this combination is in parallel with the
6 Ω resistor.
Step 4. Equivalent resistance of (2 Ω + 4 Ω)
𝑅series = 2 + 4 = 6Ω
Now, this 6 Ω is in parallel with the 6 Ω resistor:

Step 5. Total resistance in circuit
The total resistance includes the internal resistance 𝑟 = 5Ω:
𝑅total = 𝑅eq + 𝑟 = 3 + 5 = 8Ω
Step 6. Calculate current
Using Ohm’s law:

Final Answer: 1 A
Correct Option: 4)

Step 1. Use the relation
• Magnetic moment M = p × d
(where 𝑝 = pole strength, 𝑑 = distance between poles)

Step 2. Convert distance
• 20 cm = 0.20 m
Step 3. Calculate pole strength

Final Answer: 25 A·m
Correct Option: 4)

Step 1. Recall the physical meaning and units of each quantity
Let’s understand each term one by one:
(A) Magnetic Field (B)
• The magnetic field is defined as the magnetic flux per unit area.
• Its SI unit is Weber per square meter (Wb.m⁻²), which is also
equivalent to Tesla (T).
1 Tesla = 1 Weber per square meter
• Hence, the correct unit for magnetic field is Wb.m⁻².
→ Matches with (IV).
(B) Magnetic Moment (M)
• The magnetic moment of a magnet or a current-carrying coil is a
measure of its strength and direction.
• For a bar magnet, magnetic moment M = pole strength ×
distance between poles.
• Its SI unit is Ampere.meter² (A.m²).
• However, it can also be expressed as Joule per Tesla (J.T⁻¹) because
torque τ = MB sin θ, and torque has the unit of Joule (N.m).
Thus,

• Hence, the correct unit for magnetic moment is J.T⁻¹.
→ Matches with (I).
(C) Pole Strength (m)
• The pole strength is the magnetic strength of one pole of a magnet.
• Magnetic moment is given by:
𝑀 = 𝑚 × 2𝑙
where 2𝑙 is the distance between the two poles.
Therefore,

• Hence, the correct unit for pole strength is J.T⁻¹.m⁻¹.
→ Matches with (III).
(D) Permeability of Free Space (μ₀)
• The permeability of free space represents how well a magnetic field
can be established in vacuum.
• It relates the magnetic field 𝐵 and the magnetic field intensity 𝐻:
𝐵 = μ₀𝐻
• Thus,

• Hence, the correct unit for permeability of free space is T.m.A⁻¹.
→ Matches with (II).
Step 2. Match List-I with List-II
List-I
List-II
Physical Quantity
Units
(A) Magnetic field
(IV) Wb.m⁻²
(B) Magnetic moment
(I) J.T⁻¹

(C) Pole strength
(III) J.T⁻¹.m⁻¹
(D) Permeability of free space
(II) T.m.A⁻¹

Final Answer: (A) – (IV), (B) – (I), (C) – (III), (D) – (II)
Correct Option: 2)

Step 1. Concept Used – Biot–Savart Law
The magnetic field dB due to a small current element is given by:

where:

Step 2. Given Data

Since the wire is along the x-axis and the field point is on the y-axis,
θ = 90∘ ⇒ sinθ = 1.
Step 3. Substitute Values

Simplify:

Step 4. Calculate the Result

Final Answer: 4 × 10-8 T
Correct Option: 1)

Step 1. Formula and Concept Used
The magnetic force on a current-carrying conductor placed in a magnetic
field is given by:

where

Step 2. Given Data

Step 3. Apply the Cross Product

Therefore,

Step 4. Interpret the Direction
The force is in the negative x-direction (–x-axis).
Final Answer: The magnetic force acts along the negative x-axis.
Correct Option: 4)

Step 1. Concept – Converting a Galvanometer into an Ammeter
A galvanometer detects small currents.
To measure large currents, we connect a low resistance (called a shunt) in
parallel with it.
This allows most of the current to pass through the shunt and only a small
part through the galvanometer, protecting it from damage.
The total (effective) resistance of the ammeter is the parallel combination of
the galvanometer resistance 𝑅g and the shunt resistance 𝑅s.
Step 2. Formula
The effective resistance 𝑅𝐴 of the ammeter is given by:

Step 3. Substitution of Given Values

Step 4. Simplify

Step 5. Interpretation
The ammeter has low resistance so that it doesn’t affect the current in the
circuit.

Final Answer: 19.3 Ω
Correct Option: 3)

Step 1. Concept – Magnetic Field Inside a Solenoid
The magnetic field inside a long solenoid is uniform and given by the
formula:

where

Step 2. Given Data

Step 3. Calculate Number of Turns per Unit Length

Step 4. Substitute Values into Formula

Step 5. Simplify

Final Answer: 𝐵 = 20 m 𝑇
Correct Option: 3)

Step 1: Relate potential difference and velocity
When a charged particle (charge 𝑞, mass 𝑚) is accelerated through a
potential difference 𝑉:

This shows that speed 𝑢 depends on the square root of the potential 𝑉.
Step 2: Radius in a magnetic field
When the charged particle enters a magnetic field 𝐵 perpendicularly, it
moves in a circular path because the magnetic force provides the necessary
centripetal force:

So, radius 𝑟 is directly proportional to the speed 𝑢.
Step 3: Substitute the value of 𝑢

This means the radius increases with the square root of the potential
difference 𝑉.
Step 4: Compare with given options
We know 𝑢 ∝ √𝑉.

Now, check the given expressions:

Hence,

Final Answer: 𝑉/𝑢
Correct Option: 1)

Step 1. Understand the concept
This question is based on Faraday’s law of electromagnetic induction and
Lenz’s law.
• When a magnet moves relative to a coil, the magnetic flux through the
coil changes.
• A changing magnetic flux induces an emf in the coil, producing an
induced current.
• The direction of the induced current is such that it opposes the
change (Lenz’s law).
Step 2. Analyze each statement
(A) “It indicates the presence of electric current in the coil.” True.
Deflection of the galvanometer pointer shows that current is induced in the
coil - hence an electric current flows momentarily.
(B) “The deflection is found to be smaller when the magnet is pushed
towards the coil faster.” ❌ False.
According to Faraday’s law,

The faster the magnet moves, the greater the rate of change of magnetic flux,
so deflection increases, not decreases.
(C) “There is repulsion between the moving magnet and the magnetic pole
induced in the coil facing towards the N pole of the magnet.” True.
By Lenz’s law, the induced current sets up a magnetic pole that opposes the
approaching magnet - so the coil’s near face becomes a north pole, causing
repulsion.
(D) “If the bar magnet does not move, there is no induced current in the
coil.” True.
When the magnet is stationary, the magnetic flux through the coil remains
constant, so no emf or current is induced.
Step 3. Identify the correct combination
Correct Statements: (A), (C), and (D)
Final Answer: (A), (C), and (D) only
Correct Option: 1)

Step 1. Understanding the situation
We are given a rectangular conductor PQRS placed in a uniform magnetic
field.
• The magnetic field (B) is directed into the page (represented by
crosses “×”).
• The side PQ (of length 𝑙) is free to move.
• The distance between PQ and the opposite side SR is 𝑥.
• The conductor PQ moves left with constant velocity 𝑉.
As PQ moves, the area of the loop PQRS changes with time, leading to a
change in magnetic flux, which produces an induced emf according to
Faraday’s Law.
Step 2. Expression for magnetic flux
Magnetic flux (Φ) through the loop is given by:

Φ = 𝐵 × Area
Since the area of the rectangle is A = 𝑙 × 𝑥,
Φ = 𝐵𝑙𝑥
So, the magnetic flux linked with the loop at any instant is:

Step 3. Finding motional emf
According to Faraday’s Law, the induced emf (ε) is the rate of change of
magnetic flux:

Substituting Φ = 𝐵𝑙𝑥:

Since the rod moves left with constant speed 𝑉,

Taking the magnitude (emf is always positive in magnitude),
ε = 𝐵𝑙𝑉
Step 4. Physical explanation
• As PQ moves left, the loop area decreases.
• This decreases the magnetic flux (since Φ = 𝐵𝑙𝑥).
• To oppose this decrease, an induced current is produced in a
clockwise direction (by Lenz’s Law).
• The magnitude of the induced emf depends on 𝐵, 𝑙, and 𝑉.
Step 5. Final results

Final Answer: Magnetic ƒlux = 𝐵𝑙𝑥; Motional emƒ = 𝐵𝑙𝑉.
Correct Option: 3)

Step 1. Formula for induced emf in an inductor
The average emf induced in a coil is given by Faraday’s law of
electromagnetic induction:

where
𝐸 = induced emf,
𝐿 = self-inductance of the coil,
Δ𝐼 = change in current,
Δ𝑡 = time taken for the change.
Step 2. For case (A)
Given:

Substitute in formula:

But in the question, it says L = 0.266 mH, which is 1000 times smaller.
Hence, the given value is incorrect.
Step 3. For case (B)
Here, current changes from +4 A to -4 A, so

Given:

Substitute:

This matches the given 0.10 mH?
No — that’s 0.10 H = 100 mH, not 0.10 mH = 0.0001 H.
So, the given value (0.10 mH) is also incorrect.
Final Answer: Both (A) and (B) are incorrect.
Correct Option: 4)

Step 1. Concept — Condition for maximum current
In an LCR series circuit, the current is maximum at resonance, when the
inductive reactance equals the capacitive reactance:

From this, the capacitance at resonance is:

Step 2. Substitute given values
Given:

Substitute in the formula:

Step 3. Simplify

Convert to microfarads:

Final Answer: The capacitance required for maximum current is 0.32 μF
Correct Option: 2)

Step 1. Given data
𝑉 = 12 𝑉, R = 6Ω, 𝐿 = 10𝑚H = 10 × 10-3 H, Δ𝑡 = 1 𝑚s = 1 × 10-3 s
Step 2. Find initial current
When the circuit is closed for a long time, current reaches a steady value
given by Ohm’s law:

Step 3. When the switch is opened
The current in the inductor falls from 𝐼 = 2 A  to 0 A in time Δ𝑡 = 1 × 10-3 s
An emf is induced in the coil given by:

Substitute the values:

Final Answer: The average emf induced across the coil is 20 V
Correct Option: 2)

Step 1. Given information
AC source rating:

Hence, the time period of the AC signal is:

Step 2. Understanding what each value means
• RMS value (220 V) → Effective voltage that produces the same heating
effect as DC.
• Peak value → Maximum voltage of the waveform:

• Average value over a complete cycle (T = 1/50 s) → For a sinusoidal
AC:

Because the positive and negative halves cancel each other.
Step 3. Evaluate each statement
1. ❌ “The peak value over a period of (1/50) s is 220 V”
→ Incorrect, peak value = 311 V not 220 V.
2. ❌ “The average value over a period of (1/50) s is 220 V”
→ Incorrect, average over a complete cycle is 0 V.
3. “The average value over a period of (1/50) s is 0 V”
→ Correct, because for one full AC cycle, the net area under the curve
is zero.

4. ❌ “The average value over a period of (1/50) s is 220√2 V”
→ Incorrect, this is the peak value, not the average.
Final Answer: The average value over a period of (1/50) s is 0 V.
Correct Option: 3)

Step 1. Recall Faraday’s laws of electromagnetic induction
According to Faraday’s first and second laws:
1. First law: Whenever the magnetic flux linked with a circuit changes,
an emf is induced in the circuit.
2. Second law: The magnitude of the induced emf is equal to the rate of
change of magnetic flux through the circuit.

Step 2. Check each statement
(1) Correct - This directly matches Faraday’s law:

(2) ❌ Incorrect - The emf is not equal to the total change of magnetic flux;
it depends on the rate of change (how fast the flux changes), not just the
total amount.
(3) Correct - Increasing the number of turns N increases the induced
emf because

(4) Correct - This follows from Lenz’s Law, which states that the
polarity of the induced emf always opposes the change in flux that causes it.

Final Answer: “The magnitude of induced emf in a circuit is equal to the
total change of magnetic flux through the circuit” is not correct.
Correct Option: 2)

Step 1. Concept of displacement current
According to Maxwell, even when no actual charge flows (as in the gap of a
capacitor), a changing electric field produces a magnetic field just like a
current does.
This effect is called displacement current.
Step 2. Formula
The displacement current is given by:

where
ε0 = permittivity of free space,
Φ𝐸 = electric flux.
Hence, it is proportional to the rate of change of the electric field.
Step 3. Correct interpretation
• It is not due to the flow of charges (that’s conduction current).
• It is not related to gravitational or magnetic fields.
• It is caused by a changing electric field between capacitor plates or in
free space.
Final Answer: Due to changing electric field.
Correct Option: 3)

Step 1. Understanding the Question

We need to match different types of electromagnetic (EM) waves from List-I
with their wavelength ranges from List-II.
Each type of EM wave has its own unique wavelength and frequency range.
Step 2. Analyze Each Wave and Its Range
(A) X-rays → X-rays have very short wavelengths, typically between 1 nm to
10⁻³ nm.
They are used in medical imaging and material analysis.
→ Matches with (III).
(B) Radio waves → Radio waves have the longest wavelengths, usually
greater than 0.1 m.
They are used for communication systems such as radio and television.
→ Matches with (IV).
(C) Infrared waves → Infrared waves lie between visible light and
microwaves, having wavelengths from 1 mm to 700 nm.
They are responsible for heat radiation.
→ Matches with (I).
(D) Microwaves → Microwaves have wavelengths between 0.1 m to 1 mm.
They are used in microwave ovens, radar systems, and satellite
communication.
→ Matches with (II).
Final Answer: (A) – (III), (B) – (IV), (C) – (I), (D) – (II)
Correct Option: 4)

Step 1. Understanding the Question
We are given the equation of an electromagnetic wave:

where:

We are asked to find the relation between 𝐸0 and 𝐵0.
Step 2. Relation Between Electric and Magnetic Fields in an EM Wave
In an electromagnetic wave traveling in free space, the magnitudes of the
electric and magnetic fields are related by the speed of light (c):

Step 3. Express ccc in Terms of 𝜔 and 𝑘
We know that the speed of the wave is given by:

Substitute this into the relation:

Final Answer:

Correct Option: 1)

Step 1. Understanding the Question
The question asks which of the given statements about mirrors and
reflection are correct.
We must analyze each statement based on the laws of reflection and the
properties of plane and curved mirrors.

Step 2. Analyze Each Statement
(A) All mirrors follow the laws of reflection.
True.
Both plane and curved mirrors obey the laws of reflection:
1. The angle of incidence equals the angle of reflection.
2. The incident ray, reflected ray, and the normal lie in the same plane.
(B) The angle between the ray of incidence and the plane surface of the
mirror is equal to the angle between the plane surface of mirror and the ray
of reflection for plane mirror.
True.
In a plane mirror, the angle between the incident ray and the mirror surface
equals the angle between the mirror surface and the reflected ray, because
the mirror surface acts as the reference plane.
(This follows directly from the geometry of reflection.)
(C) The rays coming parallel to the principal axis will go after reflection
through the focus of the curved mirror.
True.
For a concave mirror, any light ray parallel to the principal axis reflects and
passes through the focus (F).
For a convex mirror, the rays appear to diverge from the focus.
Thus, this statement is correct for both cases conceptually.
(D) The rays coming to the pole of a curved mirror making an angle with axis
will be reflected making the equal angle with the axis on the other side of the
axis.
True.
The pole (P) of the mirror is the center point on its surface.
At the pole, the normal to the mirror coincides with the principal axis, so the
angle of incidence equals the angle of reflection, satisfying this condition.
Final Answer: All four statements are correct. (A), (B), (C) and (D)
Correct Option: 1)

Step 1. Understanding the Question
We are given four statements related to the power of a lens and must
determine which are correct.
Power (𝑃) of a lens is defined as the ability of the lens to converge or
diverge light rays, mathematically given by:

where 𝑓 is the focal length in metres and the unit of power is dioptre (D).
Step 2. Check each statement
(A) The power of a lens is the ability of the lens to converge or diverge the
incident rays.
True. This is the definition of power of a lens.
(B) S.I. unit of the power of a lens is dioptre while focal length is in
centimetres.
❌ Incorrect.
For power in dioptres, focal length must be in metres, not centimetres.
(If 𝑓 = 1 m, then 𝑃 = 1D).
(C) For a lens of larger focal length, power is smaller.
True.
Since 𝑃 = 1/𝑓, as focal length increases, power decreases.
(D) In any combination of lenses, the power of combination is not algebraic
addition of power of combined lenses.
❌ Incorrect.
For thin lenses in contact:
𝑃total = 𝑃1 + 𝑃2
So, this statement is false.

Final Answer: (A) and (C) only
Correct Option: 1)

Step 1: Find the image distance (𝑣) using the magnification formula
The magnification (𝑚) of a lens is given by the ratio of the image length (ℎ𝑖)
to the object length (ℎ𝑜), and also by the ratio of the image distance (𝑣) to
the object distance (𝑢).

Given:
• Image length (ℎ𝑖) = 1 cm
• Object length (ℎ𝑜) = 5 cm
• Object distance (𝑢) = -40 cm (negative because the object is on the
same side as the incoming light)

Step 2: Use the lens formula to find the focal length (𝑓)
The lens formula is given by:

Substitute the values for 𝑣 and 𝑢:

To add the fractions, find a common denominator, which is 40:

The focal length of a convex lens is positive. Let's re-evaluate the
problem. Since a convex lens forms a real image when the object is outside
the focal length, the image is inverted. Therefore, the image length should
be negative.

Now, use the lens formula with the corrected image distance:

Final Answer: The focal length of the lens is approximately 6.67 cm.
Correct Option: 1)

Step 1. Given data
We are given:
• Distance between slits, 𝑑 = 1.5 mm = 1.5 × 10-3 m
• Distance between slits and screen, 𝐷 = 1.2 m
• Wavelength of light, 𝜆 = 600 × 10-9 m
We need to find the fringe width (β).
Step 2. Formula used
Fringe width in Young’s double-slit experiment is given by:

Step 3. Substituting values

Final Answer: β = 0.48 mm
Correct Option: 1)

Step 1. Understanding the question
When light travels from a denser medium (like glass) to a rarer medium
(like air), it bends away from the normal.
As the angle of incidence increases, the angle of refraction also increases.
At a particular angle of incidence, the refracted ray just grazes the surface -
i.e., it makes an angle of 90° with the normal.

This particular angle of incidence is called the critical angle (iₙ).
Step 2. Definition
At the critical angle,
Angle of refraction = 90°
Beyond this angle, light is totally internally reflected instead of refracted.
Final Answer: The angle of refraction is 90°
Correct Option: 2)

Step 1. Understanding the question
There are two crossed polarizers, meaning their transmission axes are at
90° (or π/2 radians) to each other. Normally, no light passes through both
polarizers since the second one blocks all light coming from the first.
However, when a Polaroid sheet is placed between them and rotated, some
light passes through, and the intensity changes depending on the angle
between the first polarizer and the Polaroid sheet.
We need to find the angle at which the transmitted light intensity becomes
maximum.
Step 2. Using Malus’s Law
According to Malus’s law, the intensity of transmitted light through a
polarizer is given by:

where θ is the angle between the light’s polarization direction and the axis
of the polarizer.
If the light then passes through a second polarizer that makes an angle (π/2
- θ) with the first, the final intensity becomes:

Step 3. Simplify the expression
We can rewrite this as:

For maximum intensity,

This happens when:

Final Answer:

Correct Option: 2)

Step 1. Understanding the Concept
Total Internal Reflection (TIR) happens when light travels from a denser
medium to a rarer medium and the angle of incidence is greater than the
critical angle.
In this case, light is completely reflected back into the denser medium, and
no refracted ray exists.
Step 2. Checking Each Statement
(A) Total internal reflection occurs when a ray of light travels from a rarer
transparent medium to a denser medium.
→ Incorrect. ❌
TIR occurs when light travels from denser to rarer, not the other way.
(B) In total internal reflection, the incident ray of light remains in the same
medium after reflection.
→ Correct.

In TIR, light does not pass into the second medium - it remains in the denser
medium after reflection.
(C) In total internal reflection, the angle of incidence inside the denser
transparent medium is equal to the angle of reflection in the same medium.
→ Correct.
This follows the law of reflection - angle of incidence = angle of reflection.
(D) In total internal reflection inside a denser medium there is no angle of
refraction.
→ Correct.
There is no refracted ray, hence no refraction angle during TIR.
Final Answer: (B), (C) and (D) only
Correct Option: 3)

Step 1: Identify the given values and formula
The focal length (𝑓) of the concave lens is given as 50 cm.
The power of a lens (𝑃) is related to its focal length by the formula:

where 𝑓 is in meters.
Step 2: Convert the focal length to meters
The given focal length is 𝑓 = 50 cm. To convert it to meters, divide by 100:

Step 3: Determine the sign of the focal length
A concave lens is a diverging lens, and its focal length is conventionally
considered negative.
Therefore, 𝑓 = -0.5 m.

Step 4: Calculate the power of the lens
Using the formula from Step 1 and the focal length from Step 3:

The power of the lens is -2 D.
Final Answer: -2 D
Correct Option: 4)

Step 1. Concept Understanding
When light falls on a metal surface, it emits electrons - this is called the
photoelectric effect.
The emitted electrons are called photoelectrons, and the current due to
their flow is known as photoelectric current (I).
The current depends on how many electrons are emitted per second, i.e.
𝐼 ∝ 𝑛
where 𝑛 = number of photoelectrons emitted per second.
Step 2. Relation between Intensity and Number of Photoelectrons
• The intensity of light means the energy incident per unit area per
second.
• If the frequency of the light is above the threshold frequency, then:
o Increasing the intensity increases the number of photons
striking the surface per second.
o Each photon can eject one electron.
o Hence, more photons → more electrons emitted → greater
photoelectric current.
So,
𝑛 ∝ Intensity of light
Step 3. What does not affect the number of photoelectrons

• The frequency of the radiation affects only the energy of emitted
electrons, not their number.
• The number of emitted electrons depends only on intensity (for a
fixed frequency above the threshold).
Final Answer: the number of photoelectrons emitted per second is
directly proportional to the intensity of incident radiation.
Correct Option: 3)

Step 1. Given data:
Mass of the ball,

Velocity,

Planck’s constant,

Step 2. Formula used:
The de-Broglie wavelength is given by:

Step 3. Substitute the values:

Step 4. Interpretation

The wavelength associated with a macroscopic object (like a ball) is
extremely small, which is why wave nature is negligible for large objects.
Final Answer: 1.47 × 10-34 𝑚
Correct Option: 1)

Step 1. Understanding the question
We are given four statements related to the radius, volume, and density of
an atomic nucleus and must find which are correct.
Step 2. Recall important nuclear relations
1. The radius of a nucleus is given by:
𝑅 = 𝑅0𝐴1/3
where 𝑅0 ≈ 1.2 × 10-15 m, and 𝐴 is the mass number.
2. The volume of a sphere (nucleus) is proportional to 𝑅3, so:
𝑉 ∝ 𝑅3 ∝ (𝐴1/3) 3 = 𝐴
3. Density of nucleus:

Hence, nuclear density is constant and does not depend on A.
Step 3. Evaluate each statement
(A) A nucleus of mass number A has a radius 𝑅 = 𝑅₀𝐴¹ᐟ³
→ Correct, this is the standard nuclear radius formula.
(B) Volume of nucleus is proportional to mass number 𝐴
→ Correct, since 𝑉 ∝ 𝐴.
(C) ❌ The density of nucleus increases with the radius of nucleus
→ Incorrect, density is constant, independent of radius.
(D) Density of nuclear matter does not depend on its mass number A

→ Correct, because 𝑝 is constant for all nuclei.
Final Answer: (A), (B), and (D) only
Correct Option: 3)

Step 1. Given data:
• Energy absorbed by the electron = 12.09 eV
• The electron is initially in the ground state (n = 1).
We need to find the increase in angular momentum after absorption.
Step 2. Formula for energy levels of hydrogen atom:

When the electron absorbs energy, the energy difference between levels is:

Step 3. Substitute the values:

Step 4. Solve for 𝑛2:

Step 5. Angular momentum formula:

Angular momentum of an electron in orbit 𝑛 is given by:

Change in angular momentum:

Final Answer: Increase in angular momentum = 2(ℎ/2π)
Correct Option: 2)

Step 1. Understanding the question
We are given four statements about forces inside an atomic nucleus and
need to identify which are correct.
Step 2. Analyze each statement
(A) The electrostatic repulsive force between the protons can be greater
than the nuclear force to bind the nucleons together inside a nucleus.
❌ Incorrect.
Inside a nucleus, the nuclear (strong) force is much stronger than the
electrostatic repulsion between protons - otherwise, the nucleus would not
remain stable.
(B) The repulsive electrostatic force between protons in smaller nuclei is
much smaller than the nuclear force between nucleons inside a nucleus.
Correct.
For small nuclei, protons are close together, but the strong nuclear force
dominates over electrostatic repulsion, keeping the nucleus stable.
(C) The gravitational force between nucleons is much smaller than the
nuclear force between the nucleons inside a nucleus.
Correct.

The gravitational force between nucleons is negligible compared to the
strong nuclear force, which is responsible for holding the nucleus together.
(D) The binding energy per nucleon between nucleons is almost constant
because the nuclear force is a long-range force.
❌ Incorrect.
The nuclear force is a short-range force, effective only up to about 2–3
femtometers (fm). The binding energy per nucleon is nearly constant due
to saturation of nuclear force, not because it is long-range.
Final Answer: (B) and (C) only
Correct Option: 2)

Step 1. Understanding the question
We are given statements related to electronic devices, and we must identify
which ones are true.
Step 2. Analyze each statement
(A) Diodes can be used for rectifying an AC voltage.
True. A diode allows current to flow only in one direction, converting AC
into DC. Hence, it is used in rectifiers.
(B) For semiconductors, band gap energy (Eg) > 3 eV.
❌ False. For semiconductors, the band gap is less than 3 eV.
Examples:
• Silicon (Si): 1.1 eV
• Germanium (Ge): 0.7 eV
If Eg > 3 eV, the material is an insulator.
(C) By changing the external applied voltage, junction barriers can be
changed.
True.

In a p–n junction, applying forward or reverse bias changes the barrier
potential and width of the depletion region.
(D) p–n junction is the ‘key’ to all semiconductor devices.
True.
Most semiconductor devices such as diodes, transistors, LEDs, and solar
cells are based on p–n junctions.
Final Answer: (A), (C), and (D) only
Correct Option: 4)

Step 1. Understanding the question
A device X is connected in a series circuit with a battery and a resistor.
• When the battery is connected in one direction, current flows
normally.
• When the polarity of the battery is reversed, the current drops to
almost zero.
We need to identify which type of device shows this behavior.
Step 2. Analyze the options
(1) p-type semiconductor
❌ A p-type semiconductor alone allows current conduction in both
directions (it’s not a rectifying device). So, this is not correct.
(2) n-type semiconductor
❌ Similarly, an n-type semiconductor conducts in both directions when
connected to a battery, so this is also not correct.
(3) p–n junction diode
This behavior matches perfectly.
• When the diode is forward-biased (p connected to +, n to –), current
flows.

• When it is reverse-biased (p connected to –, n to +), current becomes
almost zero (only a very small leakage current flows).
Hence, the current direction sensitivity is a property of a diode.
(4) Capacitor
❌ A capacitor charges and discharges but does not behave like this for
steady current — it does not stop current completely on polarity reversal in
a DC circuit after charging.
Final Answer: p–n junction diode
Correct Option: 3)

Step 1. Recall what a p-type semiconductor is
A p-type semiconductor is made when a trivalent impurity (like boron,
gallium, or indium) is added to a pure semiconductor (like silicon or
germanium).
• The trivalent atom has 3 valence electrons, while silicon has 4 valence
electrons.
• This leaves one missing electron (a hole) in the crystal structure.
So:
• Holes act as the majority charge carriers.
• Electrons act as the minority charge carriers.
• Trivalent atoms are the dopants.
Step 2. Analyze each statement
(A) “Holes are minority carriers and pentavalent atoms are the dopants.”
❌ Incorrect — Holes are majority carriers, and trivalent, not pentavalent,
atoms are used.
(B) “Electrons are majority carriers and trivalent atoms are the dopants.”
❌ Incorrect — Electrons are minority carriers in p-type semiconductors.
(C) “Holes are majority carriers and trivalent atoms are the dopants.”

Correct — This is the true statement for a p-type semiconductor.
(D) “Electrons are minority carriers and pentavalent atoms are the
dopants.”
❌ Partially correct — Electrons are minority carriers, but pentavalent
atoms are not the dopants here (they are for n-type semiconductors).
Final Answer: (C) only
Correct Option: 2)

Step 1: Balance the atomic numbers
The sum of the atomic numbers (subscripts) on the reactant side must
equal the sum of the atomic numbers on the product side.
0 + 92 = 54 + 𝑎 + 2(0)
92 = 54 + 𝑎
𝑎 = 92 - 54
𝑎 = 38
Step 2: Balance the mass numbers
The sum of the mass numbers (superscripts) on the reactant side must
equal the sum of the mass numbers on the product side.
1 + 235 = 140 + 𝑏 + 2(1)
236 = 140 + 𝑏 + 2
236 = 142 + 𝑏
𝑏 = 236 - 142
𝑏 = 94
Final Answer: 𝑎 = 38, 𝑏 = 94
Correct Option: 1)

Step 1. de Broglie wavelength for an accelerated particle
For a particle accelerated through potential 𝑉:

Step 2. Set wavelengths equal (proton vs α-particle)
For the proton (mass 𝑚𝑝, charge e, potential 𝑉):

For the α-particle (mass 𝑚𝛼 = 4𝑚𝑝, charge 𝑞𝛼 = 2e, potential 𝑉𝛼):

Equal wavelengths ⇒ denominators equal:

Step 3. Solve for 𝑉𝛼 using 𝑚𝛼 = 4𝑚𝑝, 𝑞𝛼 = 2e

Final Answer: 𝑉/8
Correct Option: 2)