Physics (Theory) Specimen Paper 2025-2026 ISC (Science) ISC Class 12 Question Paper Solution

Two point charges +50 nc and −50 nc separated a distance of 1 mm are kept well inside a large sphere of radium 1 m. Electric flux emanating from the sphere is ______.

50 × 10⁻¹² Vm

50 × 10⁻⁹ Vm

50 × 10⁻⁶ Vm

Zero

Three straight, parallel wires are coplanar and perpendicular to the plane of the page. The currents I₁ and I₃ are directed out of the page. If wire 3 experiences no force due to the currents I₁ and I₂, then the current in the wire 2 is:

I₂ = 2 I₁ and directed into the page

I₂ = 0.5 I₁ and directed into the page

I₂ = 2 I₁ and directed out of the page

I₂ = 0.5 I₁ and directed out of the page

The variation of magnetic susceptibility (x) with absolute temperature (T) for a diamagnetic substance is:

The wavelength λ_e of an electron and λ_p of a photon of same energy E are related by ______.

λ_p ∝ λ_e

`λ_p ∝ sqrt(lambda_e)`

`λ_p ∝ 1/sqrt(lambda_e)`

`λ_p ∝ lambda_e^2`

In which of the following figures is the p-n diode forward biased?

(P)
(Q)
(R)
(S)

Only (P), (Q) and (S)

Only (R)

Only (P) and (R)

Only (Q) and (S)

When a beam of white light is incident on a prism, the prism ______.

only disperses the incident light.

only disperses the incident light.

deviates as well as disperses incident light.

neither deviates nor disperses incident light.

Assertion: The focal length of the convex mirror will increase if the mirror is placed in water.

Reason: The focal length of a convex mirror of radius R is equal to `R/2`.

Both Assertion and Reason are true and Reason is the correct explanation for Assertion.

Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.

Assertion is true and Reason is false.

Assertion is false and Reason is true.

Current I flowing through a metallic wire is gradually increased. Show graphically how heating power (P) developed in it varies with the current (I).

State one method to minimise flux loss in a transformer.

Why are giant telescopes of the reflecting type? Give any one scientific reason.

Give any one example where a ray of light travelling from one optical medium to another travels undeviated.

Two charged particles having the same charge but different masses are passed through a potential difference V. When V is varied, de-Broglie wavelength (λ) of the particles varies as shown in the graph below. Which graph is for heavier particles and why?

What happens when an electron collides with a positron?

What is the direction of flow of electrons in a solar cell?

Find the capacitance of the following combinations between terminals A and B. Area of the plate is A and the separation between the nearest two plates is ‘d’.

Find the capacitance of the following combinations between terminals A and B. Area of the plate is A and the separation between the nearest two plates is ‘d’.

The current (I)-voltage (V) graphs for a conductor are given at two different temperatures T₁ and T₂.

1. At which temperature T₁ or T₂ is the resistance higher?
2. Which temperature T₁ or T₂ is higher?

Arrangement of an oxygen ion and two hydrogen ions in a water molecule is shown in the figure below.

Calculate the electric dipole moment of a water molecule. Express your answer in terms of e (charge on hydrogen ions), l and θ.

Two cells of the same emf E but different internal resistances r₁ and r₂ are connected to an external resistance R as shown in the figure given below. The voltmeter V reads zero. Obtain an expression for R in terms of r₁ and r₂. (Assume that the voltmeter V is of infinite resistance).

Ramesh performed an experiment to determine an unknown resistance R using the circuit shown in the figure below. X is a resistance box and PQ is a 100 cm potentiometer wire. He closed the key and inserted X = 1 Ω, 2 Ω and recorded the null point (l) corresponding to different values of X.

1. Identify the principle involved in calculating R.
2. Write down a relation required to calculate the resistance R in terms of X and (l).

Two moving coil galvanometers G₁ and G₂ are identical except that they have 50 turns and 20 turns and resistances of 10 Ω and 1 Ω, respectively. Perform necessary calculations to check which one has greater voltage sensitivity.

Two similar convex lenses are made up of two different materials, as shown in the figures below. Find the number of images formed in the following setups:

(i)
(ii)

Name the electromagnetic wave used in radars.

Name the electromagnetic wave used in crystallography.

In the photoelectric effect, the maximum kinetic energy of the emitted photoelectron is ‘a’ and the work function of the metal is W₀. If the frequency of incident radiation is made ‘K’ times, then calculate the change in maximum KE of the ejected electron.

Obtain an expression for electric potential (V) at a point near a point charge ‘Q’.

Five identical charges, Q = 2μC are placed equidistant on a semicircle as shown in the figure. Another point charge q = 1μC is kept at the center of the circle of radius 2 cm. Calculate the electrostatic force experienced by the charge q.

Using Kirchhoff’s laws of electrical networks, calculate the current I₃.

Using Ampere circuital law, obtain an expression for magnetic field ‘B’ at a point at a perpendicular distance ‘r’ from a long current carrying conductor.

A student records the following data for the magnitudes (B) of the magnetic field at axial points at different distances x (See figure given below) from the centre O of a circular coil of radius a carrying a current I. Verify (for any two) that these observations are in good agreement with the expected theoretical values of B.

An electron moving along the positive X axis with a velocity of 8 × 10⁷ ms⁻¹ enters a region having a uniform magnetic field B = 1.3 × 10⁻³ T along the positive Y axis.

1. Explain why the electron describes a circular path.
2. Calculate the radius of the circular path described by the electron.

Study the diagram shown below.

Identify the following in the figure.

1. A primary wavefront
2. A secondary wavefront
3. A wave normal

In Young’s double slit experiment, show that fringe width ω (fringe separation) is given by

ω = `(lambda D)/d`

where the terms have their usual meaning.

With reference to the lens maker’s formula, answer the following questions:

1. Apply the formula (expression) of refraction at a single spherical surface to:
   1. refraction at the first spherical surface.
   2. refraction at the second spherical surface.
2. Combine these two expressions/equations to obtain an expression for the focal length of the lens.

A student studies details of a microorganism with the help of an instrument. Name the instrument used by him.

Draw a labelled ray diagram of an image formed by this instrument, assuming

1. a small upright object.
2. image lies at least distance of distinct vision.

In a hydrogen atom, an electron jumps from the first excited state to the ground state, and a photon is emitted. This photon is incident on a metal surface having a work function of 2eV. Calculate the stopping potential of the electron emitted from the metal surface.

Define the coefficient of self-induction.

1. Consider an A.C. source of frequency `(200/pi)` Hz applied across a coil. For each value of V − I in the tabulation, evaluate inductive reactance and self-inductance of the coil.
   

   S. No.	V (volt)	I (A)	Inductive reactance	Self-inductance
   1	3.0	0.5
   2	6.0	1.0
   3	9.0	1.5

2. If a D.C. source be connected to the same coil, what would be the value of inductive reactance?

Three students, X, Y and Z performed an experiment for studying the variation of ac with frequency in a series LCR circuit and obtained the graphs as shown below. They all used

• an AC source of the same emf and
• inductance of the same value.

1. Who used minimum resistance?
2. In which case will the quality Q factor be maximum?
3. What did the students conclude about the nature of impedance at resonant frequency (f₀)?
4. An ideal capacitor is connected across 220 V, 50 Hz, and 220 V, 100 Hz supplies. Find the ratio of current flowing through it in the two cases.

Study the graph shown below and answer the questions that follow. 

Indicate which region corresponds to:

1. Nuclei prone to fission
2. Nuclei prone to fusion
3. Most stable nuclei

In Rutherford’s scattering experiment when an alpha particle (charge = +2 e, mass = 4 m_p) approaches a gold nucleus (Z = 79), it is continuously repelled, so it loses its kinetic energy (K) and its potential energy increases. Finally, an α-particle comes to rest momentarily when whole of the kinetic energy is changed into the potential energy of the charge at that distance from the nucleus. Let this distance be r₀ after which the α-particle returns back again due to electrostatic repulsion. Using the above information, derive an expression for r₀.

In an atom X, electrons absorb the energy from an external source. This energy “excites” the electrons from a lower-energy level to a higher-energy level around the nucleus of the atom. When electrons return to the ground state, they emit photons.

Figure below is the energy level diagram of atom X with three energy levels, E₁ = 0.00 eV, E₂ = 1.78 eV and E₃ = 2.95 eV. The ground state is considered 0 eV for reference.

What wavelength of radiation is needed to excite the atom to energy level E₂ from E₁?

According to Bohr’s theory of the hydrogen atom, calculate:

1. angular momentum of the electron in the second Bohr orbit.
2. radius of the third Bohr orbit.

A band gap is the distance between the valence band of electrons and the conduction band. Essentially, the band gap represents the minimum energy that is required to excite an electron up to a state in the conduction band where it can participate in conduction. The lower energy level is the valence band, and thus, if a gap exists between this level and the higher energy conduction band, energy must be input for electrons to become free.

An LED is made of a p-type semiconductor material (which has a higher concentration of “holes” or positive charge carriers) and an n-type semiconductor material (which has a higher concentration of electrons or negative charge carriers). This recombination process releases energy in the form of light and heat. The specific wavelength (and therefore the colour) of the emitted light depends on the energy band gap of the semiconductor material used.

The I-V characteristic of the LED bulb is given below.

1. Identify the wavelength that has:
   1. The maximum energy gap.
   2. The minimum energy gap.
2.  E is the energy of the incident photon and E_g is the energy gap, which is produced across the depletion layer. What will happen in the following cases:
   1. E > E_g
   2. E = E_g
   3. E < E_g