CBSE Class 12 Physics Compartment Set 3 - (55/7/3) Question Paper 2026 PDF

The radius of the innermost electron orbit of a hydrogen atom is \(0.53\,\text{\AA}\). The radius of orbit in the second excited state is:

• (A) \(3.5\,\text{\AA}\)
• (B) \(4.77\,\text{\AA}\)
• (C) \(0.747\,\text{\AA}\)
• (D) \(0.43\,\text{\AA}\)

• (A) 2.0 A
• (B) 1.5 A
• (C) 1.0 A
• (D) 0.5 A

A ray of light passes from a medium of refractive index \(\sqrt{2}\) to the medium of refractive index \(1\). For the ray to just graze along the surface of separation, the angle of incidence should be:

• (A) \(\dfrac{\pi}{3}\)
• (B) \(\dfrac{\pi}{4}\)
• (C) \(\dfrac{\pi}{6}\)
• (D) \(\dfrac{2\pi}{3}\)

In forward and reverse biased silicon p-n junction, the dominant mechanisms for the motion of charge carriers are:

• (A) diffusion in forward bias, drift in reverse bias
• (B) drift in both forward bias and in reverse bias
• (C) drift in forward and diffusion in reverse bias
• (D) diffusion in both forward and reverse bias

When the distance between the slit and screen is doubled, the angular separation between two fringes in single-slit diffraction experiment will:

• (A) be doubled
• (B) be halved
• (C) remain constant
• (D) become one-fourth

If \(\nu_X\), \(\nu_G\) and \(\nu_U\) are frequencies of X-rays, Gamma-rays and UV rays respectively, then:

• (A) \(\nu_X > \nu_G > \nu_U\)
• (B) \(\nu_G > \nu_X > \nu_U\)
• (C) \(\nu_U > \nu_X > \nu_G\)
• (D) \(\nu_X > \nu_U > \nu_G\)

Which of the following is also referred to as 'heat waves'?

• (A) Gamma rays
• (B) X-rays
• (C) UV rays
• (D) Infrared rays

Two infinitely long straight conductors lie along the x-axis and y-axis in the plane of the page. If they carry current \(I\) each along \(+x\)-axis and \(+y\)-axis respectively, the net magnetic field at a point with position vector \(\vec{r} = (3\hat{i} + 4\hat{j})\) m will be:

• (A) \(\dfrac{\mu_0 I}{6\pi}\hat{k}\)
• (B) \(-\dfrac{\mu_0 I}{12\pi}\hat{k}\)
• (C) \(-\dfrac{\mu_0 I}{24\pi}\hat{k}\)
• (D) \(\dfrac{\mu_0 I}{48\pi}\hat{k}\)

Assume that the surface charge density of the Earth is 1 electron charge/m². The potential of the Earth's surface (radius 6400 km) will be:

• (A) \(-0.12\,\text{V}\)
• (B) \(-0.21\,\text{V}\)
• (C) \(+2.1\,\text{V}\)
• (D) \(+1.2\,\text{V}\)

In an electromagnetic wave, the electric field (\(\vec{E}\)) and the magnetic field (\(\vec{B}\)) oscillate along x-axis and y-axis respectively. The wave is propagating along:

• (A) \(z\)-axis
• (B) \(-z\)-axis
• (C) \(x\)-axis
• (D) \(-y\)-axis

In a series LCR circuit connected to an ac source of voltage \(V\) and frequency \(\omega\), the power loss at resonance is:

• (A) \(I^2\omega L\)
• (B) \(V^2/(\omega C)\)
• (C) \(V^2/R\)
• (D) \(V^2/\left(\omega L - \dfrac{1}{\omega C}\right)\)

• (A) \(E\) constant from \(O\) to \(R\), then decreasing for \(x > R\)
• (B) \(E\) rising from zero to a peak at \(R\) (curved rise), then decreasing
• (C) \(E\) zero from \(O\) to \(R\), then a jump at \(R\) and decreasing for \(x > R\)
• (D) \(E\) rising linearly from zero to \(R\), then decreasing

Assertion (A) : A free neutron is not a stable particle.

Reason (R) : It decays into a proton and an electron.

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• (C) Assertion (A) is true, but Reason (R) is false.
• (D) Both Assertion (A) and Reason (R) are false.

Assertion (A) : Electron emission from surface of zinc occurs when yellow light is incident on it.

Reason (R) : Energy of a photon of yellow light is more than the work function of zinc.

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• (C) Assertion (A) is true, but Reason (R) is false.
• (D) Both Assertion (A) and Reason (R) are false.

Assertion (A): If \(\vec{B}\) be the magnetic field at a small patch of vector area \(d\vec{S}\), then the magnetic flux through the patch will be \(\vec{B}\cdot d\vec{S}\).

Reason (R): The magnetic flux is a scalar quantity.

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• (C) Assertion (A) is true, but Reason (R) is false.
• (D) Both Assertion (A) and Reason (R) are false.

Assertion (A): The ratio of the speeds of the electron in the second to that in the third orbit in Bohr's hydrogen atom is \(\dfrac{3}{2}\).

Reason (R): The speed of the electron in \(n^{th}\) permitted orbit in hydrogen atom varies proportional to \(\dfrac{1}{n}\) i.e. \(v_n \propto \dfrac{1}{n}\).

• (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• (C) Assertion (A) is true, but Reason (R) is false.
• (D) Both Assertion (A) and Reason (R) are false.

An electron is revolving around a proton in a circular orbit of radius \(r\). Using classical physics, prove that the ratio of value of the angular momentum and the value of magnetic moment of electron revolving in the orbit is a constant.

Two identical circular coils A and B of radius \(10\) cm each are placed concentrically and mutually perpendicular in XY and YZ planes respectively. Currents of \(1\) A and \(\sqrt{3}\) A flow anticlockwise in the coils as seen from YZ plane. Find the magnitude of the net magnetic field at the common centre of the coils.

Find the ratio of energies of photons emitted during the transition of an electron in hydrogen atom from its:

(i) second permitted energy level to the first permitted energy level, and

(ii) the highest permitted energy level to the first permitted energy level.

A monochromatic beam of light is travelling from a rarer to a denser medium. Giving reasons, explain the following :

(i) Is the frequency of the reflected and the refracted light the same as the frequency of incident light ?

(ii) Does the decrease in speed of light in denser medium imply a reduction in the energy carried by the light wave ?

(i) The lower half of a concave mirror's reflecting surface is covered with an opaque non-reflecting material. What effect will this have on the image of an object placed in front of the mirror ?

(ii) A lens made of glass of refractive index \(1.5\) disappears, when immersed in a trough of liquid. What is the refractive index of the liquid ?

Give reasons for your answer in each case.

The number of free electrons per unit volume (\(\text{m}^3\)) in a wire made of copper (resistivity \(1.72 \times 10^{-8}\,\Omega\,\text{m}\)) is \(8.5 \times 10^{28}\). Calculate the average number of collisions made by an electron in one second when an electric field is maintained in the wire.

Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

Four point charges \(+q\), \(-q\), \(+q\) and \(-q\) are to be arranged respectively at the four corners of a square ABCD of the sides \(l\). Calculate the amount of:

(i) work done to obtain this arrangement.

(ii) extra work done to bring a point charge \(q_0\) at the centre of the square when the charges at the corners are kept fixed.

Two thin converging lenses of focal lengths \(f_1\) and \(f_2\) are placed coaxially in contact with each other. Draw a ray diagram to show the image formation by the combination. Hence, derive the expression for the focal length of the combination.

Two charges of \(8\,\mu\text{C}\) and \(-4\,\mu\text{C}\) are located at points \((-18\ \text{cm}, 0, 0)\) and \((18\ \text{cm}, 0, 0)\) respectively.

(i) Calculate the electrostatic potential energy of the system of the two charges.

(ii) The same system of charges is placed in a region where electrostatic potential \(V(r) = \dfrac{A}{r}\), where \(A = 9 \times 10^4\) V.m. Calculate the potential energy of the system.

Two converging lenses \(L_1\) and \(L_2\), of focal lengths \(144\,\text{cm}\) and \(6\,\text{cm}\) respectively, are arranged coaxially in a tube \(147\,\text{cm}\) apart. The arrangement is used to view a far off tree, keeping the eye close to \(L_2\).

(i) Draw the ray diagram depicting image formation by the combination.

(ii) How far from \(L_2\) will the final image be formed?

(iii) Calculate the magnification produced by the combination.

Comprehension:

A particle of mass m and charge q experiences a force \(\vec{F}_e\) in an electric field \(\vec{E}\) and it is directed along the field. When the particle is moving with velocity \(\vec{v}\) in a magnetic field \(\vec{B}\), it experiences a force \(\vec{F}_B\), that is perpendicular to both \(\vec{v}\) and \(\vec{B}\).

In presence of both fields, the force acting on the particle is the vector

A particle of mass m and charge q experiences a force \(\vec{F}_e\) in an electric field \(\vec{E}\) and it is directed along the field. When the particle is moving with velocity \(\vec{v}\) in a magnetic field \(\vec{B}\), it experiences a force \(\vec{F}_B\), that is perpendicular to both \(\vec{v}\) and \(\vec{B}\).

In presence of both fields, the force acting on the particle is the vector sum of that due to \(\vec{E}\) and that due to \(\vec{B}\).

A current-carrying conductor also experiences a force in presence of a magnetic field. The force \(d\vec{F}\) acting on a current-element \(I\,d\vec{l}\) is perpendicular to both the current element, and the magnetic field \(\vec{B}\). The net force acting on a conductor of a given length is the vector sum of all \(d\vec{F}\)s.

• (A) go straight, undeviated on a rectilinear path
• (B) travel on a circular path
• (C) travel on a semicircular path
• (D) travel on a helical path

A particle of mass m and charge q experiences a force \(\vec{F}_e\) in an electric field \(\vec{E}\) and it is directed along the field. When the particle is moving with velocity \(\vec{v}\) in a magnetic field \(\vec{B}\), it experiences a force \(\vec{F}_B\), that is perpendicular to both \(\vec{v}\) and \(\vec{B}\).

In presence of both fields, the force acting on the particle is the vector sum of that due to \(\vec{E}\) and that due to \(\vec{B}\).

A current-carrying conductor also experiences a force in presence of a magnetic field. The force \(d\vec{F}\) acting on a current-element \(I\,d\vec{l}\) is perpendicular to both the current element, and the magnetic field \(\vec{B}\). The net force acting on a conductor of a given length is the vector sum of all \(d\vec{F}\)s.

• (A) \(0.11\,\mu\text{s}\)
• (B) \(0.28\,\mu\text{s}\)
• (C) \(0.014\,\mu\text{s}\)
• (D) \(0.024\,\mu\text{s}\)

A particle of mass m and charge q experiences a force \(\vec{F}_e\) in an electric field \(\vec{E}\) and it is directed along the field. When the particle is moving with velocity \(\vec{v}\) in a magnetic field \(\vec{B}\), it experiences a force \(\vec{F}_B\), that is perpendicular to both \(\vec{v}\) and \(\vec{B}\).

In presence of both fields, the force acting on the particle is the vector sum of that due to \(\vec{E}\) and that due to \(\vec{B}\).

A current-carrying conductor also experiences a force in presence of a magnetic field. The force \(d\vec{F}\) acting on a current-element \(I\,d\vec{l}\) is perpendicular to both the current element, and the magnetic field \(\vec{B}\). The net force acting on a conductor of a given length is the vector sum of all \(d\vec{F}\)s.

• (A) 1.00 m
• (B) 2.00 m
• (C) 3.00 m
• (D) 4.00 m

A particle of mass m and charge q experiences a force \(\vec{F}_e\) in an electric field \(\vec{E}\) and it is directed along the field. When the particle is moving with velocity \(\vec{v}\) in a magnetic field \(\vec{B}\), it experiences a force \(\vec{F}_B\), that is perpendicular to both \(\vec{v}\) and \(\vec{B}\).

In presence of both fields, the force acting on the particle is the vector sum of that due to \(\vec{E}\) and that due to \(\vec{B}\).

A current-carrying conductor also experiences a force in presence of a magnetic field. The force \(d\vec{F}\) acting on a current-element \(I\,d\vec{l}\) is perpendicular to both the current element, and the magnetic field \(\vec{B}\). The net force acting on a conductor of a given length is the vector sum of all \(d\vec{F}\)s.

• (A) \(\left(120\,\dfrac{\text{N}}{\text{C}}\right)\hat{k}\)
• (B) \(-\left(300\,\dfrac{\text{N}}{\text{C}}\right)\hat{k}\)
• (C) \(\left(600\,\dfrac{\text{N}}{\text{C}}\right)\hat{j}\)
• (D) \(-\left(150\,\dfrac{\text{N}}{\text{C}}\right)\hat{i}\)

A particle of mass m and charge q experiences a force \(\vec{F}_e\) in an electric field \(\vec{E}\) and it is directed along the field. When the particle is moving with velocity \(\vec{v}\) in a magnetic field \(\vec{B}\), it experiences a force \(\vec{F}_B\), that is perpendicular to both \(\vec{v}\) and \(\vec{B}\).

In presence of both fields, the force acting on the particle is the vector sum of that due to \(\vec{E}\) and that due to \(\vec{B}\).

A current-carrying conductor also experiences a force in presence of a magnetic field. The force \(d\vec{F}\) acting on a current-element \(I\,d\vec{l}\) is perpendicular to both the current element, and the magnetic field \(\vec{B}\). The net force acting on a conductor of a given length is the vector sum of all \(d\vec{F}\)s.

• (A) \(\dfrac{mgdl}{I}\hat{k}\)
• (B) \(\dfrac{mg}{I}\hat{j}\)
• (C) \(-\dfrac{mg}{Idl}\hat{i}\)
• (D) \(-\left(\dfrac{Idl}{mg}\right)\hat{k}\)

Comprehension:

When radiation of suitable frequency is incident on a metal surface, electrons are emitted from the surface. This phenomenon is called photoelectric effect. Einstein explained

When radiation of suitable frequency is incident on a metal surface, electrons are emitted from the surface. This phenomenon is called photoelectric effect. Einstein explained this phenomenon considering the particle nature of radiation and using the law of conservation of energy. Wave theory of light could not explain this phenomenon.

• (A) work function of the material
• (B) wavelength of the incident radiation
• (C) intensity of the incident radiation
• (D) collector plate potential

When radiation of suitable frequency is incident on a metal surface, electrons are emitted from the surface. This phenomenon is called photoelectric effect. Einstein explained this phenomenon considering the particle nature of radiation and using the law of conservation of energy. Wave theory of light could not explain this phenomenon.

• (A) 1.20 eV
• (B) 1.48 eV
• (C) 2.08 eV
• (D) 6.48 eV

When radiation of suitable frequency is incident on a metal surface, electrons are emitted from the surface. This phenomenon is called photoelectric effect. Einstein explained this phenomenon considering the particle nature of radiation and using the law of conservation of energy. Wave theory of light could not explain this phenomenon.

• (A) \(\nu_0\)
• (B) \(1/\nu_0\)
• (C) \(e\nu_0\)
• (D) \(\nu_0/h\)

When radiation of suitable frequency is incident on a metal surface, electrons are emitted from the surface. This phenomenon is called photoelectric effect. Einstein explained this phenomenon considering the particle nature of radiation and using the law of conservation of energy. Wave theory of light could not explain this phenomenon.

• (A) \(3.2 \times 10^{-19}\) J
• (B) \(1.6 \times 10^{-19}\) J
• (C) \(1.25 \times 10^{-19}\) J
• (D) \(2.4 \times 10^{-18}\) J

When radiation of suitable frequency is incident on a metal surface, electrons are emitted from the surface. This phenomenon is called photoelectric effect. Einstein explained this phenomenon considering the particle nature of radiation and using the law of conservation of energy. Wave theory of light could not explain this phenomenon.

• (A) \(4.8 \times 10^{14}\) Hz
• (B) \(5.3 \times 10^{14}\) Hz
• (C) \(1.9 \times 10^{15}\) Hz
• (D) \(1.2 \times 10^{15}\) Hz

A small bulb is placed at the bottom of a tank containing water to a depth of \(1.00\,\text{m}\). Find the area of the surface of water through which light from the bulb can emerge from. The refractive index of water is \((4/3)\).

An object is placed at a distance of \(15\,\text{cm}\) from a convex lens of focal length \(10\,\text{cm}\). On the other side of the lens, a convex mirror is placed coaxially at a distance of \(10\,\text{cm}\) from the lens. If the image formed by this combination coincides with the object itself, draw the ray diagram and find the focal length of the convex mirror.

Differentiate between interference and diffraction of light.

Two coherent light waves, each of intensity \(I_0\) produce interference pattern on a screen. Find the intensity at a point at which the path difference between them is (i) \(\dfrac{\lambda}{3}\), and (ii) \(\dfrac{\lambda}{4}\).

In a Young's double-slit experiment, fringes are obtained on a screen placed at a distance \(D\) from the slits. It is observed that if the screen is moved \(5\,\text{cm}\) towards the slits, the fringe width changes by \(0.03\,\text{mm}\). If the distance between the slits is \(1\,\text{mm}\), calculate the wavelength of the light used.

A potential difference \(V\) is applied across the ends of a cylindrical conductor of length \(l\), area of cross-section \(A\) and resistance \(R\). It is gradually stretched till its length is tripled. How will (i) the drift speed of electrons in the conductor, and (ii) the resistance of the conductor be affected? Justify your answers.

A cell of emf \(E\) and internal resistance \(r\) is connected across a resistor of variable resistance \(R\). Draw a plot showing the variation of (i) the current (\(I\)) in the circuit with \(R\), and (ii) the terminal potential difference of the cell with \(R\).

The resistance of a heating coil is \(100\,\Omega\) at \(25^\circ\text{C}\) and \(120\,\Omega\) at \(1025^\circ\text{C}\). (i) Find its resistance at \(425^\circ\text{C}\). (ii) Draw a plot showing variation of its resistance as a function of increase in temperature.

Using a phasor diagram, derive an expression for the impedance of a series LCR circuit connected to an ac source. What is meant by resonance in this circuit? Obtain expression for the resonant frequency of this circuit.

Write two disadvantages of transmitting ac over long distances at low voltage and high current.

An ac generator consists of a coil of 500 turns and size \(25\,\text{cm} \times 100\,\text{cm}\). It is rotated at an angular speed of \(60\,\text{rad/s}\) in a uniform magnetic field \(B = 0.4\,\text{T}\) between two fixed pole pieces. If the resistance of the circuit, including that of the coil, is \(250\,\Omega\), calculate:

(I) the maximum current drawn from the generator

(II) the flux through the coil when the current is zero

Give two examples of commercial generators. How is rotation of armature achieved in them? Explain briefly.