PHYSICS BYTES
CBSE CLASS 12 PHYSICS BOARD EXAM 2026
Official Question Paper & Solutions | Set 3 | Q.P. Code 55/5/3
Time Allowed: 3 Hours
Maximum Marks: 70
GENERAL INSTRUCTIONS:
- There are 33 questions in all. All questions are compulsory.
- This question paper has five sections: Section A, Section B, Section C, Section D and Section E.
- Section A contains 16 questions of 1 mark each.
- Section B contains 5 questions of 2 marks each.
- Section C contains 7 questions of 3 marks each.
- Section D contains 2 case study-based questions of 4 marks each.
- Section E contains 3 long answer questions of 5 marks each.
- There is no overall choice. However, internal choices have been provided in some questions.
SECTION A
(1 Mark Each)
1.
A 500 nm photon is incident normally on a perfectly reflecting surface and is reflected. The value of momentum transferred to the surface is :
(A) $3.87\times10^{-43}kg~ms^{-1}$
(B) $2.5\times10^{-30}kg~ms^{-1}$
(C) $2.65\times10^{-27}kg~ms^{-1}$
(D) $1.33\times10^{-27}kg~ms^{-1}$
[1]
2.
A good diode checked by a multimeter should indicate:
(A) high resistance in reverse bias and a low resistance in forward bias
(B) high resistance in both forward bias and reverse bias
(C) low resistance in both reverse bias and forward bias
(D) high resistance in forward bias and low resistance in reverse bias
[1]
3.
A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of $60^{\circ}$ in 0.2 s. The value of emf induced in the loop will be :
(A) 5 V
(B) 3.5 V
(C) 2.5 V
(D) Zero V
[1]
4.
The magnetic field in a plane electromagnetic wave travelling in glass $(n=1.5)$ is given by $B_{y}=(2\times10^{-7}T)\sin(\alpha x+1.5\times10^{11}t)$ where x is in metres and t is in seconds. The value of $\alpha$ is:
(A) $0.5\times10^{3}m^{-1}$
(B) $6.0\times10^{2}m^{-1}$
(C) $7.5\times10^{2}m^{-1}$
(D) $1.5\times10^{3}m^{-1}$
[1]
5.
A charged particle is moving in a uniform magnetic field with a constant speed v in a circular path of radius r. Which of the following graphs represents the variation of radius of the circle, with the magnitude of magnetic field $\vec{B}$?
[1]
6.
Which of the following statements is not true for electric energy in ac form compared to that in dc form?
(A) Production of ac is economical.
(B) ac can be easily and efficiently converted from one voltage to the other.
(C) ac can be transmitted economically over long distances.
(D) ac is less dangerous.
[1]
7.
The energy of an electron in an orbit in hydrogen atom is - 3.4 eV. Its angular momentum in the orbit will be :
(A) $\frac{3h}{2\pi}$
(B) $\frac{2h}{\pi}$
(C) $\frac{h}{\pi}$
(D) $\frac{h}{2\pi}$
[1]
8.
The rms and the average value of an ac voltage $V=V_{0} \sin \omega t$ volt over a cycle respectively will be:
(A) $\frac{V_{0}}{2},\frac{V_{0}}{\sqrt{2}}$
(B) $\frac{V_{0}}{\pi};\frac{V_{0}}{2}$
(C) $\frac{V_{0}}{\sqrt{2}},0$
(D) $\frac{V_{0}}{\sqrt{2}}, \frac{V_{0}}{\pi}$
[1]
9.
The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be:
(A) $\frac{q}{4\pi\epsilon_{0}l^{2}}$ pointing along MA
(B) $\frac{q}{\pi\epsilon_{0}l^{2}}$ pointing along AM
(C) $\frac{q}{2\pi\epsilon_{0}l^{2}}$ pointing along AM
(D) Zero
[1]
10.
Consider the nuclear reaction $X\rightarrow Y+Z$ Let $M_{x}$, $M_{y}$ and $M_{z}$ be the masses of the three nuclei X, Y and Z respectively. Then which of the following relations hold true?
(A) $(M_{x}-M_{z})
(B) $(M_{x}-M_{y})
(C) $M_{x}>(M_{y}+M_{z})$
(D) $M_{x}<(M_{y}+M_{z})$
[1]
11.
Two points R and S are equidistant from two charges + Q and - 2Q. The work done in moving a charge - Q from point R to S is :
(A) Zero
(B) $-\frac{Q}{4\pi\epsilon_{0}d}$
(C) $\frac{Q}{4\pi\epsilon_{0}d}$
(D) $\frac{3Q}{4\pi\epsilon_{0}d}$
[1]
12.
The radius of a nucleus of mass number 125 is
(A) 6.0 fm
(B) 30 fm
(C) 72 fm
(D) 150 fm
[1]
Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
(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.
(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.
13.
Assertion (A): In Young's double-slit experiment, the fringe width for dark and bright fringes is the same.
Reason (R): Fringe width is given by $\beta=\frac{\lambda D}{d}$, where symbols have their usual meanings.
Reason (R): Fringe width is given by $\beta=\frac{\lambda D}{d}$, where symbols have their usual meanings.
[1]
14.
Assertion (A): Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion.
Reason (R): For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei, it decreases with increasing Z.
Reason (R): For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei, it decreases with increasing Z.
[1]
15.
Assertion (A): Photoelectric effect is a spontaneous phenomenon.
Reason (R): According to the wave picture of radiation, an electron would take hours/days to absorb sufficient energy to overcome the work function and come out from a metal surface.
Reason (R): According to the wave picture of radiation, an electron would take hours/days to absorb sufficient energy to overcome the work function and come out from a metal surface.
[1]
16.
Assertion (A): Induced emf produced in a coil will be more when the magnetic flux linked with the coil is more.
Reason (R): Induced emf produced is directly proportional to the magnetic flux.
Reason (R): Induced emf produced is directly proportional to the magnetic flux.
[1]
SECTION B
(2 Marks Each)
17.
A light copper ring is freely suspended by a light string. A bar magnet is held horizontally with its length along the axis of the ring. The magnet is moved towards the ring with its N pole facing the loop. What will happen to the ring and its position? Explain.
[2]
18.
A ray of light MN is incident normally on the face corresponding with side AB of a prism with an isosceles right-angled triangular base ABC. Trace the path of the ray as it passes through the prism when the refractive index of the prism material is (i) $\sqrt{2}$, and (ii) $\sqrt{3}$.
[2]
19.
When monochromatic light is incident on a surface separating two media, the refracted and reflected light both have the same frequency as the incident frequency but the wavelength of refracted light is different. Explain why.
[2]
20.
Suppose a pure Si crystal has $5\times10^{28}$ atoms per $m^{3}$. It is doped with $5\times10^{22}$ atoms per $m^{3}$ of Arsenic. Calculate the majority and minority carrier concentration in the doped silicon. (Given: $n_{i}=1.5\times10^{16}m^{-3})$
[2]
21.
(a) An electric iron rated 2.2 kW, 220 V is operated at 110 V supply. Find: (i) its resistance, and (ii) heat produced by it in 10 minutes.
OR
(b) A current of 4.0 A flows through a wire of length 1 m and cross-sectional area $1.0~mm^{2}$, when potential difference of 2 V is applied across its ends. Calculate the resistivity of the material of the wire.
[2]
SECTION C
(3 Marks Each)
22.
What is meant by displacement current ? A capacitor is being charged by a battery. Show that Ampere-Maxwell law justifies continuity and constancy of the current flowing in the circuit.
[3]
23.
(a) Can a transformer step up or step down dc power supply?
(b) Can a step up transformer work as a step down transformer?
(c) Does a step up transformer contradict the principle of conservation of energy? Justify your answer.
(b) Can a step up transformer work as a step down transformer?
(c) Does a step up transformer contradict the principle of conservation of energy? Justify your answer.
[3]
24.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.
[3]
25.
Two point charges $q_{1}=2.5\times10^{-7}C$ and $q_{2}=-2.5\times10^{-7}C$ are located at points (0, 0, 15 cm) and (0, 0, -15 cm) respectively. Find:
(a) the electric dipole moment of the system, and
(b) the magnitude and direction of electric field at the origin (0, 0, 0).
(a) the electric dipole moment of the system, and
(b) the magnitude and direction of electric field at the origin (0, 0, 0).
[3]
26.
Photoemission of electrons occurs from a metal $(\phi_{0}=1.96~eV)$ when light of frequency $6.4\times10^{14}Hz$ is incident on it. Calculate:
(a) Energy of a photon in the incident light,
(b) The maximum kinetic energy of the emitted electrons, and
(c) The stopping potential.
(a) Energy of a photon in the incident light,
(b) The maximum kinetic energy of the emitted electrons, and
(c) The stopping potential.
[3]
27.
(a) (i) Write any two features of nuclear forces.
(ii) If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.
(ii) If Bohr's quantization postulate (angular momentum $=\frac{nh}{2\pi})$ is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.
(ii) If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.
OR
(b) (i) Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot. (ii) If Bohr's quantization postulate (angular momentum $=\frac{nh}{2\pi})$ is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.
[3]
28.
Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field $\vec{B}$ at a point (1 m, 1 m, 0).
[3]
SECTION D
(4 Marks Case Study)
29.
Case Study Question
The electric potential (V) and electric field (E) are closely related concepts in electrostatics. The electric field is a vector quantity that represents the force per unit charge at a given point in space, whereas electric potential is a scalar quantity that represents the potential energy per unit charge at a given point in space. Electric field and electric potential are related by the equations $E_{r}=\frac{-dV}{dr}$ and $\vec{E}=E_{r}\hat{r}$, i.e., electric field is the negative gradient of the electric potential. This means that electric field points in the direction of decreasing potential and its magnitude is the rate of change of potential with distance. The electric field is the force that drives a unit charge to move from higher potential region to lower potential region and electric potential difference between the two points determines the work done in moving a unit charge from one point to the other point.
A pair of square conducting plates having sides of length 0.05 m are arranged parallel to each other in x-y plane. They are 0.01 m apart along z-axis and are connected to a 200 V power supply as shown in the figure. An electron enters with a speed of $3\times10^{7}ms^{-1}$ horizontally and symmetrically in the space between the two plates. Neglect the effect of gravity on the electron.
A pair of square conducting plates having sides of length 0.05 m are arranged parallel to each other in x-y plane. They are 0.01 m apart along z-axis and are connected to a 200 V power supply as shown in the figure. An electron enters with a speed of $3\times10^{7}ms^{-1}$ horizontally and symmetrically in the space between the two plates. Neglect the effect of gravity on the electron.
(i) The electric field $\vec{E}$ in the region between the plates is:
(A) $(2\times10^{4}\frac{V}{m})\hat{k}$
(B) $(2\times10^{2}\frac{V}{m})\hat{k}$
(C) $-(2\times10^{4}\frac{V}{m})\hat{k}$
(D) $-(2\times10^{2}\frac{V}{m})\hat{k}$
(ii) In the region between the plates, the electron moves with an acceleration $\vec{a}$ given by :
(A) $-(3.5\times10^{15}ms^{-2})\hat{k}$
(B) $(3.5\times10^{15}ms^{-2})\hat{k}$
(C) $(3.5\times10^{13}ms^{-2})\hat{i}$
(D) $-(3.5\times10^{13}ms^{-2})\hat{i}$
(iii) (a) Time interval during which an electron moves through the region between the plates is:
(A) $9.0\times10^{-9}s$
(B) $1.67\times10^{-8} s$
(C) $1.67\times10^{-9}s$
(D) $2.17\times10^{-9}$ s
OR
(b) The vertical displacement of the electron which travels through the region between the plates is :
(A) 10 mm
(B) 4.9 mm
(C) 5.9 mm
(D) 3.0 mm
(iv) Which one of the following is the path traced by the electron in between the two plates?
(A) a
(B) b
(C) c
(D) d
[4]
30.
Case Study Question
In a Young's double-slit experiment, the two slits behave as coherent sources. When coherent light waves superpose over each other they create an interference pattern of successive bright and dark regions due to constructive and destructive interference. Two slits 2 mm apart are illuminated by a source of monochromatic light and the interference pattern is observed on a screen 5.0 m away from the slits as shown in the figure.
(i) What property of light does this interference experiment demonstrate?
(A) Wave nature of light
(B) Particle nature of light
(C) Transverse nature of light
(D) Both wave nature and transverse nature of light
(ii) (a) The wavelength of light used in this experiment is:
(A) 720 nm
(B) 590 nm
(C) 480 nm
(D) 364 nm
OR
(b) The fringe width in the interference pattern formed on the screen is:
(A) 1.2 mm
(B) 0.2 mm
(C) 4.2 mm
(D) 6.8 mm
(iii) The path difference between the two waves meeting at point P, where there is a minimum in the interference pattern is:
(A) $8.1\times10^{-7}m$
(B) $7.2\times10^{-7}m$
(C) $6.5\times10^{-7}m$
(D) $6.0\times10^{-7}m$
(iv) When the experiment is performed in a liquid of refractive index greater than 1, then fringe pattern will:
(A) disappear
(B) become blurred
(C) be widened
(D) be compressed
[4]
SECTION E
(5 Marks Each)
31.
(a) (i) A parallel beam of monochromatic light falls normally on a single slit of width 'a' and a diffraction pattern is observed on a screen placed at distance D from the slits. Explain: (I) the formation of maxima and minima in the diffraction pattern, and (II) why the maxima go on becoming weaker and weaker with its increasing number (n).
(ii) Write any two points of difference between interference pattern due to double-slit and diffraction pattern due to single-slit.
(ii) (I) The real image of an object placed between f and 2f from a convex lens can be seen on a screen placed at the image location. If the screen is removed, is the image still there? Explain.
(II) Plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances? Explain.
(ii) Write any two points of difference between interference pattern due to double-slit and diffraction pattern due to single-slit.
OR
(b) (i) With the help of a ray diagram, describe the construction and working of a compound microscope. (ii) (I) The real image of an object placed between f and 2f from a convex lens can be seen on a screen placed at the image location. If the screen is removed, is the image still there? Explain.
(II) Plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances? Explain.
[5]
32.
(a) (i) Derive the condition for which a Wheatstone Bridge is balanced.
(ii) Determine the current in 3 $\Omega$ branch of a Wheatstone Bridge in the circuit shown in the figure.
(ii) The resistance of a metal wire at $20^{\circ}C$ is 1.05 $\Omega$ and at $100^{\circ}C$ is 1.38 $\Omega$. Determine the temperature coefficient of resistivity of this metal.
(ii) Determine the current in 3 $\Omega$ branch of a Wheatstone Bridge in the circuit shown in the figure.
OR
(b) (i) Consider a cylindrical conductor of length $l$ and area of cross-section A. Current I is maintained in the conductor and electrons drift with velocity $v_{d}(|\vec{v}_{d}|=\frac{e|\vec{E}|}{m}\tau)$, (where symbols have their usual meanings). Show that the conductivity $\sigma$ of the material of the conductor is given by $\sigma=\frac{ne^{2}}{m}\tau$. (ii) The resistance of a metal wire at $20^{\circ}C$ is 1.05 $\Omega$ and at $100^{\circ}C$ is 1.38 $\Omega$. Determine the temperature coefficient of resistivity of this metal.
[5]
33.
(a) (i) A rectangular loop of sides a and b carrying current I is placed in a magnetic field $\vec{B}$ such that its area vector $\vec{A}$ makes an angle $\theta$ with $\vec{B}$. With the help of a suitable diagram, show that the torque $\vec{\tau}$ acting on the loop is given by $\vec{\tau}=\vec{m}\times\vec{B}$, where $\vec{m}(=I\vec{A})$ is the magnetic dipole moment of the loop.
(ii) A circular coil of 100 turns and radius $(\frac{10}{\sqrt{\pi}})$ cm carrying current of 5.0 A is suspended vertically in a uniform horizontal magnetic field of 2.0 T. The field makes an angle $30^{\circ}$ with the normal to the coil. Calculate: (I) the magnetic dipole moment of the coil, and (II) the magnitude of the counter torque that must be applied to prevent the coil from turning.
(ii) A part of a wire carrying 2.0 A current and bent at $90^{\circ}$ at two points is placed in a region of uniform magnetic field $\vec{B}=-(0.50~T)\hat{k}$, as shown in the figure. Calculate the magnitude of the net force acting on the wire.
(ii) A circular coil of 100 turns and radius $(\frac{10}{\sqrt{\pi}})$ cm carrying current of 5.0 A is suspended vertically in a uniform horizontal magnetic field of 2.0 T. The field makes an angle $30^{\circ}$ with the normal to the coil. Calculate: (I) the magnetic dipole moment of the coil, and (II) the magnitude of the counter torque that must be applied to prevent the coil from turning.
OR
(b) (i) Derive an expression for the force $\vec{F}$ on a conductor of length L and area of cross-section A carrying current I and placed in a magnetic field $\vec{B}$. (ii) A part of a wire carrying 2.0 A current and bent at $90^{\circ}$ at two points is placed in a region of uniform magnetic field $\vec{B}=-(0.50~T)\hat{k}$, as shown in the figure. Calculate the magnitude of the net force acting on the wire.
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