PHYSICS BYTES

HP BOARD FINAL QUESTION PAPER 2026

Subject: PHYSICS (Theory) | Class: XII

Time Allowed: 3 Hours
Max Marks: 60

GENERAL INSTRUCTIONS:

  • (1) There are 27 questions in all. All questions are compulsory.
  • (2) This question paper has five sections: Section A, Section B, Section C, Section D and Section E.
  • (3) All the sections are compulsory.
  • (4) Section A contains twelve MCQ's and Assertion Reasoning based questions of 1 mark each, Section B contains four questions of two marks each, Section C contains seven questions of three marks each, Section D contains one case study based questions of four marks and Section E contains three long answer questions of five marks each.
  • (5) There is no overall choice. However, an internal choice has been provided in some questions. You have to attempt only one of the choices in such questions.
  • (6) Use of calculators is not allowed.

Section - 'A'

(Multiple Choice Questions)

Note: Question number 1 to 12 are Multiple Choice Questions (MCQ). Choose the correct option and mark it on the OMR sheet of your answer book in the space provided there.

For questions number 1 and 2, two statements are given - one labelled Assertion (A) and other labelled Reason (R). Select the correct answer to these questions from the options given below.
(A) Both Assertion and Reason are true, and reason is the correct explanation
(B) Both Assertion and Reason are true, but the Reason is not the correct explanation
(C) Assertion is true, but Reason is false.
(D) Assertion is false, but Reason is true.
1.
Assertion (A): Two infinitely long straight conductors carrying current in the same direction attract each other.
Reason (R): The net magnetic field at a point exactly halfway between two infinitely long straight conductors carrying current in the same direction is zero.
1
2.
Assertion (A): The electrical conductivity of a semiconductor increases on doping.
Reason (R): Doping always increases the number of electrons in the semiconductor.
1
3.
For a p-type semiconductor, which of the following statement is true?
(A) Holes are majority carriers and trivalent atoms are the dopants
(B) Holes are majority carriers and pentavalent atoms are the dopants
(C) Electrons are majority carriers and pentavalent atoms are the dopants
(D) Electrons are majority carriers and trivalent atoms are the dopants
1
4.
Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average e.m.f. of 100 V induced, give an estimate of the self-inductance of the circuit.
(A) $L=4\text{ H}$
(B) $L=20\text{ H}$
(C) $L=40\text{ H}$
(D) $L=2\text{ H}$
1
5.
If a wave gets refracted into a denser medium, then which of the following is true?
(A) wavelength, speed and frequency decrease.
(B) wavelength increases, speed decreases and frequency remain constant.
(C) wavelength and speed decrease but frequency remains constant.
(D) wavelength, speed and frequency increase.
1
6.
A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. The location of the image is
(A) formed at 6.67 cm behind the mirror.
(B) formed at 67 cm behind the mirror.
(C) formed at 70 cm same side of the mirror.
(D) formed at 5.57 cm same side of the mirror.
1
7.
Let the point P be at distance r from the centre of the dipole on the side of the charge q, as shown in Figure, then.
[Insert Electric Dipole Diagram Here]
(A) $\vec{E}_{+q}=\frac{q}{4\pi\epsilon_{0}(r+a)^{2}}\hat{P}$
(B) $\vec{E}_{+q}=\frac{q}{4\pi\epsilon_{0}(r-a)^{2}}\hat{P}$
(C) $\vec{E}_{+q}=-\frac{q}{4\pi\epsilon_{0}(r+a)^{3}}\hat{P}$
(D) None of these
1
8.
The resistance of a wire is 'R' ohm. If it is melted and stretched to 5 times its original length, its new resistances will be
(A) 5 R
(B) $\frac{R}{5}$
(C) 25 R
(D) $\frac{R}{25}$
1
9.
To convert a galvanometer into a voltmeter,
(A) a high resistance is connected in parallel
(B) a low resistance is connected in series
(C) a low resistance is connected in parallel
(D) a high resistance is connected in series
1
10.
In an a.c. circuit having pure inductor, current
(A) leads the voltage by an angle of $\frac{\pi}{2}$
(B) leads the voltage by an angle of $\pi$
(C) lags the voltage by an angle of $\frac{\pi}{2}$
(D) lags the voltage by an angle of $\pi$
1
11.
The work function of caesium metal is 2.14 eV. When light of frequency $6\times10^{14}\text{ Hz}$ is incident on the metal surface, photoemission of electrons occurs. What is the Stopping potential?
(A) 34 V
(B) 3.4 V
(C) 340 V
(D) 0.34 V
1
12.
The energy equivalent of 1 mg of substance is
(A) $9\times10^{10}\text{ J}$
(B) $9\times10^{13}\text{ J}$
(C) $1.35\times10^{14}\text{ J}$
(D) $3\times10^{13}\text{ J}$
1

Section - 'B'

13.
A solenoid of length 0.5 m has a radius of 1 cm and has 500 turns. It carries current of 5 A. What is the magnitude of the magnetic field inside the solenoid?
OR
Out of an ammeter, voltmeter and galvanometer, which one has lowest and highest resistance? Justify your response.
2
14.
Apply the Kirchhoff's loop rule to the closed loop ABCA of the network shown in the figure, and write the relevant equation.
[Insert Kirchhoff's Loop Circuit Diagram Here]
2
15.
Describe two important properties of paramagnetic substances.
2
16.
Verify the laws of photoelectric emission using the photoelectric equation.
2

Section - 'C'

17.
Define one atomic mass unit. Find the energy equivalent of one atomic mass unit, first in Joules and then in MeV.
3
18.
Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude $17.0\times10^{-22}\text{ C/m}^{2}$. What is $\vec{E}$:
(a) in the outer region of the first plate,
(b) in the outer region of the second plate, and
(c) between the plates?
3
19.
Write a short note on microwaves and infrared waves.
3
20.
Define electric energy and power. Where does the power come from? Equation $P=\frac{V^{2}}{R}$ has an important application to power transmission. How can power loss be minimised in the transmission cables connecting the power stations to homes and factories.
3
21.
What are the drawbacks of Rutherford's nuclear model of the atom? State and explain the postulates of Bohr's model of the atom.
3
22.
What is meant by self-induction? Define self inductance. Derive an expression for the self inductance of a long solenoid.
3
23.
Derive the laws of refraction of light on the basis of 'Huygens' wave theory of light.
3

Section - 'D'

(Case Study - Based Questions)

24.
Read the following and answer the questions that follow. Consider the charges $q_{1}$ and $q_{2}$ initially at infinity and determine the work done by an external agency to bring the charges to the given locations. Suppose, first the charge $q_{1}$ is brought from infinity to the point $r_{1}$. There is no external field against which work needs to be done, so work done in bringing $q_{1}$ from infinity to $r_{1}$ is zero.

From the definition of potential, work done in bringing charge $q_{2}$ from infinity to the point $r_{2}$ is $q_{2}$ times the potential at $\vec{r_{2}}$ due to $q_{1}$.
[Insert 2 Charges Diagram Here]
Let us calculate the potential energy of a system of three charges $q_{1}$, $q_{2}$ and $q_{3}$ located at $\vec{r_{1}}$, $\vec{r_{2}}$, $\vec{r_{3}}$ respectively as shown in the figure below. To bring $q_{1}$ first from infinity to $r_{1}$, no work is required ($W_{1}=0$).
[Insert 3 Charges Diagram Here]

(i) To bring $q_{2}$ from infinity to $r_{2}$. The work done in this step is

(A) $W_{2}=\frac{1}{4\pi\epsilon_{0}}\frac{2q_{1}q_{2}}{r_{12}^{3}}$
(B) $W_{2}=\frac{1}{4\pi\epsilon_{0}}\frac{q_{1}q_{2}}{r_{12}^{3}}$
(C) $W_{2}=\frac{1}{4\pi\epsilon_{0}}\frac{q_{1}q_{2}}{r_{12}^{2}}$
(D) $W_{2}=\frac{1}{4\pi\epsilon_{0}}\frac{q_{1}q_{2}}{r_{12}}$

(ii) The charges $q_{1}$ and $q_{2}$ produce a potential, which at any point P will be

(A) $V_{1,2}=\frac{1}{4\pi\epsilon_{0}}\left(\frac{q_{1}}{r_{1P}^{2}}+\frac{q_{2}}{r_{2P}^{2}}\right)$
(B) $V_{1,2}=\frac{1}{4\pi\epsilon_{0}}\left(\frac{q_{1}}{r_{1P}}+\frac{q_{2}}{r_{2P}}\right)$
(C) $V_{1,2}=\frac{1}{4\pi\epsilon_{0}}\left(\frac{q_{1}}{r_{1P}}-\frac{q_{2}}{r_{2P}}\right)$
(D) $V_{1,2}=\frac{1}{4\pi\epsilon_{0}}\left(\frac{2q_{1}}{r_{1P}}+\frac{3q_{2}}{r_{2P}}\right)$

(iii) The work done in bringing $q_{3}$ from infinity to the point $r_{3}$ is -

(A) $W_{3}=\frac{1}{4\pi\epsilon_{0}}\left(\frac{2q_{1}q_{3}}{r_{13}}+\frac{2q_{2}q_{3}}{r_{23}}\right)$
(B) $W_{3}=\frac{1}{4\pi\epsilon_{0}}\left(\frac{q_{1}q_{2}}{r_{12}}+\frac{q_{1}q_{3}}{r_{13}}\right)$
(C) $W_{3}=\frac{1}{4\pi\epsilon_{0}}\left(\frac{q_{1}q_{3}}{r_{13}}+\frac{q_{2}q_{3}}{r_{23}}\right)$
(D) $W_{3}=\frac{1}{4\pi\epsilon_{0}}\left(\frac{q_{1}q_{3}}{r_{12}}-\frac{q_{2}q_{3}}{r_{23}}\right)$

(iv) The total work done in assembling the system of three charges $q_{1}$, $q_{2}$ and $q_{3}$ at the given locations is given by

(A) $U=\frac{1}{4\pi\epsilon_{0}}\left(\frac{q_{1}q_{2}}{r_{12}}+\frac{q_{1}q_{3}}{r_{13}}+\frac{q_{2}q_{3}}{r_{23}}\right)$
(B) $U=\frac{1}{4\pi\epsilon_{0}}\left(\frac{q_{1}q_{2}}{r_{12}}-\frac{q_{1}q_{3}}{r_{13}}+\frac{q_{2}q_{3}}{r_{23}}\right)$
(C) $U=\frac{1}{4\pi\epsilon_{0}}\left(\frac{q_{1}q_{2}}{r_{12}}+\frac{q_{1}q_{3}}{r_{13}}-\frac{q_{2}q_{3}}{r_{23}}\right)$
(D) $U=\frac{1}{4\pi\epsilon_{0}}\left(\frac{q_{1}q_{2}}{r_{13}}+\frac{q_{1}q_{3}}{r_{22}}+\frac{q_{2}q_{3}}{r_{12}}\right)$
4

Section - 'E'

25.
Using phasor diagram, derive an expression for the impedance of a series LCR - circuit. What do you mean by the resonance condition of a series LCR - circuit. Calculate its resonant frequency.
OR
A series LCR circuit connected to a variable frequency 230 V source. $L=5.0\text{ H}$, $C=80\text{ }\mu\text{F}$, $R=40\text{ }\Omega$.
(a) Determine the source frequency which drives the circuit in resonance.
(b) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.
(c) Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.
5
26.
(i) If $f=0.5\text{ m}$ for a glass lens, what is the power of the lens?
(ii) The radii of curvature of the faces of a double convex lens are 10 cm and 15 cm. Its focal length is 12 cm. What is the refractive index of glass?
(iii) A convex lens has 20 cm focal length in air. What is its focal length in water? (Refractive index of air-water $=1.33$, refractive index for air-glass $=1.5$)
OR
By stating assumptions and new cartesian sign convention, derive the lens maker's formula for a convex lens. Using the formula, determine the radius of curvature required to manufacture a double convex lens to be made from glass of refractive index 1.55, given that both faces have the same radius of curvature and the focal length of the lens is 20 cm.
5
27.
(i) What are intrinsic semiconductors?
(ii) C, Si and Ge have same lattice structure. Why is C insulator while Si and Ge are intrinsic semiconductors?
(iii) Using a schematic two-dimensional representation of Si or Ge structure showing covalent bonds at low temperature, explain how are charge carriers generated in an intrinsic semiconductor?
5
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