Class: 12 Physics Sample Paper 2

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Board EXAMINATION 2025-2026

Class: 12 | Subject: Chemistry (043) | Set: 2

Max Marks: 70 | Time: 3 Hours

Date: 13/12/2025

General Instructions:

• This question paper contains 33 questions. All sections are compulsory.
• Section A: Contains 16 questions: twelve MCQs and four Assertion-Reasoning based of 1 mark each.
• Section B: Contains five questions of two marks each.
• Section C: Contains seven questions of three marks each.
• Section D: Contains two case study-based questions of four marks each.
• Section E: Contains three long answer questions of five marks each.
• There is no overall choice. However, an internal choice has been provided in two questions in Section B, one question in Section C and all three questions in Section E. You have to attempt only one of the choices in such questions.

Physical Constants:

• (i) \( c = 3 \times 10^{8} \, m/s \)
• (ii) \( m_{e} = 9.1 \times 10^{-31} \, kg \)
• (iii) \( e = 1.6 \times 10^{-19} \, C \)
• (iv) \( \mu_{0} = 4\pi \times 10^{-7} \, TmA^{-1} \)
• (v) \( h = 6.63 \times 10^{-34} \, Js \)
• (vi) \( \epsilon_{0} = 8.854 \times 10^{-12} \, C^{2}N^{-1}m^{-2} \)
• (vii) Bohr radius \( = 0.53 \times 10^{-10} \, m \)

SECTION A (1 Mark Each)

1. Which transition corresponding to the absorption of energy 5 eV using the energy level diagram?

1. D
2. A
3. B
4. C

2. In a p-n junction diode under biasing, the current in the circuit is in \( \mu A \). This is due to:

1. drifting of minority carriers in forward biasing
2. drifting of majority carriers in reverse biasing
3. drifting of minority carriers in reverse biasing
4. drifting of majority carriers in forward biasing

3. Suppose a pure Si crystal has \( 5 \times 10^{28} /m^{3} \). It is doped by 50 ppm concentration of Boron. The number density of electrons is [\( n_{i} = 1.5 \times 10^{16} /m^{3} \)]:

1. \( 2.250 \times 10^{8} /m^{3} \)
2. \( 2.50 \times 10^{24} /m^{3} \)
3. \( 2.250 \times 10^{11} /m^{3} \)
4. \( 2.50 \times 10^{18} /m^{3} \)

4. A charged particle q is placed at the centre O of the cube (ABCDEFGH) of length L. Another similar charge q is placed at a distance L from O. Then, the electric flux through ABCD is:

1. \( q/\epsilon_{0} \)
2. \( q/6\epsilon_{0} \)
3. Zero
4. \( 2q/6\epsilon_{0} \)

5. The physical quantity \( X = \sigma V/L \) having usual meaning [V is the potential difference, \( \sigma \) is the conductivity]. The SI unit of X is:

1. \( A/m^{2} \)
2. \( m^{2}/V-S \)
3. ohm - m
4. V - m

6. Three identical cells, each of e.m.f. 2 V and unknown internal resistance are connected in parallel. This combination is connected to a 9 ohm resistor. If the terminal voltage across the cell is 1.5 volt, the internal resistance of each cell is:

1. 3 \( \Omega \)
2. 9 \( \Omega \)
3. 12 \( \Omega \)
4. 4.5 \( \Omega \)

7. A network of four capacitors \( C_{1}=2C, C_{2}=6C, C_{3}=3C, C_{4}=4C \) are connected as shown in figure. The ratio of the potential difference on \( C_{2} \) to \( C_{4} \) is:

1. 4:1
2. 1:8
3. 1:4
4. 1:6

8. A circular loop of radius R carrying current I produces magnetic field at a point P at a distance X from the centre of the same current loop along its axis is \( 1/8 \)th of B. The value of X is:

1. 2R
2. 3R
3. \( \sqrt{8} R \)
4. \( \sqrt{3} R \)

9. Two identical solenoids X and Y, one is wound over a material whose \( \chi \) is low positive and another one is wound over a material whose \( \chi \) is low negative respectively. A graph is plotted between current in the solenoid Vs magnetic flux. The solenoid in which the magnetic material of low positive is wound, is:

1. X since self inductance is high
2. Y since self inductance is low
3. X since self inductance is low
4. Y since self inductance is high

10. A plano-convex lens is made of a material of refractive index \( \mu = 1.5 \). The radius of curvature of curved surface of the lens is 20 cm. If its plane surface is silvered, the focal length of the silvered lens will be:

1. 10 cm
2. 20 cm
3. 40 cm
4. 80 cm

11. The de Broglie wavelength associated with moving deutron particle which is accelerated by a potential of V is:

1. \( \lambda = h/\sqrt{2(2m)eV} \)
2. \( \lambda = h/\sqrt{2(m)eV} \)
3. \( \lambda = h/4\sqrt{(m)eV} \)
4. \( \lambda = h/\sqrt{2(m)(2e)V} \)

12. Radius of the Bohr's orbit in hydrogen atom is \( r_0 \). The radius of the orbit whose KE of the electron is 1.51 eV is:

1. \( 3 r_0 \)
2. \( 9 r_0 \)
3. \( r_0/3 \)
4. \( r_0/9 \)

Directions for Questions 13 to 16: Two statements are given - one labelled Assertion (A) and other labelled Reason (R). Select the correct answer from the codes (a), (b), (c), and (d) as given below:

• (a) If both Assertion and Reason are true and Reason is correct explanation of Assertion.
• (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
• (c) If Assertion is true but Reason is false.
• (d) If both Assertion and Reason are false.

13. Assertion: Two identical sodium vapour lamps connected to a same source cannot be coherent sources.
Reason: The phase difference of the light waves from the two sodium vapour lamps changes with time ie they have phase instability.

14. Assertion: As the mass number of the nucleus increases, the radius of the nuclei also increases.
Reason: The volume of the nucleus is directly proportional to \( A^{1/3} \) where A is the mass number.

15. Assertion: When two unlike charges are separated by a distance d, the zero electric field point is lying outside the line joining the two charges, nearer to lesser magnitude side.
Reason: Electric field is a vector quantity.

16. Assertion: Two bulbs A and B each power P are connected in series to a source. When bulb A is replaced with another bulb of power \( P/2 \), the brightness of bulb B decreases.
Reason: Since current in the circuit decreases, due to increase in the resistance of the circuit, brightness of the bulb B decreases.

SECTION B (2 Marks Each)

17. An electron is revolving around the nucleus in a stable orbit whose circumference is 5.325 nm. Find the principle quantum number of the orbit and draw suitable diagram of standing waves to fit in this orbit.

18. Draw energy band diagram of extrinsic semiconductor in which boron is doped with intrinsic semiconductor \( (T>0 K) \). In this crystal, how neutrality is maintained though the majority carriers dominate minority carriers?

OR

Draw output waveform across load resistor \( R_L \) and across diode for the given input waveform as shown.

19. A infinitely long charged plane sheet of charge density \( 5 \times 10^{-16} C/m^{2} \). A dipole of dipole moment \( 2 \times 10^{-7} C-m \) is placed as shown figure. Then the dipole is rotated by \( 30^{\circ} \) in clockwise and further it is rotated by \( 60^{\circ} \). Find the potential energy in all the three positions of dipole.

OR

A pendulum of mass m carrying charge Q is suspended between two infinitely long charged plane sheets as shown in figure. The pendulum makes an angle of \( \theta \) with vertical at equilibrium. Obtain an expression for \( \tan\theta \) in terms of m, \( \theta \), q.

20. Obtain the condition for the path difference in constructive and destructive interference if the displacement of the light waves are given below:

\( y_{1} = A \cos \omega t \) and \( y_{2} = A \cos(\omega t + \phi) \)

21. (i) If 'n' incoherent identical sources of light each intensity of light I are meeting at a point in interference experiment, what is the resultant intensity of light?

(ii) When light travels from a rarer to a denser medium, the speed decreases. Does the reduction in speed imply a reduction in the energy carried by the light wave? Explain.

SECTION C (3 Marks Each)

22. A graph is plotted between \( V_{max}^{2} \) Vs \( 1/\lambda \) graph in photo electric emission for a metal surface P. The intercept on X axis gives the value of \( 1.6 \times 10^{6} /m \) and on Y axis gives \( 7 \times 10^{11} \) in SI unit. Give SI unit of the slope. Calculate the value of work function in eV. If a light of energy 4 eV is incident on the metal surface P, calculate the stopping potential.

23. Plot a graph between the binding energy per nucleon \( E_{bn} \) versus the mass number A for a large number of nuclei. Explain the importance of the graph which explaining nuclear fission and fusion process. What is the reason for the constancy of the binding energy per nucleon between \( 30 < A < 170 \)?

24. (i) Four charges each charge q are placed at the corners of the square of side 'a'. Another charge Q is placed at the centre of the square. Find the value of Q in terms of q so that the system of charges are in equilibrium.

(ii) A spherical shell of radius 20 cm carries a charge of 10 µC. What is the work done in moving a charge of 2 µC diametrically opposite points along the surface of the spherical shell?

OR

(i) Three concentric spherical shells A, B and C of radius a, b, c having surface charge density \( +\sigma, -\sigma, +\sigma \) respectively. [\( a < b < c \)]. If the potential of A and C are equal then how will you relate a, b and c?

(ii) A capacitor of capacitance C is connected to battery of pd V. It is disconnected from battery and the distance between the plates of capacitor is doubled, how will the energy stored in the capacitor be changed?

25. When a magnetic substance is placed in external magnetic field lines, the magnetic field lines around the substance is as shown in figure.

(i) Identify the type of magnetic material whether it is para or dia magnetic substance? Give one example.

(ii) Why is the intensity of magnetisation of this material positive?

(iii) Plot a graph between magnetic susceptibility of this magnetic material Vs variation of temperature.

26. A slider of length l is moving with velocity v away from the frame normal to MF of strength B acting inward. Obtain an expression for an induced current across the slider if the resistance of frame is R and mark the polarity of emf induced in the slider. Are you doing work against any force when a slider is moved in magnetic field normally? Explain.

27. (i) Show that during the charging of a parallel plate capacitor, the rate of change of charge on each plate equals \( \epsilon_{0} \) times the rate of change of electric flux (\( \Phi_{E} \)) linked with it. What is the name given to the term \( \epsilon_{0} [d\Phi_{E}/dt] \)? A capacitor is connected to dc source and when the capacitor is fully charged, what is the value of conduction current?

(ii) A special device like Klystron valve, is used for the production of EMW. Name the EM waves and also write one application of it.

28. An angular magnification (magnifying power) of 30X is desired using an objective of focal length 1.25 cm and an eyepiece of focal length 5 cm. How will you set up the compound microscope?

SECTION D (Case Study - 4 Marks Each)

29. Case Study: p-n Junction Diode

A p-n junction is the basic building block of many semiconductor devices like diodes, transistor, etc. Consider a thin p-type silicon (p-Si) semiconductor wafer. By adding precisely a small quantity of pentavalent impurity, part of the p-Si wafer can be converted into n-Si. There are several processes by which a semiconductor can be formed. The wafer now contains p-region and n-region and a metallurgical junction between p-, and n- region.

(i) In an unbiased p-n junction, holes diffuse from the p-region to n-region because:

1. free electrons in the n-region attract them.
2. they move across the junction by the potential difference.
3. hole concentration in p-region is more as compared to n-region.
4. All the above.

(ii) During the formation of the diode, which one of the following is not correct statement?

1. Due to diffusion of electrons and holes, a depletion region is formed.
2. Due to junction field, electron from P side drifts towards the n side.
3. The thickness of the depletion region is in the order of \( 1/10 \) th of micrometer.
4. In a unbiased p-n junction diode, under equilibrium, there is net drift current since number density of electron is greater than number density of hole.

(iii) Figure a represents of barrier potential of diode. Which one of the statement represents correctly?

1. (1) without battery, (2) Low battery voltage, and (3) High voltage battery, in reverse biasing.
2. (1) without battery, (2) high battery voltage, and (3) low voltage battery, in forward biasing.
3. (1) without battery, (2) Low battery voltage, and (3) High voltage battery, in forward biasing.
4. (1) without battery, (2) high battery voltage, and (3) low voltage battery, in reverse biasing.

(iv) Which one of the following will not take place in forward biasing of diode?

1. Thickness of the depletion layer decreases.
2. Minority carrier injection takes place.
3. The current is due to drift of electron from p side to n side and holes from n side to p side.
4. In diode, n side of the diode is more negative than p side.

OR

(v) The effective resistance of the circuit containing resistors and ideal diodes during positive and negative half cycle of signal of the circuit respectively is:

1. R, 3R
2. 3R/4, 3R/4
3. 5R/3, 3R/4
4. 2R/3, 4R/3

30. Case Study: Motion of Charged Particle in Magnetic Field

A proton is moving with velocity \( 8 \times 10^{6} m/s \) entering a uniform magnetic field of strength 0.04 T such that the velocity vector makes an angle of \( 30^{\circ} \) with the field. The ratio of charge to mass of proton is \( 10^{8} C/kg \).

(i) The radius of the path described by the proton is:

1. 1 m
2. 1 cm
3. 0.5 m
4. 2 m

(ii) The path described by the proton due to horizontal component of velocity in uniform MF is:

1. Helix
2. Straight
3. Circular
4. All the above

(iii) The kinetic energy of the proton in MeV is:

1. 0.16
2. 22.7
3. 0.66
4. 0.33

(iv) The frequency of the rotation of proton is:

1. \( 0.64 \times 10^{6} Hz \)
2. \( 1.2 \times 10^{6} Hz \)
3. \( 0.32 \times 10^{6} Hz \)
4. \( 2.4 \times 10^{6} Hz \)

OR

(v) The correct expression for the pitch of the proton is:

1. \( v \cos\theta \times (Bq/2\pi m) \)
2. \( v \cos\theta \times (2\pi m/Bq) \)
3. \( v \sin\theta \times (Bq/2\pi m) \)
4. \( v \sin\theta \times (2\pi m/Bq) \)

SECTION E (Long Answer - 5 Marks Each)

31. (i) Derive mirror formula for a curved mirror, in which virtual enlarged image is obtained.

(ii) Two lenses, one is convex lens of power 5D and another one is concave lens of power 6.25D are placed co-axially. An object is placed infront of the convex lens at a distance of 30cm from the convex lens. The distance between the two lenses is 48cm. Find the final image distance from the concave lens, what is the nature of final image and calculate total magnification.

OR

(iii) Draw a neat labeled ray diagram of prism. Obtain relation between a) angle of refraction of two surfaces and refracting angle of prism and b) angle of deviation, angle of incidence, angle of emergence with refracting angle of prism. Plot a graph between angle of deviation with variation of angle of incidence.

(iv) A convex lens of focal length 20cm in air (Refractive index of lens \( n=1.5 \)). It is dipped completely in liquid of refractive index \( n_1 \), the focal length of lens now becomes 20cm and behaves as an divergent. Find the value of \( n_1 \). What is the value of refractive index of \( n_1 \) so that power of the convex lens becomes zero?

32. (i) Define drift velocity of electron in a metallic conductor and relaxation time and obtain relation between drift velocity and relaxation time. Plot a graph between drift velocity of electron with variation of temperature.

(ii) In the Wheatstone network, find the value of R if the current drawn from the battery is 2A.

OR

(iii) Define resistivity of material of substance. Obtain relation relating resistivity and relaxation time.

(iv) Calculate the current drawn from the battery.

33. (i) A series L-C-R circuit is connected to an AC source. Using the phasor diagram, derive the expression for impedance of the circuit. Using the same phasor diagram, obtain an expression for the average power consumed by this circuit in terms of R and I.

(ii) Calculate the current drawn by the primary of a transformer which step-downs 200 V to 20 V to operate a device of resistance 20 \( \Omega \). Assuming the efficiency the transformer to be 80%.

OR

(iii) An ideal capacitor is connected to ac source \( E = E_{0} \cos(\omega t) \). Obtain an expression for the capacitive reactance and phase relation between voltage and current and plot a graph to show the instantaneous value of voltage and current in this circuit with time.

(iv) An inductor of 5 H, capacitor of 20 µF and resistor of 40 ohm are connected in series to an ac source of \( E = 200\sqrt{2} \sin \omega t \). It is found that voltage across resistor and supply voltage are same, calculate the value of current and \( \omega \) of this circuit.