UP Board 12th Physics Model Paper 2027 — Full Paper With Solutions

This model paper follows the official UPMSP blueprint for Class 12th Physics 2027. Theory: 70 marks in 3 hours 15 minutes. Practical: 30 marks separately.

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Paper Structure

Section	Type	Questions	Marks
Section A	MCQ	10	10
Section B	Very Short Answer (2 marks)	8	16
Section C	Short Answer (3 marks)	5	15
Section D	Long Answer with derivation (5 marks)	3	15
Section E	Numerical Problems	7	14

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SECTION A — Objective Questions (1 Mark Each)

Q1. The SI unit of electric flux is:

(a) N/C (b) N·m²/C (c) C/m² (d) V/m

Answer: (b) N·m²/C

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Q2. A convex lens of focal length 20 cm is used as a magnifying glass. The image is formed at the near point (25 cm). The magnification is:

(a) 1.25 (b) 2.25 (c) 3.25 (d) 4.25

Answer: (b) 2.25
(m = 1 + D/f = 1 + 25/20 = 2.25)

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Q3. In a photoelectric effect experiment, the stopping potential depends on:

(a) Intensity of light (b) Frequency of incident light (c) Area of metal surface (d) Number of photons

Answer: (b) Frequency of incident light

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Q4. The wavelength of de Broglie wave associated with a particle of mass m moving with velocity v is:

(a) h/mv (b) mv/h (c) h·mv (d) m/hv

Answer: (a) h/mv
(de Broglie equation: λ = h/p = h/mv)

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Q5. Which of the following electromagnetic waves has the highest frequency?

(a) Radio waves (b) Microwaves (c) X-rays (d) Gamma rays

Answer: (d) Gamma rays

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Q6. The half-life of a radioactive element is 5 years. After 20 years, the fraction of the original sample that remains is:

(a) 1/2 (b) 1/4 (c) 1/8 (d) 1/16

Answer: (d) 1/16
(Number of half-lives = 20/5 = 4; fraction = (1/2)⁴ = 1/16)

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Q7. In a p-n junction diode under forward bias, the width of the depletion layer:

(a) Increases (b) Decreases (c) Remains unchanged (d) Becomes zero

Answer: (b) Decreases

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Q8. Lenz's law is a consequence of the law of conservation of:

(a) Charge (b) Mass (c) Energy (d) Momentum

Answer: (c) Energy

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Q9. The refractive index of glass with respect to air is 1.5. The refractive index of air with respect to glass is:

(a) 1.5 (b) 2.5 (c) 0.67 (d) 0.5

Answer: (c) 0.67
(μ_air w.r.t. glass = 1/1.5 = 0.67)

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Q10. Ohm's Law states that:

(a) V ∝ R (b) I ∝ V (at constant R) (c) R ∝ V (d) I ∝ R

Answer: (b) I ∝ V (at constant R)

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SECTION B — Very Short Answer (2 Marks Each)

Q11. State Gauss's Law in electrostatics and write its mathematical expression.

Answer: Gauss's Law states that the total electric flux through any closed surface is equal to 1/ε₀ times the total charge enclosed within the surface.
Mathematical form: ΦE = ∮E·dA = q/ε₀
where q = total charge enclosed, ε₀ = permittivity of free space = 8.85 × 10⁻¹² C²/N·m²

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Q12. What is electromagnetic induction? State Faraday's first law.

Answer: The phenomenon of production of an induced EMF (and hence current) in a conductor due to change in magnetic flux linked with it is called electromagnetic induction.

Faraday's First Law: Whenever the magnetic flux linked with a closed circuit changes, an EMF is induced in the circuit. The induced EMF lasts only as long as the magnetic flux is changing.

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Q13. Define the work function of a metal in photoelectric effect.

Answer: The minimum energy required to remove an electron from the surface of a metal against the attractive forces is called the work function (W₀) of that metal.
W₀ = hν₀ where h = Planck's constant, ν₀ = threshold frequency
The kinetic energy of emitted electrons: KEmax = hν − W₀

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Q14. What is meant by mass defect and binding energy of a nucleus?

Answer:
Mass defect (Δm): The difference between the sum of masses of individual nucleons (protons and neutrons) and the actual mass of the nucleus.
Δm = [Z·mₚ + (A−Z)·mₙ] − M

Binding Energy (BE): The energy equivalent of mass defect.
BE = Δm × c² (in Joules) or BE = Δm × 931.5 MeV (using atomic mass units)

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Q15. Distinguish between intrinsic and extrinsic semiconductors.

Answer:

Property	Intrinsic	Extrinsic
Purity	Pure semiconductor	Doped with impurity
Conductivity	Low at room temperature	Higher
Examples	Pure Si, Pure Ge	n-type Si (P doped), p-type Si (B doped)
Charge carriers	Equal holes and electrons	Depends on type of doping

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SECTION C — Short Answer (3 Marks Each)

Q16. Derive the expression for equivalent capacitance when capacitors are connected in series.

Answer:
Let C₁, C₂, C₃ be capacitors connected in series with a potential V across them.

In series, the charge Q on each capacitor is the same.
V₁ = Q/C₁, V₂ = Q/C₂, V₃ = Q/C₃

Total voltage: V = V₁ + V₂ + V₃
Q/Ceq = Q/C₁ + Q/C₂ + Q/C₃

Dividing by Q:
1/Ceq = 1/C₁ + 1/C₂ + 1/C₃

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Q17. What is total internal reflection? State its two conditions and give two applications.

Answer:
When a ray of light travels from a denser medium to a rarer medium and the angle of incidence exceeds the critical angle, the ray is completely reflected back into the denser medium. This is called total internal reflection.

Conditions:

1. Light must travel from denser to rarer medium
2. Angle of incidence must be greater than the critical angle

Applications:

1. Optical fibres — used in telecommunications and endoscopy
2. Brilliance of diamond — multiple total internal reflections

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Q18. State and explain Kirchhoff's laws.

Answer:

Kirchhoff's Current Law (KCL — Junction Rule):
The algebraic sum of all currents meeting at a junction is zero.
ΣI = 0 at any junction
(Based on conservation of charge)

Kirchhoff's Voltage Law (KVL — Loop Rule):
The algebraic sum of all EMFs and potential drops in any closed loop is zero.
ΣEMF = ΣIR
(Based on conservation of energy)

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SECTION D — Long Answer with Derivation (5 Marks Each)

Q19. Derive an expression for the electric field due to an infinite plane sheet of charge using Gauss's Law.

Answer:
Consider an infinite plane sheet with surface charge density σ (charge per unit area).

Step 1: By symmetry, the electric field E is perpendicular to the sheet and points away from it on both sides.

Step 2: Choose a cylindrical Gaussian surface (pill box) of cross-sectional area A with its axis perpendicular to the sheet, passing through it.

Step 3: Apply Gauss's Law: ΦE = q/ε₀
Flux through curved surface = 0 (E perpendicular to area vector)
Flux through two flat faces = E·A + E·A = 2EA
Charge enclosed = σA

Step 4: 2EA = σA/ε₀
E = σ/2ε₀

Direction: Away from the sheet for positive charge, towards for negative charge.

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Q20. Derive the lens maker's equation: 1/f = (n−1)(1/R₁ − 1/R₂)

Answer:
Consider a thin lens with refractive index n₂ = n in medium n₁ = 1 (air), with radii of curvature R₁ (first surface) and R₂ (second surface).

Refraction at first surface (applying n₂/v − n₁/u = (n₂−n₁)/R):
n/v₁ − 1/u = (n−1)/R₁ ... (i)

Refraction at second surface (v₁ acts as virtual object):
1/v − n/v₁ = (1−n)/R₂ ... (ii)

Adding (i) and (ii):
1/v − 1/u = (n−1)(1/R₁ − 1/R₂)

Since 1/f = 1/v − 1/u for thin lens:
1/f = (n−1)(1/R₁ − 1/R₂)

This is the Lens Maker's Equation.

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SECTION E — Numerical Problems (2 Marks Each)

Q21. A capacitor of capacitance 6 μF is charged to a potential of 100 V. Find the energy stored in the capacitor.

Solution: E = ½CV² = ½ × 6 × 10⁻⁶ × (100)² = ½ × 6 × 10⁻⁶ × 10⁴ = 0.03 J = 30 mJ

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Q22. The threshold frequency for a metal is 5 × 10¹⁴ Hz. Find its work function. (h = 6.6 × 10⁻³⁴ J·s)

Solution: W₀ = hν₀ = 6.6 × 10⁻³⁴ × 5 × 10¹⁴ = 3.3 × 10⁻¹⁹ J = 2.06 eV

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Q23. Two charges of +3 μC and −3 μC are placed 10 cm apart. Find the electric field at the midpoint.

Solution:
At midpoint (5 cm from each):
E₁ = kq/r² = 9×10⁹ × 3×10⁻⁶ / (0.05)² = 1.08 × 10⁷ N/C (towards −ve charge)
E₂ = same magnitude, same direction
Total E = 2.16 × 10⁷ N/C (towards the negative charge)

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Practice Problems (Self Test)

1. A wire of resistance 10Ω is stretched to double its length. Find its new resistance.
2. An object is placed 30 cm from a concave mirror of focal length 20 cm. Find image position and nature.
3. The half-life of Ra-226 is 1600 years. Find the activity of 1 gram of Ra-226.
4. Find the de Broglie wavelength of an electron moving at 10⁶ m/s.

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Chapter-Wise Weightage

Chapter	Marks
Electrostatics	10
Current Electricity	9
Optics	12
Modern Physics	10
Magnetism	8
Electromagnetic Induction	8
Semiconductors	7
Electromagnetic Waves	3
Communication Systems	3

Tip: Derivations carry 5 marks each in UP Board. Memorise derivations for Gauss's Law, Lens Maker's Equation, and Biot-Savart Law. These three alone can deliver 15 marks every year.