See how the paper maps to your syllabus strengths.
| Chapter | Marks | Weightage (%) | Your Proficiency |
|---|---|---|---|
| Electrostatics | 8 | 11 | High |
| Current Electricity | 7 | 10 | Medium |
| Magnetism | 6 | 8 | Low |
| EM Induction & AC | 7 | 10 | Medium |
| EM Waves | 3 | 4 | High |
| Optics | 14 | 19 | Medium |
| Dual Nature & Matter | 4 | 6 | Low |
| Atoms & Nuclei | 5 | 7 | High |
| Semiconductor Electronics | 6 | 8 | Medium |
Source: CBSE Sample Question Paper 2024-25 & your mock test analytics
Electric Charges & Fields – Challenge
State Gauss’s law and derive the electric field around an infinitely long, uniformly charged straight wire of linear charge density \( \lambda \).
No diagram provided
Choose a coaxial cylindrical Gaussian surface of radius \( r \) and length \( L \).
Only the curved surface contributes: \( \Phi_E = E(2\pi r L) \).
Set \( \Phi_E = \lambda L/\varepsilon_0 \) and solve: \( E = \dfrac{\lambda}{2\pi \varepsilon_0 r} \).
Use symmetry: field is radial and uniform over the curved surface.
Verify \( E \) has units of N C\(^{-1}\).
Sketch the wire and surrounding cylinder to see why only the curved surface matters.
If \( r \) doubles, the expression shows \( E \) halves. Does that make sense?
Struggle is normal! Try to solve on your own before checking the hints.
Physics | CBSE 12
An electron moves in a uniform magnetic field describing a circle of radius \(r_0\) with period \(T_0\). What happen to the radius and time period if its speed becomes \(2v_0\)?
Start with \(qvB = \frac{mv^{2}}{r}\) to express \(r\) in terms of \(v\).
Compute \(r_{new}/r_0\) after substituting \(2v_0\); it doubles.
Use \(T = \frac{2\pi m}{qB}\). Since \(v\) cancels, \(T_{new} = T_0\).
Hold \(q\) and \(B\) fixed; see how changing \(v\) alone affects each formula.
Do not plug \(2v_0\) into \(T\); velocity is absent from the period expression.
Draw two circles; observe the radius doubles while rotation rate stays constant.
Imagine halving \(v\); predict \(r\) and \(T\) to check your reasoning pattern.
Struggle is normal! Try to solve on your own before checking the hints.
Physics | CBSE 12
In a series LCR circuit \(V_R = V_C = V_L = 10\,\text{V}\). If the capacitor is short-circuited, what is the new voltage across the inductor?
No diagram required.
Equal voltages signal resonance, so \(X_L = X_C\).
Shorting the capacitor leaves an RL series circuit with \(Z=\sqrt{R^2+X_L^2}\).
Find \(I\) from \(V_R = I R\) (source voltage unchanged). Then compute \(V_L = I X_L\) using the same frequency.
Contrast the circuit at resonance with the RL circuit after the short.
At resonance \(Z=R\); remember \(I = V/R\).
Redraw the phasor triangle before and after removing \(C\).
Imagine \(R=0\) to see how \(V_L\) responds purely to \(X_L\).
Struggle is normal! Try to solve on your own before checking the hints.
Wave Optics – Multi-wavelength YDSE | Physics | CBSE 12
In a Young’s double-slit experiment, light of wavelengths 400 nm and 600 nm illuminate the same slits. Find the minimum distance \(y\) from the central bright fringe where both colours produce a dark fringe simultaneously. Express \(y\) in terms of slit separation \(d\) and screen distance \(D\).
No diagram provided
For each colour, dark fringes satisfy \( \Delta = (m+\tfrac{1}{2})\lambda \).
Find the smallest path difference that is a half-integer multiple of both wavelengths.
Once \(\Delta_{\text{min}}\) is known, use \( y = \frac{\Delta_{\text{min}}D}{d} \) to express the required distance.
Write separate dark-fringe equations before combining them.
LCM of numbers aligns repeating patterns—apply that to path differences.
Sketch the two fringe sets and mark overlaps for insight.
Imagine \(\lambda_2 = 2\lambda_1\) to see how common darks appear.
Struggle is normal! Try to solve on your own before checking the hints.
Physics | CBSE 12
Using the B.E./A versus mass-number curve, decide which labelled nuclei (W, X, Y, Z) are most suitable for (i) fission and (ii) fusion, giving reasons.
No diagram required.
Check each label’s mass number relative to the \(A\approx60\) peak on the curve.
For fission, pick the heaviest labelled nucleus that still has a noticeably lower B.E./A than the peak.
For fusion, choose the lightest labelled nucleus far left of the peak; products should shift significantly toward \(A\approx60\).
Steeper rise toward the peak implies a larger possible energy gain.
Avoid picking nuclei already at or near the peak; they cannot release much extra energy.
Draw arrows from the chosen nuclei toward the peak to see the direction of energy release.
Recall how splitting \(^{235}\text{U}\) or fusing deuterons releases energy; apply the same idea here.
Struggle is normal! Try to solve on your own before checking the hints.
Physics | CBSE 12
Derive expressions for the capacitance of a parallel-plate capacitor of area \(A\) and plate separation \(d\) when (i) a dielectric slab of thickness \(t\) and permittivity \(\varepsilon\) and (ii) a metal slab of the same thickness (\(t<d\)) are inserted between the plates.
No figure provided
Split the capacitor gap into two parts: the slab (\(t\)) and the remaining air (\(d-t\)).
For each region use \(C=\varepsilon A/\Delta x\). Take \(\varepsilon=\varepsilon_0\) for air, \(\varepsilon=\kappa\varepsilon_0\) for the dielectric.
Combine the two capacitances in series: \(1/C=1/C_1+1/C_2\). For a metal slab, the potential drop occurs only across the air gap \((d-t)\); effectively \(C=\varepsilon_0 A/(d-t)\).
Metal removal of gap boosts capacitance more than any finite-κ dielectric.
A conductor does not merely raise κ; it sets \(E=0\) inside, cancelling that part of the distance.
Verify your formula for \(t\to0\) and \(t\to d\) to detect algebra slips.
Sketch field lines and potential drop across each region to clarify the series model.
Struggle is normal! Try to solve on your own before checking the hints.
Electromagnetic Waves – Displacement Current
A parallel-plate capacitor of area 0.001 m² and plate separation 0.0001 m is connected to a source whose voltage rises at \(1\times10^{8}\,\text{V s}^{-1}\). Find the displacement current through the capacitor.
Use \(E=V/d\); hence \(\dfrac{dE}{dt}=\dfrac{1}{d}\,\dfrac{dV}{dt}\).
Insert this \(dE/dt\) into \(I_d=\varepsilon_0 A dE/dt\) and substitute the numerical values.
Keep track of powers of ten; the final answer should be a few mA.
Do not drop the area \(A\); forgetting it makes the answer 10⁴ times smaller.
Displacement current ensures Ampere–Maxwell law holds when the capacitor is charging.
List given values, write the formula, then substitute step by step.
Sketch field lines between plates to see how a changing field creates \(I_d\).
Struggle is normal! Try to solve on your own before checking the hints.
Physics | CBSE 12
Platinum (work function 5.63 eV) is illuminated by \(1.6\times10^{15}\,\text{Hz}\) light. Find the minimum de Broglie wavelength of the emitted electrons.
No diagram provided.
Use \(E = h\nu\). Convert photon energy from joules to electron-volts.
Compute \(K_{\text{max}} = E - \phi\). Keep everything in SI units for accuracy.
Find \(p = \sqrt{2m_e K_{\text{max}}}\). Finally, \(\lambda = \frac{h}{p}\) gives the minimum wavelength.
Work in SI until the last step to avoid conversion errors.
Do not use \(c = \lambda \nu\) for electrons—only photons follow that relation.
Draw an energy bar: photon energy, work function, and leftover kinetic energy.
Check what happens when \(\nu\) is just at the threshold to verify your method.
Struggle is normal! Try to solve on your own before checking the hints.
Semiconductor Electronics – Diode Logic
An ideal diode, a cell, switch S, and a bulb are in series. Will the bulb glow (a) when S is open, (b) when S is closed? Justify each answer using band-diagram reasoning.
Which diode terminal is linked to the positive cell terminal?
With S open, ask: does any closed path exist for charge to reach and return from the bulb?
When S closes, check the diode's bias. If forward-biased, model it as a short; if reverse-biased, as an open. Then trace current through the bulb.
Analyse the open-switch and closed-switch cases separately.
Remember: forward bias ≈ short circuit, reverse bias ≈ open circuit for an ideal diode.
Sketch energy bands for forward and reverse bias to see carrier movement.
Assume zero diode drop and verify if current can complete the loop.
Struggle is normal! Try to solve on your own before checking the hints.
Physics | CBSE 12
A 100 V battery (internal resistance 1 Ω) drives 10 A through a heater at 20 °C. After the heater reaches 320 °C, calculate the power dissipated inside the battery. Use \( \alpha = 3.7\times10^{-4}\,^{\circ}\mathrm{C}^{-1} \).
First, find the heater’s hot resistance using \( R_T = R_0(1+\alpha \Delta T) \).
With the new \( R \), current is \( I = \frac{V}{R + r} \).
Finally, compute \( P_{\text{battery}} = I^{2} r \). Finish the arithmetic yourself.
Keep the heater’s \( R \) and battery’s \( r \) distinct when forming equations.
Current should drop only slightly; a huge change signals an error.
Draw a simple circuit diagram with updated resistance values.
Set \( \alpha = 0 \) to verify your equations before using actual data.
Struggle is normal! Try to solve on your own before checking the hints.
Physics | CBSE 12
A coil with \(N\) turns and area \(A\) rotates at angular speed \( \omega \) in a uniform field \(B\). Derive the instantaneous emf induced in the coil and name the energy source in an a.c. generator.
Express magnetic flux through the rotating coil first.
Use \( \Phi = N B A \cos(\omega t) \).
Differentiate flux to get \( e = -\frac{d\Phi}{dt} = N B A \omega \sin(\omega t) \). Mechanical work from the prime mover is the energy source.
Apply Lenz’s law to decide the negative sign in \(e\).
Don’t forget the factor \(N\) while writing the emf expression.
Sketch coil positions at \( \omega t = 0^\circ \) and \(90^\circ\) to see flux change.
Check your formula for \( \omega t = 0 \) and \( \omega t = \pi/2 \).
Struggle is normal! Try to solve on your own before checking the hints.
Ray Optics – Telescope Magnification | Physics CBSE 12
A refracting telescope has an objective of focal length 15 m and an eyepiece of 1 cm. Calculate (i) its angular magnification in normal adjustment, and (ii) the diameter of the moon’s image formed at the objective.
No diagram required.
Put both focal lengths in metres before taking their ratio for magnification.
Use the small-angle formula \( \theta \approx \frac{3.48\times10^{6}}{3.8\times10^{8}} \) rad to estimate the moon’s angular size.
After finding \( \theta \), multiply it by the 15 m focal length to obtain the image diameter in metres, then convert to millimetres.
Solve part (i) first; reuse its result to sanity-check part (ii).
Recall that normal adjustment places the final image at infinity, so magnification is just the focal-length ratio.
Sketch parallel rays from the moon hitting the objective to see where the image forms.
Try using \( \theta = 0.01 \) rad to estimate image size, then refine with the exact angle.
Struggle is normal! Try to solve on your own before checking the hints.
Physics | CBSE 12 – Atoms
Why does a sample of hydrogen, with only one electron per atom, still show many distinct spectral lines in its emission spectrum?
Different atoms can occupy different excited states at the same moment.
Each allowed drop, such as n = 4→2 or 3→1, releases its own unique wavelength.
Combine ideas: a large ensemble of identical one-electron atoms + all possible downward jumps predicted by Bohr → many discrete spectral lines.
One electron cannot jump multiple gaps at once; each photon comes from a single transition.
Recall Bohr’s postulate: energy depends only on quantum numbers ni and nf.
Sketch the energy-level diagram and draw every downward arrow you can.
Imagine a single atom: one line per jump. Add many atoms, lines accumulate.
Struggle is normal! Try to solve on your own before checking the hints.
Quickly recap and write core formulas; remember them and avoid late corrections.
Always state answers with correct SI units—simple thing to remember for full marks.
Draw neat, labeled diagrams; they earn instant points and clarify concepts.
Substitute symbols before numbers; compute step-wise to avoid arithmetic slips.
Finish sure-shot questions first; return to lengthy ones with remaining time.
Box the final result; examiner sees it instantly and awards marks quickly.