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NCERT Formula Reference
Class 12 Science Formulas
Quick-reference formulas for Class 12 Physics (8 chapters), Chemistry (5 chapters), and Biology (5 chapters). Covers electrostatics, optics, solutions, reproduction, ecology, biotechnology, and more.
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Physics
8 chapters1
Full chapter notesElectrostatics
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Electrostatics — Formulas
Quick reference — NCERT board exam formulas
Coulomb & Electric Field
- Coulomb's law:F = k q₁q₂/r² ; k = 1/(4πε₀)
- Electric field:E⃗ = F⃗/q ; E = kQ/r² (point charge)
- Potential:V = kQ/r ; E = −dV/dr
- Dipole (on axis):E ∝ 1/r³
Gauss's Law & Capacitors
- Gauss:∮ E⃗·dA⃗ = Q_enclosed/ε₀
- Infinite wire:E = λ/(2πε₀r)
- Infinite plane:E = σ/(2ε₀)
- Parallel plate:C = ε₀A/d
- Energy:U = ½CV² = ½Q²/C
- Series:1/C_eq = 1/C₁ + 1/C₂
- Parallel:C_eq = C₁ + C₂
2
Full chapter notesCurrent Electricity
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Current Electricity — Formulas
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Current & Resistance
- Current:I = Q/t = nAve_d
- Ohm's law:V = IR
- Resistance:R = ρL/A
- Power:P = VI = I²R = V²/R
Circuits & Cells
- Series:R_eq = R₁+R₂ ; same I
- Parallel:1/R_eq = 1/R₁+1/R₂ ; same V
- Kirchhoff:ΣI at junction = 0 ; ΣV in loop = 0
- Wheatstone bridge:Balanced when P/Q = R/S
- Cell:V = ε − Ir
3
Full chapter notesMagnetic Effects of Current
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Magnetic Effects of Current — Formulas
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Magnetic Field & Force
- Lorentz force:F⃗ = q(v⃗×B⃗)
- Force on wire:F = BIL sin θ
- Long straight wire:B = μ₀I/(2πr)
- Solenoid:B = μ₀nI (interior)
- Circular loop (centre):B = μ₀I/(2R)
- Galvanometer torque:τ = NIAB sin θ
4
Full chapter notesElectromagnetic Induction
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Electromagnetic Induction — Formulas
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Induction Laws
- Magnetic flux:Φ = B·A cos θ
- Faraday:ε = −dΦ/dt
- Motional EMF:ε = Blv
- Self-inductance:ε = −L dI/dt ; L = NΦ/I
- Energy:U = ½LI²
- AC peak EMF:ε₀ = NABω
5
Full chapter notesOptics
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Optics — Formulas
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Ray Optics
- Mirror:1/f = 1/v + 1/u ; f = R/2
- Lens:1/f = 1/v − 1/u
- Lens maker:1/f = (n−1)(1/R₁−1/R₂)
- Power:P = 1/f (dioptre)
- Magnification:m = h'/h = v/u
- Snell's law:n₁ sin i = n₂ sin r
Wave Optics
- Fringe width:β = λD/d
- Bright fringe:Path diff = nλ
- Dark fringe:Path diff = (n+½)λ
- Brewster angle:tan i_p = n
6
Full chapter notesDual Nature of Radiation
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Dual Nature of Radiation — Formulas
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Photoelectric Effect
- Einstein:K_max = hν − φ = eV₀
- Photon energy:E = hν = hc/λ
- Photon momentum:p = h/λ = E/c
- Threshold:ν₀ = φ/h
de Broglie Waves
- Matter wave:λ = h/p = h/(mv)
- Electron:λ = 1.22/√V nm (V in volts)
- Shortcut:hc ≈ 1240 eV·nm
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Full chapter notesAtoms and Nuclei
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Atoms and Nuclei — Formulas
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Bohr Model
- Radius:r_n ∝ n²/Z
- Energy:E_n = −13.6 Z²/n² eV
- Spectral line:1/λ = R(1/n₁² − 1/n₂²)
Nuclear Physics
- Mass defect:Δm = [Zm_p + Nm_n] − M_nucleus
- Binding energy:BE = Δm·c²
- Activity:A = λN = A₀e^(−λt)
- Half-life:T₁/₂ = 0.693/λ
8
Full chapter notesElectronic Devices
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Electronic Devices — Formulas
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Semiconductors & Diodes
- Forward bias:p to +, n to − ; low resistance
- Reverse bias:Small leakage current
- Rectifier:AC → DC (half/full wave)
Logic Gates
- OR:Y = A + B
- AND:Y = A·B
- NOT:Y = Ā
- NAND / NOR are universal gates
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Chemistry
5 chapters1
Full chapter notesSolutions
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Solutions — Formulas
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Concentration Terms
- Molarity:M = moles solute / L solution
- Molality:m = moles solute / kg solvent
- Mole fraction:X_A = n_A / (n_A + n_B)
- Mass %:(mass solute / mass solution) × 100
- Dilution:M₁V₁ = M₂V₂
Raoult's Law & Colligative Properties
- Vapour pressure:P_A = X_A · P°_A
- Boiling elevation:ΔT_b = K_b m
- Freezing depression:ΔT_f = K_f m
- Osmotic pressure:π = MRT
- van't Hoff factor:i = observed particles / formula units
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Full chapter notesElectrochemistry
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Electrochemistry — Formulas
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Electrochemical Cells
- Galvanic cell:Spontaneous ; anode (−) oxidation, cathode (+) reduction
- EMF:E°_cell = E°_cathode − E°_anode
- Nernst (298 K):E = E° − (0.0591/n) log Q
- Gibbs:ΔG° = −nFE°
Electrolysis & Conductivity
- Faraday 1st:m = ZIt = ZQ
- Faraday constant:F ≈ 96500 C/mol
- Conductivity:κ = 1/ρ
- Molar conductivity:Λ_m = κ/c
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Full chapter notesChemical Kinetics
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Chemical Kinetics — Formulas
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Rate Laws
- Rate:Rate = k[A]^m[B]^n
- Zero order:[A] = [A]₀ − kt
- First order:ln[A] = ln[A]₀ − kt
- Half-life (1st order):t₁/₂ = 0.693/k
- Arrhenius:k = Ae^(−E_a/RT)
4
Full chapter notesd and f Block Elements
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d and f Block Elements — Formulas
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Transition & f-Block
- Transition metals: partially filled d orbitals
- KMnO₄:Mn oxidation state = +7
- K₂Cr₂O₇:Cr oxidation state = +6
- Colour: d-d transitions (unpaired e⁻)
- Lanthanoid contraction: gradual decrease in 4f series size
- Zn²⁺ colourless: d¹⁰ (no d-d transition)
5
Full chapter notesCoordination Compounds
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Coordination Compounds — Formulas
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Coordination Chemistry
- Complex:[ML_n]^(charge) ; ligands donate electron pairs
- Coordination number:Number of donor atoms bonded to metal
- Primary valence:Ionisable (Werner)
- Secondary valence:Non-ionisable bonds to ligands
- Chelate: polydentate ligand forms ring with metal
- CFT: crystal field splitting Δ_o explains colour & magnetism
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Biology
5 chapters1
Full chapter notesBiotechnology
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Biotechnology — Formulas
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rDNA Technology
- Steps:Isolate gene → restrict → ligate into vector → transform host → clone & express
- Restriction enzyme:Cuts DNA at specific palindromic sequences ; creates sticky ends
- DNA ligase:Joins DNA fragments (phosphodiester bonds)
- Vector (plasmid):ori + selectable marker + cloning site
- Selectable marker:Antibiotic resistance — identifies transformed cells
PCR & Applications
- PCR cycle:Denaturation (~95°C) → Annealing (~50–65°C) → Extension (~72°C, Taq polymerase)
- Taq polymerase:Thermostable DNA polymerase from Thermus aquaticus
- Gel electrophoresis:Separates DNA fragments by size (smaller → farther)
- Humulin:Recombinant human insulin from E. coli
- Bt cotton:Cry toxin gene from Bacillus thuringiensis → insect resistance
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Full chapter notesEcology and Environment
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Ecology and Environment — Formulas
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Ecosystem & Energy
- 10% law (Lindeman):~10% energy transferred to next trophic level
- GPP:Gross primary production — total energy fixed by producers
- NPP:NPP = GPP − R (R = respiration)
- Energy pyramid: always upright (energy lost as heat at each level)
- Food chain: linear ; food web: interconnected chains
Biodiversity & Pollution
- Biomagnification:Fat-soluble toxins (DDT, Hg) increase concentration up food chain
- Eutrophication:Excess N, P → algal bloom → O₂ depletion → fish death
- In situ conservation: national parks, sanctuaries (natural habitat)
- Ex situ conservation: zoos, botanical gardens, gene banks
- Primary succession: bare rock/lava ; secondary: existing soil after disturbance
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Full chapter notesHuman Health and Disease
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Human Health and Disease — Formulas
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Diseases — Pathogen & Vector
- Typhoid:Salmonella typhi (bacterium) ; Widal test
- Malaria:Plasmodium (protozoan) ; vector: female Anopheles
- Amoebiasis:Entamoeba histolytica (protozoan)
- Ringworm:Dermatophyte fungi (not a worm)
- AIDS:HIV destroys helper T cells (CD4+) ; detected by ELISA / Western blot
Immunity
- Innate immunity:Non-specific — skin, mucus, phagocytes, inflammation, fever
- Acquired immunity:Specific — B cells (antibodies) + T cells (cell-mediated)
- Active immunity:Body produces own antibodies (infection / vaccination)
- Passive immunity:Ready-made antibodies (mother → baby via IgA in colostrum)
- Vaccination:Antigen exposure → memory B & T cells → faster secondary response
- Antibodies (immunoglobulins): Y-shaped proteins produced by plasma B cells
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Full chapter notesMicrobes in Human Welfare
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Microbes in Human Welfare — Formulas
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Microbes in Food & Medicine
- Curd:Lactobacillus — lactose → lactic acid → protein coagulation
- Bread / alcohol:Saccharomyces cerevisiae — fermentation produces CO₂ / ethanol
- Penicillin:Penicillium notatum (fungus) — Alexander Fleming
- Streptomycin:Streptomyces griseus — first effective anti-TB antibiotic
- Statins:Monascus purpureus — cholesterol-lowering
- Cyclosporin A:Trichoderma polysporum — immunosuppressant for transplants
Sewage, Biogas & Biofertilisers
- BOD:Biochemical oxygen demand — indicator of organic water pollution
- Biogas:Anaerobic digestion → mainly CH₄ (methane) + manure
- Rhizobium:Root nodules on legumes — nitrogenase fixes N₂ → NH₃
- Azospirillum / Azotobacter:Free-living nitrogen-fixing bacteria in soil
- Mycorrhiza:Fungus + root symbiosis — improves phosphorus uptake
- Secondary sewage treatment: aerobic microbes reduce BOD of effluent
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Full chapter notesReproduction
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Reproduction — Formulas
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Plant Reproduction
- Double fertilisation:Syngamy (male gamete + egg → zygote 2n) + triple fusion (male gamete + polar nuclei → PEN 3n)
- Pollen grain:Haploid male gametophyte — 2 male gametes in pollen tube
- Embryo sac:7-celled, 8-nucleate (Polygonum type)
- Post-fertilisation: ovule → seed ; ovary → fruit
Human Reproduction & Cycle
- Spermatogenesis:Seminiferous tubules of testes ; continuous from puberty
- Oogenesis:Graafian follicle in ovary ; arrested phases in development
- Ovulation:Triggered by LH surge (~day 14 of 28-day cycle)
- Luteal phase:Corpus luteum → progesterone ; maintains uterine lining
- Placenta:Foetal-maternal exchange ; secretes hCG, progesterone, oestrogen
Each chapter links to full notes, solved examples, and MCQs on Rishtaara.