GATE IN cheat sheet

Ohm's law: V = IR; power P = VI = I²R = V²/R; for AC, use RMS values and include power factor cos φ.

Thevenin equivalent: open-circuit voltage V_th across the terminals, short-circuit current I_sc through them, R_th = V_th/I_sc; maximum power transfer when R_load = R_th.

First law of thermodynamics: ΔU = Q − W; for a closed system W = ∫P dV, and for steady flow the enthalpy form h₁ + V₁²/2 + gz₁ + q = h₂ + V₂²/2 + gz₂ + w applies.

Carnot efficiency of a heat engine: η = 1 − T_C/T_H with absolute temperatures; COP of a refrigerator = T_C/(T_H − T_C) for the reversible cycle.

Beam bending: σ = My/I and deflection follows EI d²y/dx² = M(x); maximum shear stress in a rectangular section is 1.5 × average shear stress.

Bernoulli along a streamline: P + ½ρV² + ρgz = constant for steady, incompressible, inviscid flow; add head-loss terms for real fluids.

Reynolds number Re = ρVD/μ; pipe flow is laminar below about 2300 and turbulent above about 4000 for circular pipes.

Feedback amplifier gain: A_cl = A/(1 + Aβ); the loop gain Aβ determines desensitisation, bandwidth extension and stability margins.

For a first-order RC circuit the time constant is τ = RC; after one τ the response has completed about 63.2% of its final change.

TCP uses a three-way handshake (SYN, SYN-ACK, ACK) and provides reliable, ordered delivery; UDP is connectionless with no retransmission.

IPv4 address = 32 bits, IPv6 = 128 bits; usable hosts in a subnet = 2^(32 − prefix) − 2, subtracting network and broadcast addresses.

Time complexity order: O(1) < O(log n) < O(n) < O(n log n) < O(n²) < O(2ⁿ); comparison sorting has a lower bound of Ω(n log n).

A binary search tree with n nodes has average search cost O(log n) but worst case O(n) when it degenerates into a chain.

Normalisation: 1NF removes repeating groups, 2NF removes partial dependencies on part of a composite key, 3NF removes transitive dependencies.

Amdahl's law: speedup = 1/((1 − f) + f/s), where f is the parallel fraction and s the parallel speedup; it bounds gains from parallelisation.

Cache hierarchy: L1 is fastest and smallest, main memory is larger and slower; hit ratio and locality of reference drive average access time.

In public-key cryptography, encryption uses the recipient's public key and signatures use the sender's private key; RSA security rests on integer factorisation.

Scale drawing: a 1:100 plan means 1 unit on paper represents 100 units on site; areas scale by the square of the ratio.

Floor Area Ratio = total built-up floor area ÷ plot area; ground coverage = footprint area ÷ plot area, and both are capped by local bye-laws.

Standard人体 dimensions drive design: a door leaf of about 900 mm clear width and a stair riser of 150–190 mm with tread 250–300 mm satisfy the 2R + T ≈ 600–640 mm rule.

Daylight factor = (indoor illuminance at a point ÷ simultaneous outdoor horizontal illuminance) × 100%, expressed without units.

Thermal comfort is assessed by PMV/PPD (ISO 7730); the predicted percentage of dissatisfied should stay below about 10% for good design.

A simply supported beam carries a sagging (positive) bending moment; a cantilever under downward load carries hogging (negative) moment at the support.

Concrete mix designation M25 means characteristic cube compressive strength of 25 N/mm² at 28 days; nominal mixes follow IS 456 proportions.

Universal design principles include equitable use, flexibility in use, simple and intuitive use, and perceptible information.

Newton's second law: F = ma = dp/dt; momentum p = mv is conserved in the absence of external forces.

Kinetic energy KE = ½mv²; gravitational potential energy near Earth's surface U = mgh; work W = F·d cos θ.

Ideal gas law: PV = nRT with R = 8.314 J mol⁻¹ K⁻¹; at STP one mole of ideal gas occupies about 22.4 L.

pH = −log₁₀[H⁺]; a buffer resists pH change and works best when pH ≈ pKa of the weak acid component.

Mendelian monohybrid cross gives a 3:1 phenotypic and 1:2:1 genotypic ratio in the F2 generation of true-breeding parents.

DNA replication is semi-conservative; the central dogma runs DNA → RNA (transcription) → protein (translation).

Half-life: after n half-lives the remaining fraction is (1/2)ⁿ; radioactive decay follows N = N₀e^(−λt) with λ = ln2 / t½.

Snell's law: n₁ sin θ₁ = n₂ sin θ₂; total internal reflection occurs beyond the critical angle sin θ_c = n₂/n₁ when n₁ > n₂.

Accounting equation: Assets = Liabilities + Equity; every transaction keeps it balanced under double-entry bookkeeping.

Gross profit = Revenue − Cost of Goods Sold; net profit = gross profit − operating and other expenses − tax.

Current ratio = current assets ÷ current liabilities; quick ratio excludes inventory and is a stricter liquidity test.

Break-even quantity = Fixed cost ÷ (Selling price − Variable cost per unit); contribution margin per unit is the denominator.

Time value of money: PV = FV/(1 + r)ⁿ; NPV = Σ CF_t/(1 + r)^t − initial outlay, and accept projects with positive NPV.

GST is a destination-based value-added tax levied on supply of goods and services; input tax credit prevents cascading of tax.

Depreciation by straight-line method = (Cost − Salvage value) ÷ Useful life; written-down value method applies a fixed rate to the reducing balance.

Return on equity = Net income ÷ Shareholders' equity; earnings per share = Net income ÷ Number of outstanding shares.

Elements of visual art: line, shape, form, space, texture, value and colour; principles include balance, contrast, emphasis, rhythm and unity.

Colour theory: primary colours of light are red, green and blue (additive); primary pigments are traditionally red, yellow and blue (subtractive).

In Indian classical music the saptak has seven notes (Sa Re Ga Ma Pa Dha Ni); a raga defines a melodic framework and a tala defines the rhythmic cycle.

Bharatanatyam, Kathak, Kathakali, Kuchipudi, Odissi, Manipuri, Mohiniyattam and Sattriya are the eight classical dance forms recognised by the Sangeet Natak Akademi.

Rasa theory from the Natyashastra lists nine rasas, including shringara (love), hasya (comic), karuna (compassion) and veera (heroic).

Perspective drawing uses a horizon line and vanishing points; one-point perspective has a single vanishing point for lines parallel to the viewing direction.

A fresco is painted on wet lime plaster; tempera binds pigment in an emulsion such as egg yolk, and oil painting uses a drying oil medium.

Plato's theory of Forms holds that perceptible objects are imperfect copies of eternal, non-material Forms; the allegory of the cave illustrates this.

Aristotle's syllogism: two premises sharing a middle term yield a conclusion; a valid form is Barbara - All M are P, All S are M, therefore All S are P.

Kant's categorical imperative: act only on maxims that could be willed as universal law; treat humanity always as an end, never merely as a means.

Utilitarianism (Bentham, Mill) judges actions by the greatest happiness of the greatest number; Mill distinguishes higher and lower pleasures.

Descartes' cogito: 'I think, therefore I am' establishes the existence of the thinking self as a foundation that resists radical doubt.

In linguistics, a phoneme is the smallest contrastive sound unit; a morpheme is the smallest meaningful unit, and free morphemes stand alone.

Historiography distinguishes primary sources (contemporary records) from secondary sources (later interpretation), and internal from external criticism.