IB JIO Grade-II Technical cheat sheet

Constitutional bodies: UPSC, Election Commission, CAG, Finance Commission are established by the Constitution; NITI Aayog, CBI, NHRC are statutory/executive bodies.

Fundamental Rights (Part III) are enforceable via writs under Articles 32 (Supreme Court) and 226 (High Courts); Directive Principles (Part IV) are non-justiciable.

RBI functions: currency issue, monetary policy via MPC (6 members, repo rate target), banker to government, custodian of forex reserves.

Indian space milestones: Chandrayaan-3 soft landing near lunar south pole (2023), Aditya-L1 solar observatory at L1, Gaganyaan as crewed programme.

Key indices: CPI (base 2012, compiled by NSO), WPI (base 2011-12, Office of Economic Adviser), IIP (base 2011-12).

International bodies: UN Security Council has 5 permanent veto members; IMF handles balance-of-payments support; World Bank funds development projects.

Bharat Ratna is India's highest civilian award; Param Vir Chakra is the highest wartime gallantry award; Ashoka Chakra is the highest peacetime gallantry award.

Appointments: Chief Election Commissioner and CAG removed only by impeachment-like process; CVC appointed by a committee of PM, Home Minister and Leader of Opposition.

Coding-decoding: convert letters to positions (A=1 ... Z=26); check for constant shifts, reversal (Atbash: A-Z, B-Y) or alternating patterns before assuming a single rule.

Blood relations: draw a family tree; vertical lines for generations, horizontal for siblings/spouse; '+' male, '−' female is a common notation.

Series completion: test differences, then ratios, then squares/cubes, then alternating sub-series at odd and even positions.

Syllogism: use Venn diagrams; 'All A are B' plus 'All B are C' implies 'All A are C'; 'Some' statements are reversible, 'All' statements are not.

Direction sense: track net displacement with vectors; North=+y, East=+x; final distance = sqrt(x² + y²).

Seating arrangement: fix the most constrained person first, then place neighbours; circular facing-centre means left is clockwise, right anticlockwise.

Clock: angle between hands = |30H − 5.5M| degrees; hands coincide 11 times in 12 hours, are opposite 11 times.

Calendar: a normal year shifts the weekday by 1, a leap year by 2; 400-year cycle repeats exactly, so 1 Jan 2000 and 1 Jan 2400 fall on the same weekday.

Percentage change: successive changes of a% and b% give net change a + b + ab/100 percent.

Profit and loss: SP = CP × (100 + profit%)/100; discount is always calculated on marked price, profit on cost price.

Simple interest = PRT/100; compound interest = P[(1 + R/100)^T − 1]; CI − SI for 2 years = P(R/100)².

Time-speed-distance: convert km/h to m/s by multiplying by 5/18; a train of length L crossing a pole takes L/speed.

Work: if A takes a days and B takes b days, together they take ab/(a+b) days; use LCM of days as total work units.

Mixtures: alligation rule gives ratio of cheaper to dearer = (mean price − cheap price) : (dear price − mean price).

Averages: new average after adding a value x to n items = (n·old average + x)/(n+1); for consecutive numbers average equals the middle term.

Permutation and combination: nPr = n!/(n−r)!, nCr = n!/[r!(n−r)!]; probability = favourable outcomes / total equally likely outcomes.

Subject-verb agreement: 'one of the + plural noun' takes a singular verb; 'each, every, either, neither' are singular.

Articles: 'a' before consonant sounds, 'an' before vowel sounds (an hour, a university); 'the' with superlatives, unique objects and rivers/ranges.

Prepositions: 'since' with a point of time, 'for' with a duration; 'between' for two, 'among' for more than two.

Tenses: present perfect (has/have + past participle) for past actions with present relevance; past perfect for the earlier of two past actions.

Active to passive: object becomes subject, verb becomes be + past participle, agent introduced by 'by'; keep tense unchanged.

Direct to indirect speech: shift present to past, change pronouns per the reporting subject, and convert 'today' to 'that day', 'tomorrow' to 'the next day'.

Common confusables: affect (verb) vs effect (noun); principal (chief) vs principle (rule); complement (complete) vs compliment (praise).

Idioms: 'once in a blue moon' = very rarely; 'to bite the bullet' = to endure a difficult situation bravely; 'a wild goose chase' = a futile search.

Newton's second law F = ma; momentum p = mv is conserved in the absence of external force; impulse = change in momentum.

Projectile motion: range R = u²sin2θ/g, maximum height H = u²sin²θ/(2g), maximum range at θ = 45°.

Work-energy theorem: W_net = ΔKE; for a spring, potential energy = ½kx²; friction force = μN.

Ohm's law V = IR; series resistance R = R1 + R2, parallel 1/R = 1/R1 + 1/R2; power P = VI = I²R = V²/R.

Kirchhoff's laws: junction rule (charge conservation), loop rule (energy conservation); Wheatstone bridge is balanced when R1/R2 = R3/R4.

Lens and mirror formula 1/f = 1/v − 1/u (lens) and 1/f = 1/v + 1/u (mirror); power of a lens in dioptres P = 1/f (metres).

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

Photoelectric effect: hν = φ + KE_max; stopping potential depends on frequency, not intensity; de Broglie wavelength λ = h/p.

Quadratic ax² + bx + c = 0: roots sum to −b/a and product to c/a; discriminant D = b² − 4ac decides real, equal or complex roots.

Arithmetic progression: nth term a + (n−1)d, sum n/2[2a + (n−1)d]; geometric progression sum a(rⁿ−1)/(r−1) for r ≠ 1.

Binomial theorem: (a+b)ⁿ = Σ nCr a^(n−r) b^r; general term nCr a^(n−r) b^r.

Identities: sin²θ + cos²θ = 1; sin2θ = 2 sinθ cosθ; cos2θ = 1 − 2sin²θ; a/sinA = b/sinB = c/sinC (sine rule).

Derivative rules: d/dx(xⁿ) = nx^(n−1), product rule (uv)' = u'v + uv', chain rule dy/dx = dy/du · du/dx.

Integration: ∫xⁿ dx = x^(n+1)/(n+1) + C for n ≠ −1; definite integral gives area under the curve.

Mean of grouped data = Σfx/Σf; median class located where cumulative frequency crosses N/2; mode = 3 median − 2 mean (empirical).

Standard deviation is the square root of variance; variance = Σ(x − mean)²/N for population; coefficient of variation = SD/mean × 100 percent.

Data units: 1 byte = 8 bits; 1 KB = 1024 bytes, 1 MB = 1024 KB, 1 GB = 1024 MB; binary uses base 2, hexadecimal base 16.

Number conversion: decimal to binary by repeated division by 2; binary 1011 equals decimal 11 and hex B.

CPU components: ALU performs arithmetic/logic, control unit decodes and sequences instructions, registers hold operands; clock speed in GHz.

Memory hierarchy by speed: registers > cache > RAM > SSD/HDD > optical/tape; RAM is volatile, ROM is non-volatile.

Operating system roles: process scheduling, memory management, file system, device drivers, user interface; kernel runs in privileged mode.

Software types: system software (OS, utilities), application software (browsers, editors), firmware stored in ROM/EEPROM.

File formats: .docx word processing, .xlsx spreadsheet, .pptx presentation, .pdf fixed-layout document, .csv comma-separated values.

Boolean logic gates: AND outputs 1 only if all inputs 1; OR if any input 1; XOR if inputs differ; NAND and NOR are universal gates.

OSI seven layers: Physical, Data Link, Network, Transport, Session, Presentation, Application; TCP/IP collapses these to four.

IPv4 addresses are 32-bit dotted decimal; IPv6 is 128-bit hexadecimal; private ranges are 10.0.0.0/8, 172.16.0.0/12, 192.168.0.0/16.

TCP is connection-oriented and reliable (three-way handshake, acknowledgements); UDP is connectionless and faster, used for streaming and DNS.

Common ports: HTTP 80, HTTPS 443, FTP 21, SSH 22, SMTP 25, DNS 53, Telnet 23, POP3 110.

DNS resolves domain names to IP addresses; DHCP assigns IP addresses dynamically; NAT maps private addresses to a public address.

Cyber threats: phishing (deceptive emails), pharming (DNS redirection), ransomware (encrypts data for ransom), DDoS (flooding a service), SQL injection.

Security controls: firewall filters packets, IDS detects intrusions, VPN encrypts tunnels, digital signature gives authenticity and integrity, TLS secures HTTPS.

Indian cyber law: Information Technology Act 2000 (amended 2008) governs electronic records, digital signatures and cyber offences; CERT-In is the national nodal agency.

Semiconductor diodes: forward bias lowers the depletion barrier (silicon cut-in ≈ 0.7 V); reverse bias blocks current until breakdown.

Rectifiers: half-wave uses one diode, full-wave centre-tap uses two, bridge uses four; ripple frequency is 2f for full-wave.

Transistor as amplifier: common emitter gives voltage and current gain with 180° phase inversion; β = IC/IB, α = β/(β+1).

Amplifier classes: A conducts 360°, B 180°, AB between, C less than 180°; class C is used for RF power with high efficiency.

Modulation: AM varies carrier amplitude, FM varies frequency; FM has better noise immunity but wider bandwidth (Carson's rule ≈ 2(Δf + fm)).

Sampling theorem: sample at least twice the highest signal frequency (Nyquist rate) to reconstruct without aliasing.

Digital modulation: ASK, FSK, PSK, QAM; QAM combines amplitude and phase to carry multiple bits per symbol.

Multiplexing: FDM divides frequency bands, TDM divides time slots, WDM uses wavelengths in optical fibre; PCM converts analogue to digital via sampling, quantisation, encoding.