MAH MCA CET cheat sheet

Percentage change = (new − old)/old × 100; a 20% rise followed by a 20% fall leaves a net 4% loss, since multipliers 1.2 × 0.8 = 0.96.

Simple interest SI = PRT/100; compound interest CI = P(1 + R/100)^T − P. For 2 years the CI − SI gap equals P(R/100)².

Speed–time relation: Distance = Speed × Time. For a train of length L crossing a platform of length P, time = (L + P)/Speed; crossing a pole uses L alone.

Boats: downstream speed = u + v, upstream = u − v; so u = (down + up)/2 and v = (down − up)/2, where u is boat speed in still water.

Work: if A alone takes a days and B alone b days, together they take ab/(a + b) days; combined rate is 1/a + 1/b per day.

Permutations nPr = n!/(n − r)!; combinations nCr = n!/[r!(n − r)!]. nCr = nC(n − r), and nC0 = nCn = 1.

Probability of an event = favourable outcomes / total equally likely outcomes; P(A ∪ B) = P(A) + P(B) − P(A ∩ B).

Mensuration: circle area πr², circumference 2πr; sphere volume (4/3)πr³; cylinder volume πr²h; cone volume (1/3)πr²h.

Sum of first n natural numbers = n(n + 1)/2; sum of squares = n(n + 1)(2n + 1)/6; sum of cubes = [n(n + 1)/2]².

Number series: check successive differences first, then ratios; alternating series often split into odd-position and even-position sub-series with separate rules.

Letter series uses A = 1 … Z = 26; opposite letter of position p is (27 − p), so A↔Z, B↔Y, C↔X.

Coding–decoding: compare plain and coded letters position-wise to detect a fixed shift (+1, −2), reversal, or letter-to-number mapping before assuming a pattern.

Blood relations: draw a family tree; vertical lines mark parent–child, horizontal lines mark siblings or spouses, and always apply the relation from the speaker's viewpoint.

Direction sense: track net displacement on north–south and east–west axes separately; final distance = √(x² + y²) when both components are non-zero.

Syllogism: only conclusions true in every possible Venn diagram of the premises are valid; 'some A are B' does not imply 'some B are not A'.

Seating arrangement: fix the facing direction first (north-facing means left = west), then place definite clues before conditional ones.

Clock: angle between hands = |30H − 5.5M| degrees; hands coincide every 65 5/11 minutes and are opposite every 32 8/11 minutes.

Calendar: an ordinary year shifts the weekday by 1, a leap year by 2; a century year is a leap year only if divisible by 400.

Subject–verb agreement: singular subjects take singular verbs; with 'either … or' or 'neither … nor' the verb agrees with the nearer subject.

Articles: 'a' before consonant sounds, 'an' before vowel sounds; 'the' is used for unique or already-specified nouns and is omitted before uncountable general nouns.

Tenses: present perfect (has/have + past participle) links past action to present; past perfect (had + participle) marks the earlier of two past actions.

Active to passive: object becomes subject, verb becomes be + past participle, agent follows 'by'; tense of the original is preserved.

Direct to indirect speech: present tense shifts to past, 'today' becomes 'that day', 'tomorrow' becomes 'the next day', and pronouns shift to the reporter's viewpoint.

Prepositions of time: 'in' for months, years and long periods; 'on' for days and dates; 'at' for clock times and fixed points.

Commonly confused pairs: affect (verb) vs effect (noun); advice (noun) vs advise (verb); principal (chief) vs principle (rule).

Idiom meaning is non-literal: 'to bite the bullet' means to endure a difficult situation bravely, not to chew metal.

One-word substitution and synonym/antonym items are scored by exact meaning; eliminate options that fit grammar but reverse the sense.

Computer generations: first used vacuum tubes, second transistors, third integrated circuits, fourth microprocessors, fifth AI and parallel processing.

Memory hierarchy by speed: registers > cache > RAM > secondary storage; RAM is volatile, ROM is non-volatile and retains firmware.

1 byte = 8 bits; 1 KB = 1024 bytes, 1 MB = 1024 KB, 1 GB = 1024 MB, 1 TB = 1024 GB.

OSI model has 7 layers (physical, data link, network, transport, session, presentation, application); TCP/IP collapses these into 4.

IP addresses: IPv4 is 32-bit dotted decimal, IPv6 is 128-bit hexadecimal; HTTP uses port 80, HTTPS 443, FTP 21, SMTP 25.

Programming: compiler translates the whole program before execution; interpreter translates line by line; both convert source code to machine code.

Database keys: primary key uniquely identifies a row, foreign key references another table's primary key, and SQL SELECT retrieves data.

Shortcuts: Ctrl+C copy, Ctrl+V paste, Ctrl+X cut, Ctrl+Z undo, Ctrl+S save, Alt+F4 close window, F5 refresh.

Indian general awareness: Constitution adopted 26 November 1949 and enforced 26 January 1950; ISRO is headquartered at Bengaluru.