Agniveer Vayu cheat sheet

Subject-verb agreement: a singular subject takes a singular verb; compound subjects joined by 'and' take a plural verb unless they form one idea.

Articles: 'a' before consonant sounds, 'an' before vowel sounds (an hour, a university); 'the' for specific or already-mentioned nouns.

Active to passive: move object to subject position, use form of 'be' plus past participle, and add 'by' plus the original subject.

Direct to indirect speech: shift present to past tense and change pronouns and time words (now to then, today to that day).

Synonyms share meaning; antonyms oppose it. Choose the option closest in sense and grammatical class to the given word.

Idioms are non-literal: 'to let the cat out of the bag' means to reveal a secret; 'once in a blue moon' means very rarely.

One-word substitutions: 'philanthropist' is a lover of mankind; 'omnipotent' means all-powerful; 'ephemeral' means short-lived.

Spotting errors: check for double comparatives ('more better'), redundant words ('return back'), and wrong prepositions after verbs.

Equations of motion: v = u + at, s = ut + ½at², v² = u² + 2as for uniform acceleration in a straight line.

Newton's second law: F = ma; weight equals mg, and g near Earth's surface is about 9.8 m/s².

Work is force times displacement along the force (W = Fs cosθ); kinetic energy is ½mv² and potential energy is mgh.

Ohm's law: V = IR; resistors in series add (R = R₁ + R₂), while in parallel 1/R = 1/R₁ + 1/R₂.

Electrical power: P = VI = I²R = V²/R; energy consumed in kWh equals power in kW times time in hours.

Speed of light in vacuum is about 3 × 10⁸ m/s; light travels in straight lines and reflects with angle of incidence equal to angle of reflection.

Lens/mirror formula: 1/v − 1/u = 1/f for lenses and 1/v + 1/u = 1/f for mirrors, with sign convention applied carefully.

Sound is a longitudinal mechanical wave needing a medium; its speed is highest in solids and lowest in gases.

Quadratic formula: for ax² + bx + c = 0, x = [−b ± √(b² − 4ac)] / 2a; discriminant b² − 4ac decides the nature of roots.

Arithmetic progression: nth term aₙ = a + (n − 1)d and sum Sₙ = (n/2)[2a + (n − 1)d].

Geometric progression: nth term ar^(n−1) and sum Sₙ = a(rⁿ − 1)/(r − 1) for r ≠ 1.

Trigonometric identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Standard values: sin 30° = ½, cos 60° = ½, tan 45° = 1, sin 90° = 1, cos 90° = 0.

Distance between points (x₁,y₁) and (x₂,y₂) is √[(x₂−x₁)² + (y₂−y₁)²]; midpoint is the average of the coordinates.

Area and volume: circle area πr², sphere volume (4/3)πr³, cylinder volume πr²h, cone volume (1/3)πr²h.

Probability of an event = favourable outcomes / total equally likely outcomes, always between 0 and 1 inclusive.

Number series: compute differences or ratios between consecutive terms; alternating sub-series often appear in longer sequences.

Coding-decoding: map letters to positions (A=1 … Z=26) and test shifts or reversals against the given example before applying.

Blood relations: draw a family tree, using separate symbols for male/female and horizontal lines for siblings, vertical for parent-child.

Direction sense: track net displacement with a sketch; north/south and east/west components combine at right angles.

Clock problems: angle between hands = |30H − 5.5M|, where H is the hour and M the minute.

Odd-one-out: identify the shared property (prime, perfect square, all vowels) and select the item that breaks it.

Analogy: state the relationship in words (cause-effect, part-whole, synonym) before choosing the matching pair.

Indian Constitution came into force on 26 January 1950; Dr B. R. Ambedkar chaired the Drafting Committee.

Fundamental Rights are in Part III (Articles 12–35); Fundamental Duties were added by the 42nd Amendment in 1976.

Indian Armed Forces: Army, Navy, and Air Force; the President is the supreme commander of the armed forces.

National symbols: peacock is the national bird, tiger the national animal, and 'Jana Gana Mana' the national anthem.

ISRO is India's space agency, headquartered in Bengaluru; DRDO is the defence research organisation.

Static GK anchors: capital, currency, and head of state for major countries, plus headquarters of UN bodies such as the UN in New York.

Current affairs: track national defence exercises, ISRO missions, and award announcements for the exam year, verifying dates from official sources.

Aerobic capacity is assessed by timed runs (e.g., 1.6 km); lower completion time indicates higher cardiovascular endurance.

BMI = weight in kg / (height in m)²; a value of 18.5–24.9 is classified as normal for adults.

Push-ups and sit-ups measure muscular endurance; the score is the number of correct repetitions within a fixed time.

Sit-and-reach tests measure hamstring and lower-back flexibility, recorded as the farthest reach in centimetres.

Target heart rate during exercise is commonly estimated as 60–80% of maximum heart rate, where maximum ≈ 220 − age.

Progressive overload means gradually increasing training load; rest days are required for adaptation and injury prevention.

Adaptability scenarios test composure: state the problem, choose a practical action, and communicate it clearly to the team.

Hydration and warm-up before physical tests reduce cramp and injury risk; cool-down aids recovery.