Part I: Physics

Physics in a general-competition paper is not asking you to solve a numerical — it is asking you to recognise a unit, complete a formula, or match a scientist to a discovery, usually inside one line of a larger "which of the following is correctly matched" question. That changes what "knowing physics" means for this exam: precision on symbols, units and names matters more than depth of derivation.

SI Units — The Full Table

The International System of Units (SI), adopted globally since 1960, rests on seven base quantities — everything else (force, energy, pressure, power) is a "derived unit," built by combining these seven through a formula. This distinction — base vs derived — is itself a recurring exam question ("which of these is NOT a base SI unit"), so learn the seven cold before anything else in this book. How it's tested: examiners frequently list six correct base units and slip in a derived unit (like the newton) disguised as a seventh — recognising the closed set of seven is what catches the trick.

Quantity	SI Unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd

Memory hook — "My Kid Should Always Try, Mostly Candidly": Metre, Kilogram, Second, Ampere, Temperature (kelvin), Mole, Candela — one silly sentence for all seven base units, in a fixed peg order you can always recite the same way.

Beyond the seven base units, a set of derived units recurs constantly in general-science questions precisely because each one is named after a scientist — testing both the unit and the person in one line:

Quantity	SI Unit	Symbol	Named after
Force	newton	N	Isaac Newton
Energy / Work	joule	J	James Prescott Joule
Power	watt	W	James Watt
Pressure	pascal	Pa	Blaise Pascal
Frequency	hertz	Hz	Heinrich Hertz
Electric charge	coulomb	C	Charles-Augustin de Coulomb
Electric potential	volt	V	Alessandro Volta
Electric resistance	ohm	Ω	Georg Simon Ohm
Electric capacitance	farad	F	Michael Faraday
Magnetic flux density	tesla	T	Nikola Tesla
Radioactivity (activity)	becquerel	Bq	Henri Becquerel
Absorbed radiation dose	gray	Gy	Louis Harold Gray

Practice Recall: Without looking, name the seven SI base units and their symbols, in order — then name which four derived units above are named after people also famous for other things (Newton for gravitation, Watt for the steam engine, Volta for the battery, Faraday for induction).

Units and Dimensions

Why this section exists: a "dimensional formula" question looks intimidating the first time you see it, but it is really just a bookkeeping trick — every derived physical quantity can be expressed as some combination of the powers of mass (M), length (L), and time (T) (and, where relevant, current A, temperature K, and so on). Once you know how a quantity is defined (its formula), writing its dimensional formula is almost automatic, which is exactly why this is a low-effort, high-return topic rather than a deep one.

How dimensions are found — the method in one line: take the defining formula, replace every quantity in it with its own dimensional formula, and simplify like ordinary algebra. For example, speed = distance/time, so its dimensional formula is [L]/[T] = [M⁰L¹T⁻¹].

Quantity	Formula used	Dimensional formula
Area	length × breadth	[M⁰L²T⁰]
Volume	length³	[M⁰L³T⁰]
Speed / velocity	distance/time	[M⁰L¹T⁻¹]
Acceleration	velocity/time	[M⁰L¹T⁻²]
Density	mass/volume	[M¹L⁻³T⁰]
Momentum	mass × velocity	[M¹L¹T⁻¹]
Force	mass × acceleration	[M¹L¹T⁻²]
Work / Energy	force × distance	[M¹L²T⁻²]
Power	work/time	[M¹L²T⁻³]
Pressure	force/area	[M¹L⁻¹T⁻²]
Frequency	1/time period	[M⁰L⁰T⁻¹]

Why dimensional analysis matters practically: it lets you sanity-check whether an equation could be correct without solving anything — the dimensions on both sides of a valid physical equation must match exactly (this is called the "principle of homogeneity of dimensions"), which is precisely why an exam question sometimes asks you to spot a formula that is dimensionally impossible (e.g., an equation that tries to add a length to a time). It also explains why constants like G and h carry such strange-looking units (N·m²/kg² and J·s respectively) — those units exist purely so the dimensions on both sides of their governing equations balance out.

Memory hook — "MLT does it all": almost every mechanical quantity in this table reduces to some combination of just three letters — Mass, Length, Time — so instead of memorising ten dimensional formulas separately, memorise the defining formula of each quantity (which you likely already know) and derive the dimensions on the spot.

Physical Constants Worth Knowing Cold

A "fill in the constant" or "match the constant to its symbol" question appears in nearly every general-science paper. These values don't need ten decimal places — exams test the order of magnitude and the correct symbol, not precision engineering.

Constant	Symbol	Approximate Value
Speed of light (vacuum)	c	3 × 10⁸ m/s
Planck's constant	h	6.626 × 10⁻³⁴ J·s
Gravitational constant	G	6.674 × 10⁻¹¹ N·m²/kg²
Avogadro's number	Nₐ	6.022 × 10²³ per mole
Boltzmann constant	k	1.381 × 10⁻²³ J/K
Charge on an electron	e	1.602 × 10⁻¹⁹ C
Acceleration due to gravity (standard, Earth)	g	9.8 m/s² (≈ 9.81)
Universal gas constant	R	8.314 J/(mol·K)
Mass of electron	mₑ	9.109 × 10⁻³¹ kg
Mass of proton	mₚ	1.673 × 10⁻²⁷ kg

Why these particular ten: c anchors all of relativity and optics; h anchors quantum mechanics (energy of a photon, E = hν); G anchors gravitation (below); Nₐ is the bridge between the atomic-scale world and the gram-scale lab bench (one mole of any substance contains Avogadro's number of particles); g is the one every mechanics formula on this page needs; and e anchors all of electricity, since current is nothing but a flow of these elementary charges.

Memory hook: Anchor each constant to a picture rather than a number string. c: light circling the Earth ~7.5 times in a second. Nₐ: more particles in a mole than grains of sand on every beach on Earth, many times over. g: a dropped object gains about "10" (9.8, rounded) metres-per-second of speed every single second it falls — the most-used approximation in this whole table.

Mechanics: Motion, Force, Work-Energy-Power

The three equations of motion describe uniformly accelerated motion — a body whose acceleration (a) is constant, starting at velocity u, reaching velocity v, covering distance s, in time t:

Equation	What it tells you
v = u + at	Final speed = starting speed + (how much a constant push adds over time)
s = ut + ½at²	Distance covered = what constant speed alone would cover, plus the "extra" from accelerating
v² = u² + 2as	Final speed², without needing to know time directly — useful for braking-distance-style questions

How this is tested: examiners rarely ask you to solve these (that belongs to a numerical-ability paper) — instead they present a small scenario ("a body starts from rest and accelerates uniformly...") and ask which equation applies, or state one equation with a term swapped and ask you to spot the error. Knowing why each equation looks the way it does (not just memorising the symbol string) is what lets you catch a swapped sign or misplaced exponent instantly.

Newton's three laws of motion are the conceptual foundation under every mechanics question in this exam bracket:

1. First law (inertia): a body at rest stays at rest, and a body in motion stays in uniform motion, unless acted on by a net external force. This is why you lurch forward when a bus brakes suddenly — your body's inertia keeps trying to continue moving even as the bus stops. How it's tested: almost always through a real-life scenario ("passengers lean forward when a bus stops suddenly — this illustrates...") rather than the bare definition, so practise recognising the law inside a story, not just reciting it.
2. Second law (F = ma): the net force on a body equals its mass times its acceleration. This single formula is the most frequently tested line in all of classical mechanics — it is also, equivalently, "rate of change of momentum," since momentum p = mv and F = dp/dt.
3. Third law (action-reaction): for every action, there is an equal and opposite reaction, acting on two different bodies (never the same body) — which is why a rocket can push exhaust gas backward and be pushed forward by the reaction, even in the vacuum of space where there's nothing to "push against" externally. A frequent trap: a question may claim the two forces "cancel out" — they never do, precisely because they act on two different bodies, so there is nothing for them to cancel against on either single body.

Work, energy, power — the trio that's almost always tested together, since each is defined in terms of the last:

Quantity	Formula	SI Unit	One-line meaning
Work	W = F × d (force × displacement, along the direction of force)	joule (J)	Energy transferred by a force acting through a distance
Kinetic energy	KE = ½mv²	joule (J)	Energy a body has because it is moving
Potential energy (gravitational)	PE = mgh	joule (J)	Energy a body has because of its height above a reference level
Power	P = W/t (work done per unit time)	watt (W)	The rate at which work is done — not how much work, but how fast

Why the KE formula has a "square" and PE doesn't: kinetic energy grows with the square of velocity because doubling an object's speed requires four times the force applied over the same distance (or the same force over four times the distance) to reach that speed — this is exactly why a car crash at double the speed is roughly four times as destructive, not merely twice, a fact worth remembering both for exams and for road safety.

Law of conservation of energy, the master principle behind this whole trio: energy can neither be created nor destroyed, only transformed from one form to another — a ball dropped from a height converts its potential energy into kinetic energy as it falls, and (ignoring air resistance) the total mechanical energy at every point of the fall stays constant. This is the same principle re-appearing later as the "first law of thermodynamics," so recognise it as one idea wearing two different names in two different sections of this book.

Practice Recall: Write, from memory, all three equations of motion and Newton's three laws in one sentence each — then check the tables above. If you got F = ma right but forgot which one is the "third law," you've just found the gap the acronym below fixes.

Memory hook — Newton's laws, "Inertia, Impact, Interaction": Inertia (1st — nothing changes without a push), Impact (2nd — F = ma, how big a push changes things), Interaction (3rd — every push pushes back). Three "I" words in the same order as the three laws.

Simple Machines

A simple machine is any device that changes the direction or magnitude of an applied force to make a task easier — it never creates energy, it only trades force for distance (or vice versa). This trade-off is captured by mechanical advantage (MA) — the ratio of load lifted to effort applied (MA = Load/Effort) — and velocity ratio (VR), the ratio of the distance moved by the effort to the distance moved by the load. Efficiency = (MA/VR) × 100%; a machine is never 100% efficient in practice because some effort is always lost to friction, which is why real machines have an efficiency below the "ideal" figure a frictionless calculation would predict.

• Lever: a rigid rod that pivots about a fixed point (the fulcrum), used to lift a load with less effort than lifting it directly. Levers come in three classes, distinguished purely by the relative position of fulcrum, load, and effort: Class I (fulcrum in the middle — a see-saw, a pair of scissors, a crowbar); Class II (load in the middle — a wheelbarrow, a nutcracker, a bottle-opener); Class III (effort in the middle — a pair of tongs, a fishing rod, the human forearm lifting a weight). Why it's tested: exams love matching an everyday tool to its lever class, since the three-class system is a clean, closed, memorisable set.
• Pulley: a wheel with a grooved rim that changes the direction of an applied force (a single fixed pulley, as on a flagpole or well) or additionally reduces the effort needed (a movable or compound pulley system, as in a crane) at the cost of pulling a longer length of rope.
• Inclined plane: a sloped surface (a ramp) that lets a load be raised using less effort than lifting it vertically, by trading a smaller force for a longer distance travelled — the working principle behind ramps for wheelchairs and loading trucks, and behind the screw and the wedge, both of which are really an inclined plane wound around an axis (screw) or used edge-on (wedge, as in an axe blade).
• Wheel and axle: a wheel fixed to a smaller axle so that turning the (larger) wheel through one full circle moves the smaller axle the same one turn but with mechanical advantage — the principle behind a doorknob, a steering wheel, and a screwdriver.

Memory hook — "FLE" for lever class: picture the middle element in each class — Class I: Fulcrum in the middle; Class II: Load in the middle; Class III: Effort in the middle — "F-L-E," in numerical order I, II, III.

Practice Recall: Name the three classes of lever, give one everyday tool as an example of each, and state the formula for mechanical advantage — then explain, in one line, why no real machine reaches 100% efficiency.

Gravitation

Newton's law of universal gravitation states that every object in the universe attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centres:

F = G(m₁m₂)/r²

Why this matters beyond the formula itself: the "inverse square" part is why gravity weakens so quickly with distance (double the distance, and the force drops to a quarter, not a half) — the same inverse-square logic governs light intensity, electrostatic force (Coulomb's law), and even sound intensity, so recognising the pattern pays off across the whole Physics section, not just this one formula. Acceleration due to gravity (g) varies slightly with location — it is greater at the poles than at the equator (because Earth bulges at the equator, putting the equator's surface farther from the centre) and decreases with both altitude (going up) and depth (going down toward the centre), reaching zero at Earth's very centre.

Escape velocity — the minimum speed an object needs to permanently break free of a planet's gravitational pull without further propulsion — is about 11.2 km/s for Earth; this is why every rocket launch is fundamentally a fight against gravity to reach and sustain such speeds, and why more massive planets (with stronger surface gravity) require a correspondingly higher escape velocity. Weight vs mass, a standing conceptual trap: mass is the amount of matter in a body and stays constant everywhere; weight (= mg) is the force of gravity acting on that mass and therefore changes with location — an astronaut has the same mass on the Moon as on Earth but weighs roughly one-sixth as much, because the Moon's gravity is about one-sixth of Earth's.

Fluid Mechanics

Fluid mechanics questions in this exam bracket concentrate on three named principles, each with an immediately recognisable everyday application — exactly the kind of "principle → device" pairing that gets tested as a matching question.

• Pascal's Law: pressure applied to an enclosed, incompressible fluid is transmitted equally and undiminished in all directions throughout the fluid. Why it matters: this single idea underlies every hydraulic machine — a hydraulic lift, a hydraulic brake, a hydraulic jack — because a small force applied over a small area at one end produces a much larger force over a larger area at the other end (force = pressure × area, and pressure stays constant), letting a mechanic lift an entire car with modest hand or foot effort.
• Archimedes' Principle: when a body is fully or partially submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid it displaces. Why it matters / how it's tested: this is the principle behind flotation — a body floats if its own weight is less than or equal to the weight of fluid it can displace, which is why a massive steel ship floats (its hollow shape displaces a huge volume of water) while a small solid steel ball sinks (it can't displace enough water to match its own weight). Exams also like the "Eureka!" story — Archimedes reportedly discovered this while stepping into a bath and realising the water displaced could reveal a crown's density, and hence whether it was pure gold.
• Bernoulli's Principle: within a steadily flowing fluid, as the speed of the fluid increases, its pressure decreases (and vice versa) — a statement, essentially, of energy conservation applied to moving fluids. Why it matters: this explains how an aircraft wing generates lift (air moves faster over the curved upper surface than the flatter lower surface, so pressure below exceeds pressure above, pushing the wing — and the plane — upward), why a shower curtain gets "sucked inward" when water flows fast through it, and why a spinning cricket/football ball curves in flight (the Magnus effect, a close cousin of the same underlying idea).

Memory hook — "PAB, in order of what they act on": Pascal (a fluid transmits pressure everywhere equally — hydraulics), Archimedes (a fluid pushes up on a submerged body — buoyancy/floating), Bernoulli (a moving fluid trades pressure for speed — flight/lift). Three names, three distinct fluid behaviours, never to be swapped with each other.

Practice Recall: State Pascal's Law, Archimedes' Principle, and Bernoulli's Principle in one sentence each, then name one everyday device or phenomenon each principle explains — without checking, say which of the three explains why a ship floats and which explains why an aircraft wing generates lift.

Heat and Thermodynamics

• Temperature scales: Celsius (°C), Fahrenheit (°F), and Kelvin (K) are the three scales tested. Conversion: K = °C + 273; °F = (°C × 9/5) + 32. Kelvin is the SI unit and the only scale with a true zero (absolute zero, 0 K = −273°C, the theoretical point at which all molecular motion stops).
• Heat vs temperature: a favourite conceptual trap. Temperature measures the average kinetic energy of a substance's particles; heat is the total thermal energy transferred between bodies due to a temperature difference. A cup of boiling water and a swimming pool of lukewarm water can have the pool contain far more total heat energy despite a much lower temperature, simply because it has vastly more molecules.
• Modes of heat transfer: conduction (through direct contact, typically solids — a metal spoon heating up in hot tea), convection (through the bulk movement of a fluid — warm air rising, driving room heating and monsoon-related atmospheric circulation), and radiation (through electromagnetic waves, needing no medium at all — this is how the Sun's heat reaches Earth across the vacuum of space).
• The three laws of thermodynamics, one line each: Zeroth law — if two systems are each in thermal equilibrium with a third, they're in equilibrium with each other (this is what makes a thermometer meaningful at all). First law — energy can neither be created nor destroyed, only converted from one form to another (conservation of energy, the same principle met above in mechanics). Second law — heat flows spontaneously only from hot to cold, never the reverse without external work (this is why a refrigerator needs electricity to move heat "uphill"). How the second law is tested: as the reason a perpetual-motion machine (one that runs forever without energy input) is impossible — a favourite "why is this claimed invention a scam" style question.
• Specific heat capacity, in one line: the amount of heat needed to raise the temperature of one kilogram of a substance by one degree Celsius (or kelvin); water has an unusually high specific heat capacity compared to most substances, which is why coastal areas have milder, less extreme temperature swings than landlocked areas — the large nearby body of water absorbs and releases heat slowly, moderating the local climate.

Electricity

Ohm's Law is the single most tested electricity formula in this exam bracket: at constant temperature, the current through a conductor is directly proportional to the voltage across it —

V = IR (Voltage = Current × Resistance)

Quantity	Symbol	SI Unit
Voltage (potential difference)	V	volt (V)
Current	I	ampere (A)
Resistance	R	ohm (Ω)
Electric power	P	watt (W), where P = VI = I²R = V²/R

Resistances in series vs parallel is a standing favourite because the two combination rules are opposites of each other:

	Series	Parallel
Formula	R = R₁ + R₂ + R₃ + ...	1/R = 1/R₁ + 1/R₂ + 1/R₃ + ...
Current	Same through every resistor	Divides across each branch
Voltage	Divides across each resistor	Same across every branch
Net resistance	Always greater than the largest individual resistor	Always smaller than the smallest individual resistor
Household wiring uses	—	Parallel (so one appliance failing doesn't cut power to the rest, and each runs at full mains voltage)

Memory hook — "series adds, parallel halves-and-more": Series resistance formulas look like ordinary addition (R = R₁+R₂); parallel formulas look like fraction addition (1/R = 1/R₁+1/R₂) — the more complicated-looking formula (parallel) is the one that gives you the smaller total resistance, which feels backward until you remember parallel branches give current more paths, so less overall opposition.

Practice Recall: State Ohm's Law in symbols, then say — without checking — whether household wiring uses series or parallel circuits, and why.

AC vs DC, a frequently tested pair: Direct Current (DC) flows in one constant direction (batteries, solar cells); Alternating Current (AC) periodically reverses direction (the standard supply from household mains, generated at power stations). India's household mains supply is 220–230 V AC at 50 Hz — worth knowing cold, since "frequency of Indian household supply" is a recurring one-liner question. AC is preferred for long-distance transmission because its voltage can be easily stepped up or down using a transformer (an application of electromagnetic induction, below), letting power travel at high voltage/low current — which loses far less energy to resistive heating in the wires — before being stepped back down for safe household use.

Fuse, in one line: a short length of wire with a low melting point, deliberately placed in a circuit so that it melts and breaks the circuit if current exceeds a safe limit — a simple, sacrificial safety device that prevents fires from short circuits or overloads before they can damage the rest of the wiring or connected appliances.

Magnetism and Electromagnetism

• Magnetic field, in one line: the region around a magnet (or a current-carrying conductor) within which a magnetic force can be detected — visualised using magnetic field lines, which always run from the north pole to the south pole outside the magnet, and are denser where the field is stronger. Like poles repel, unlike poles attract — the magnetic mirror of the electrostatic rule for charges.
• Oersted's discovery (1820): a current-carrying wire produces a magnetic field around it — the first demonstrated link between electricity and magnetism, and the seed from which the whole field of electromagnetism grew.
• Electromagnetic induction (Faraday's Law): a changing magnetic field induces an electric current in a nearby conductor — the single principle that makes every electric generator, transformer, and induction stove work. Why it's the reverse of a motor: a motor converts electrical energy into mechanical motion (using a magnetic field to push a current-carrying coil); a generator does the exact reverse, converting mechanical motion into electrical energy (moving a coil through a magnetic field) — the same basic hardware, running in opposite directions, is a favourite "motor vs generator" contrast question.
• Fleming's Left-Hand Rule (for motors): with the thumb, forefinger, and middle finger of the left hand held mutually perpendicular, the forefinger points in the direction of the magnetic Field, the middle finger in the direction of the Current, and the thumb gives the direction of the resulting Motion (force) — used to find the direction a current-carrying conductor moves inside a magnetic field.
• Fleming's Right-Hand Rule (for generators): the same three-finger setup on the right hand — forefinger for Field, thumb for Motion, middle finger gives the direction of the induced Current — used to find the direction of current generated when a conductor moves through a magnetic field.

Memory hook — "Left for motor, Right for generator, FCM order both times": both rules use Field (forefinger), Current, Motion(thumb) in the same finger assignment, just swapping which hand and which of Current/Motion is the "input" vs the "output" — motors take in current to make motion (left hand), generators take in motion to make current (right hand).

Electromagnet, one line: a temporary magnet created by passing current through a coil of wire wound around a soft-iron core — unlike a permanent magnet, its strength can be controlled (more current/turns = stronger field) and switched off entirely by cutting the current, which is exactly why electromagnets, not permanent magnets, are used in devices like electric bells, cranes that lift scrap iron, and the coils inside a loudspeaker and an electric motor.

Practice Recall: State Fleming's Left-Hand and Right-Hand rules, name which is used for a motor and which for a generator, and explain in one line why an electromagnet is preferred over a permanent magnet in a scrap-lifting crane.

Optics

• Reflection's two laws: (1) the angle of incidence equals the angle of reflection; (2) the incident ray, reflected ray, and the normal (an imaginary line perpendicular to the surface) all lie in the same plane.
• Refraction's key idea: light bends when passing from one medium into another of different optical density, because its speed changes — this is why a straw looks "bent" at the water's surface. Snell's Law relates the angle of incidence (i) and angle of refraction (r): n = sin(i)/sin(r), where n is the refractive index of the second medium relative to the first.
• Mirror formula: 1/f = 1/v + 1/u, where f = focal length, v = image distance, u = object distance — used identically for both concave and convex mirrors, with sign conventions distinguishing them.
• Lens formula: 1/f = 1/v − 1/u — nearly identical to the mirror formula but with a minus sign, a distinction worth memorising precisely because exams like to swap the sign as a trick.
• Convex vs concave, one-line distinguishers: a convex lens/mirror converges light (bulges outward; a convex lens can form a real, inverted image, and is the lens used to correct long-sightedness/hypermetropia); a concave lens/mirror diverges light (curves inward; a concave lens corrects short-sightedness/myopia). Concave mirrors are used in torches, headlights, and shaving mirrors (magnified image up close); convex mirrors are used as vehicle side-mirrors (smaller image but a wider field of view — "objects in mirror are closer than they appear").
• Dispersion: white light splits into its seven-colour spectrum (VIBGYU — Violet, Indigo, Blue, Green, Yellow, Orange, Red) when passed through a prism, because each colour (wavelength) bends by a slightly different amount — the same basic phenomenon that produces a rainbow, with water droplets acting as tiny natural prisms.
• Total internal reflection, a frequently tested application: when light travelling from a denser to a rarer medium hits the boundary at an angle greater than the "critical angle," it reflects entirely back into the denser medium instead of refracting out — the principle behind optical fibres (used in internet/telecom cables and medical endoscopes) and the sparkle of a well-cut diamond.

Waves and Sound

Sound is a mechanical wave — unlike light, it needs a material medium to travel and cannot travel through a vacuum, a fact tested constantly as a "which of these can/cannot travel through space" question. The speed of sound depends on the medium: it travels fastest through solids, slower through liquids, and slowest through gases (roughly 343 m/s in air at room temperature, ~1,480 m/s in water, and over 5,000 m/s in steel) — because particles that are more tightly packed transmit vibrations more efficiently. Speed of sound in air also increases with temperature (particles move faster, colliding and transmitting vibration more quickly).

Frequency ranges worth knowing: the normal human audible range is roughly 20 Hz to 20,000 Hz (20 kHz); sound below 20 Hz is infrasound (too low-pitched for humans to hear — elephants communicate over long distances using infrasound); sound above 20 kHz is ultrasound (too high-pitched for humans — used in medical imaging/sonography and by bats and dolphins for echolocation).

The Doppler Effect, in one line: the apparent frequency (pitch) of a wave changes when the source and observer are in relative motion — pitch appears higher as a source approaches and lower as it recedes, which is why an ambulance siren sounds higher-pitched as it approaches you and drops in pitch as it passes and moves away. The same underlying principle, applied to light instead of sound, is what lets astronomers detect a star or galaxy moving away from us via "redshift" — the basis of the discovery that the universe is expanding.

Echo and reverberation, one line each: an echo is heard when a reflected sound reaches the ear at least about 0.1 second after the original (the minimum gap the human ear can distinguish as two separate sounds), requiring a reflecting surface at least around 17 metres away in air — which is why echoes are noticeable in a large hall or against a distant cliff but not off a nearby wall; reverberation is the persistence of sound in an enclosed space due to multiple, closely spaced reflections arriving too quickly to be perceived as distinct echoes, which is why auditorium design deliberately uses sound-absorbing materials to control it. Resonance, in one line: when a vibrating body is driven at a frequency matching another body's own natural frequency, the second body is set into unusually large-amplitude vibration — the principle behind tuning a musical instrument, and, in a famous cautionary example, why soldiers are traditionally ordered to break step (stop marching in unison) while crossing a bridge, to avoid accidentally driving the bridge at its own resonant frequency.

Semiconductors and Electronics

• Conductors, insulators, semiconductors — the three-way split: a conductor (copper, silver, aluminium) allows electric charge to flow through it easily, because its outer electrons are loosely bound and free to move; an insulator (rubber, glass, wood, plastic) strongly resists the flow of charge, its electrons being tightly bound; a semiconductor (silicon, germanium) sits in between — a poor conductor in its pure state, but one whose conductivity can be precisely and deliberately increased by adding tiny, controlled impurities, a process called doping. Why it's tested: this three-way distinction, and the fact that silicon specifically underlies essentially all modern electronics, is one of the most commonly asked "applied physics" one-liners in this exam bracket.
• Doping — n-type and p-type, one line each: adding an impurity with more valence electrons than silicon (like phosphorus) creates an n-type semiconductor with extra free electrons (negative charge carriers); adding an impurity with fewer valence electrons (like boron) creates a p-type semiconductor with "holes" that behave as positive charge carriers. Joining a p-type and n-type semiconductor together creates the simplest useful electronic device, the p-n junction diode.
• Diode, one line: a device that allows current to flow easily in only one direction (forward bias) and blocks it in the other (reverse bias) — used to convert AC to DC (rectification), among many other uses.
• Transistor, one line: a three-terminal semiconductor device that can amplify a weak electrical signal or act as a fast electronic switch — the fundamental building block of essentially all modern computing and electronics; invented in 1947 at Bell Labs (Bardeen, Brattain, and Shockley), a discovery that later won them the Nobel Prize in Physics (1956) and is frequently cited as one of the most consequential inventions of the 20th century.
• Laser, one line (an "applied modern physics" fact worth keeping alongside this section): a laser produces light that is coherent (all waves in phase) and monochromatic (single wavelength), unlike ordinary light sources, which is why a laser beam stays narrow and focused over long distances instead of spreading out and mixing colours the way a torch beam does.

Practice Recall: Distinguish a conductor, an insulator, and a semiconductor in one line each, name the process used to increase a semiconductor's conductivity, and state one everyday use each of a diode, a transistor, and a laser.

Famous Scientists and Their Discoveries

This table is tested almost every single cycle in a "match the scientist to the discovery" format — treat it as unmissable, low-effort marks.

Scientist	Known for
Isaac Newton	Three laws of motion; law of universal gravitation; foundational work in optics (splitting white light) and calculus
Albert Einstein	Special and general theory of relativity (E = mc²); explained the photoelectric effect (his actual Nobel-winning work, not relativity)
Michael Faraday	Laws of electromagnetic induction — the principle behind every electric generator and transformer
Niels Bohr	Bohr model of the atom — electrons orbit the nucleus in fixed, quantised energy levels
Ernest Rutherford	Gold foil experiment; discovered the atomic nucleus, showing atoms are mostly empty space with a dense positive centre
Marie Curie	Discovered radium and polonium; pioneering research on radioactivity (a term she coined); only person to win Nobel Prizes in two different sciences (Physics and Chemistry)
James Clerk Maxwell	Unified electricity, magnetism and light into one theory of electromagnetism
Chandrasekhara Venkata (C.V.) Raman	Discovered the Raman Effect (1928) — the scattering of light changes wavelength when it passes through a transparent medium; won India's first Nobel Prize in the sciences (Physics, 1930); National Science Day (28 February) commemorates this discovery
Homi J. Bhabha	"Father of the Indian nuclear programme"; founded the Tata Institute of Fundamental Research (TIFR) and what became the Bhabha Atomic Research Centre (BARC)
J.C. Bose	Pioneering work on radio waves/wireless signalling and plant response to stimuli (invented the crescograph)

Practice Recall: Cover the right column and name what each of these ten scientists is remembered for, then check yourself — pay special attention to the Raman Effect, since Indian-context questions on it (year, National Science Day date, what the effect actually demonstrates) recur almost every cycle.

Indian Institutions and Nobel Laureates

Key Indian physics/science research institutions, expanded beyond the nuclear-specific list, since general-science papers frequently ask "which institution is located where / does what":

Institution	Location	Focus
Bhabha Atomic Research Centre (BARC)	Mumbai	Nuclear research and reactor technology
Tata Institute of Fundamental Research (TIFR)	Mumbai	Fundamental physics, mathematics; founded by Homi Bhabha
Physical Research Laboratory (PRL)	Ahmedabad	Space, atmospheric and planetary sciences; founded by Vikram Sarabhai
Indian Institute of Astrophysics (IIA)	Bengaluru	Astronomy and astrophysics
Indian Institute of Science (IISc)	Bengaluru	Multidisciplinary science and engineering research, oldest of its kind in India (est. 1909)
Council of Scientific and Industrial Research (CSIR)	New Delhi (HQ)	Umbrella body coordinating a network of national science labs across disciplines
Indian Space Research Organisation (ISRO)	Bengaluru (HQ)	India's national space agency (see the dedicated section below)
Vikram Sarabhai Space Centre (VSSC)	Thiruvananthapuram	Launch vehicle design and development

Nobel laureates of Indian origin in the sciences — a table exam-setters return to constantly, since it combines "science" with "India" in one question:

Laureate	Year	Field	Contribution
C.V. Raman	1930	Physics	Raman Effect (scattering of light); first Indian (and first Asian) to win a science Nobel
Har Gobind Khorana	1968	Physiology or Medicine	Interpretation of the genetic code and its function in protein synthesis (shared prize; became a US citizen)
Subrahmanyan Chandrasekhar	1983	Physics	Chandrasekhar limit — the mass threshold beyond which a dying star collapses into a neutron star or black hole rather than becoming a white dwarf
Venkatraman Ramakrishnan	2009	Chemistry	Structure and function of the ribosome (studies conducted while a US/UK-based scientist of Indian origin)
Amartya Sen	1998	Economic Sciences	Welfare economics and social choice theory (included here for completeness, though outside the "hard science" scope)
Abhijit Banerjee	2019	Economic Sciences	Experimental approach to alleviating global poverty (shared; included for completeness)

Why the distinction between "Indian citizen" and "Indian-origin" matters for this exam: only C.V. Raman won while an Indian citizen, based in India, for work done in India — a distinction exams sometimes test directly ("who is the only Nobel laureate in the sciences who was an Indian citizen at the time of the award").

Practice Recall: Name three Indian research institutions and one focus area each, then name three Nobel laureates of Indian origin in the sciences with their field and contribution — without checking, say which of them was an Indian citizen at the time of the award.

Space and ISRO Facts

Space and ISRO one-liners appear constantly in Indian general-science sections, often blurring into current-affairs territory — the following core facts, however, are stable enough to memorise as settled general knowledge.

• ISRO (Indian Space Research Organisation), headquartered in Bengaluru, was established in 1969, evolving from the earlier Indian National Committee for Space Research (INCOSPA) set up in 1962 under Vikram Sarabhai, widely regarded as the "Father of the Indian Space Programme." India's first satellite, Aryabhata, was launched in 1975 (using a Soviet rocket, since India's own launch capability came later).
• Satellite orbit types, one line each: a Low Earth Orbit (LEO) satellite (a few hundred to ~2,000 km up) circles the Earth quickly (used for Earth observation and the International Space Station); a Geostationary Orbit (GEO) satellite sits at about 36,000 km above the equator, orbiting at exactly the same rate the Earth rotates, so it appears to "hang" fixed over one point on Earth (used for communication and weather satellites); a Polar Orbit satellite passes over (or near) both poles on each revolution while the Earth rotates beneath it, letting it scan the entire surface over successive orbits (used heavily for remote-sensing/mapping satellites).
• PSLV (Polar Satellite Launch Vehicle): ISRO's most reliable and frequently used launch vehicle, primarily designed to place satellites into polar and sun-synchronous orbits, though also used for some other missions; it carried India's Chandrayaan-1 (2008) and Mars Orbiter Mission/Mangalyaan (2013) into their initial trajectories.
• GSLV (Geosynchronous Satellite Launch Vehicle): a more powerful launch vehicle designed to place heavier satellites into geostationary transfer orbit; the GSLV Mk III (also marketed as LVM3) is ISRO's heaviest-lift launch vehicle and carried the Chandrayaan-3 mission (2023), which achieved a successful soft landing near the Moon's south polar region, making India the first country to do so and only the fourth to achieve any soft lunar landing.
• Chandrayaan and Mangalyaan, one line each: Chandrayaan-1 (2008) confirmed the presence of water molecules on the Moon's surface; Mangalyaan/Mars Orbiter Mission (2013–14) made India the first country to reach Mars orbit in its very first attempt, and one of the most cost-efficient interplanetary missions ever flown; Chandrayaan-3 (2023) achieved the soft landing described above via its Vikram lander and Pragyan rover.
• Aditya-L1 (launched 2023): India's first dedicated solar-observation mission, placed in a halo orbit around the Sun-Earth Lagrange point L1, from where it can continuously observe the Sun without being eclipsed by the Earth or Moon.

Memory hook — "P for Polar, G for Geo": PSLV → Polar orbits (lighter payload, most-used workhorse); GSLV → Geosynchronous orbits (heavier payload, more powerful) — match the first letter of the vehicle to the first letter of its target orbit type.

Practice Recall: Distinguish PSLV from GSLV, name the mission that achieved India's soft lunar landing and the launch vehicle that carried it, and explain the difference between a LEO, a GEO, and a polar-orbit satellite in one line each.

Modern Physics One-Liners

• Radioactivity is the spontaneous emission of particles or energy from an unstable atomic nucleus, occurring in three main forms: alpha decay (emits a helium nucleus, weakly penetrating, stopped by paper), beta decay (emits an electron, more penetrating, stopped by a few mm of aluminium), and gamma decay (emits high-energy electromagnetic radiation, most penetrating, needs thick lead or concrete to stop).
• Nuclear fission splits a heavy nucleus (like uranium-235) into lighter nuclei, releasing energy — the principle behind nuclear power plants and the atomic bomb. Nuclear fusion combines light nuclei (like hydrogen isotopes) into a heavier one, releasing even more energy per reaction — the process that powers the Sun and all stars, and the (still experimental, for controlled power generation) hydrogen bomb.
• Key Indian physics/nuclear institutions: Bhabha Atomic Research Centre (BARC, Mumbai) — nuclear research; Tata Institute of Fundamental Research (TIFR, Mumbai) — fundamental physics research, founded by Homi Bhabha; Indian Institute of Astrophysics (Bengaluru); Physical Research Laboratory (PRL, Ahmedabad) — space and atmospheric sciences, founded by Vikram Sarabhai.
• Semiconductors and lasers are two "applied modern physics" one-liners worth knowing: a semiconductor (like silicon) conducts electricity better than an insulator but worse than a conductor, and its conductivity can be finely tuned — the basis of all modern electronics; a laser produces light that is coherent (all waves in phase) and monochromatic (single wavelength), unlike ordinary light sources. (See the dedicated Semiconductors and Electronics section above for a fuller treatment.)

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