CUCET Study Hub

Everything you need, explained simply

📅 Exam: 30 May 2025

1. Work, Energy & Power

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What is Work?

Imagine pushing a box. Work is done only when the box actually moves. Push a wall and it doesn't move? Zero work done!

W = F × s × cos(θ)

F = force, s = distance moved, θ = angle between force and motion direction. If you push straight ahead → θ=0° → cos(0°)=1 → W = F×s

Kinetic Energy (energy of motion)

A fast cricket ball has more energy than a slow one. Mass and speed both matter.

KE = ½ × m × v²

Potential Energy (stored energy)

A ball held up high has PE. Drop it → PE converts to KE.

PE = m × g × h

g = 10 m/s², h = height from ground

Power

Same work done in less time = more power. Sports car is more powerful than a truck.

P = W / t = F × v

Unit = Watt (W). 1 Horsepower = 746 W

⚡ Remember: PE + KE = constant (if no friction). Energy is always conserved!

2. Momentum & Collisions

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What is Momentum?

A fast cricket ball hurts more than a slow one — that "punch" is momentum. Depends on both mass and speed.

p = m × v

Conservation of Momentum

When two objects collide, total momentum before = total momentum after. Nobody creates or destroys momentum.

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Types of Collisions

TypeKE conserved?Momentum conserved?
Elastic✅ Yes✅ Yes
Inelastic❌ No✅ Yes
Perfectly inelastic (stick together)❌ No✅ Yes
⚡ Momentum is ALWAYS conserved. KE is only conserved in elastic collisions.

3. Current Electricity

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Ohm's Law

Think of a water pipe: Voltage = water pressure, Current = water flow, Resistance = pipe thickness. More resistance → less current.

V = I × R

V = Volts, I = Amperes, R = Ohms (Ω)

Series vs Parallel

Series: R_total = R₁ + R₂ + R₃
Parallel: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃

Series = resistance adds up = less current. Parallel = more paths = more current.

Power in Circuits

P = V×I = I²R = V²/R
⚡ Metals: resistance increases with temp. Semiconductors: resistance DECREASES with temp.

4. Rotational Motion

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Torque

Torque is rotational force. Opening a door — push near the hinge = less torque. Push at the edge = more torque.

τ = r × F

Moment of Inertia

Rotational mass — more spread-out mass = harder to spin.

ShapeMoment of Inertia
Ringmr²
Disc½mr²
Solid Sphere2/5 mr²
Rod (about center)1/12 mL²
⚡ Ice skater pulls arms in → moment of inertia decreases → spins faster. Angular momentum (L=Iω) is conserved!

5. Waves

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Basic Wave Formula

v = f × λ

v = wave speed, f = frequency (Hz), λ = wavelength (m)

Standing Waves

Node = point that never moves (zero displacement). Antinode = point that moves the most (maximum displacement).

Node to antinode = λ/4   |   Node to node = λ/2

Sound Facts

Sound = longitudinal wave. Speed in air ≈ 340 m/s at room temperature. Speed increases with temperature.

⚡ Doppler effect: ambulance coming toward you → pitch sounds higher. Going away → pitch sounds lower.

6. Thermodynamics

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First Law

Energy can't be created or destroyed. Heat given to gas = increase in internal energy + work done by gas.

ΔU = Q - W

Types of Processes

ProcessWhat stays constant
IsothermalTemperature (T)
AdiabaticNo heat exchange (Q = 0)
IsochoricVolume (V)
IsobaricPressure (P)

Carnot Engine Efficiency

Most efficient engine possible. Uses two temperatures (always in Kelvin).

η = 1 - (T₂ / T₁)
⚡ Degrees of freedom: monoatomic gas = 3, diatomic = 5. Internal energy = (f/2) nRT

7. Modern Physics & Semiconductors

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Photoelectric Effect

Shine light on a metal → electrons come out. Only works above a minimum frequency. More intensity = more electrons, but higher frequency = more energetic electrons.

E = h × f = hc / λ

h = Planck's constant = 6.63 × 10⁻³⁴ Js

Radioactivity

TypeWhat is itPenetration
Alpha (α)Helium nucleusLeast (stopped by paper)
Beta (β)ElectronMedium
Gamma (γ)EM waveMost (needs lead to stop)

Semiconductors

n-type = doped with pentavalent element (extra electrons). p-type = doped with trivalent element (holes). p-n junction = diode = current flows only one way.

⚡ Forward biased diode = conducts. Reverse biased = doesn't conduct.

1. Periodic Trends

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Atomic Radius

Size of atom. Goes LEFT → bigger (more electrons). Goes DOWN → bigger (more shells).

Left→Right: DECREASES  |  Top→Bottom: INCREASES

Ionization Energy

Energy needed to remove an electron. Opposite trend to atomic radius.

Left→Right: INCREASES  |  Top→Bottom: DECREASES

Electronegativity

How strongly an atom pulls shared electrons toward itself. Fluorine = highest in the entire table.

Left→Right: INCREASES  |  Top→Bottom: DECREASES
🧪 Trick: IE and electronegativity follow the SAME trend. Atomic radius is OPPOSITE to both.

2. Chemical Bonding & VSEPR

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Types of Bonds

Ionic: metal gives electron to non-metal (NaCl). Covalent: both share electrons (H₂O). Metallic: sea of electrons in metals.

VSEPR Theory

Electron pairs repel each other → arrange as far apart as possible → gives molecule its shape.

MoleculeShapeBond Angle
BeCl₂Linear180°
BF₃Trigonal planar120°
CH₄Tetrahedral109.5°
NH₃Pyramidal107°
H₂OBent / V-shape104.5°
🧪 Lone pairs take more space → reduce bond angle. NH₃ has 1 lone pair, H₂O has 2 → H₂O has smallest angle.

3. Solid State

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Frenkel Defect

An ion leaves its spot and squeezes into a gap (interstitial site) within the crystal. Density stays the same. Common in AgCl, AgBr (small cation + large anion).

Schottky Defect

Equal number of cations and anions go missing from the crystal. Density decreases. Common in NaCl, KCl (similar sized ions).

F-Centre (Colour Centre)

An electron gets trapped where an anion is missing. This gives the crystal a colour. Example: NaCl heated in Na vapour → turns yellow.

🧪 Frenkel = ion moves within crystal (density same). Schottky = ions leave crystal (density drops).

4. Thermodynamics & Electrochemistry

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First Law

ΔU = Q - W

ΔH negative = exothermic (releases heat, e.g. burning). ΔH positive = endothermic (absorbs heat, e.g. melting ice).

Electrochemistry Basics

Electrochemical cell: chemical energy → electrical energy. Anode = oxidation (loss of electrons). Cathode = reduction (gain of electrons).

Cell potential = E°cathode - E°anode
🧪 OIL RIG: Oxidation Is Loss, Reduction Is Gain (of electrons). Classic trick — never forget it.

5. Biomolecules & Polymers

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Carbohydrates

Made of C, H, O. Main energy source. Glucose & fructose = monosaccharides. Sucrose & lactose = disaccharides. Starch & cellulose = polysaccharides.

Proteins & Nucleic Acids

Proteins = amino acids joined by peptide bonds. Enzymes are proteins. DNA stores genetic info. RNA helps make proteins.

Polymers

Natural: rubber, silk, cellulose. Synthetic: Nylon (polyamide), PVC, Teflon, Bakelite, Terylene (polyester).

🧪 Nylon = polyamide. Terylene/Dacron = polyester. Both are condensation polymers.

1. Logarithms

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What is log?

log₁₀(100) = 2 means "10 to the power of 2 = 100". Log asks: "what power do I raise the base to, to get this number?"

Key Rules (memorise all 4)

log(a × b) = log a + log b
log(a / b) = log a - log b
log(aⁿ) = n × log a
log(1) = 0   |   log(base itself) = 1
📐 log₁₀(10)=1, log₁₀(100)=2, log₁₀(1000)=3. Easy pattern — just count the zeros!

2. Derivatives

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What is a derivative?

Rate of change. Speed is the derivative of distance. It tells you how fast something is changing at any moment.

Must-Know Formulas

d/dx (xⁿ) = n·xⁿ⁻¹
d/dx (log x) = 1/x
d/dx (sin x) = cos x
d/dx (cos x) = -sin x
d/dx (eˣ) = eˣ
d/dx (constant) = 0
📐 Chain rule: d/dx[f(g(x))] = f'(g(x)) × g'(x). Example: d/dx(sin x²) = cos(x²) × 2x

3. Matrices & Determinants

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What is a Matrix?

A grid of numbers in rows and columns. A 2×2 matrix has 2 rows and 2 columns.

Determinant of 2×2

| a b | | c d | = (a×d) - (b×c)

Cross multiply diagonally and subtract. That's it!

Transpose

Flip rows and columns. Row 1 becomes Column 1, Row 2 becomes Column 2, etc.

📐 If determinant = 0, the matrix is singular (no inverse exists).

4. AP & GP

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Arithmetic Progression (AP)

Each term differs by a fixed amount (d). Like 2, 5, 8, 11... → d = 3

nth term: aₙ = a + (n-1)d
Sum of n: Sₙ = n/2 × [2a + (n-1)d]

Geometric Progression (GP)

Each term is multiplied by a fixed ratio (r). Like 2, 6, 18, 54... → r = 3

nth term: aₙ = a × rⁿ⁻¹
Sum of n: Sₙ = a(rⁿ - 1) / (r - 1)
📐 AP = adding same number each time. GP = multiplying same number each time.

5. Sets & Functions

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Sets Basics

A set is just a collection. A = {1, 2, 3}. Empty set = {} = φ.

Union (A∪B): all elements in A or B
Intersection (A∩B): elements in BOTH A and B

Functions

Takes an input (x) and gives exactly one output (y). Domain = all valid inputs. Range = all possible outputs.

f(x) = 1/x → domain: all x except 0
f(x) = √x → domain: x ≥ 0
📐 Every function is a relation, but not every relation is a function. One input → exactly ONE output.

1. Synonyms & Antonyms

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High-frequency word pairs

WordSynonymAntonym
AbundantPlentifulScarce
BenevolentKindMalevolent
CandidFrankDeceptive
DiligentHardworkingLazy
EloquentArticulateInarticulate
FrugalThriftyExtravagant
GloomyDismalCheerful
HastyRashCareful
ImpartialUnbiasedBiased
JovialCheerfulGloomy
LenientMildStrict
MeticulousCarefulCareless
📝 Strategy: eliminate obvious opposites first. The answer is the closest in meaning, not the most dramatic.

2. Grammar Essentials

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Tenses Quick Reference

TenseExample
Simple presentHe runs every day
Present continuousHe is running now
Simple pastHe ran yesterday
Present perfectHe has run 5km today
Past perfectHe had run before it rained

Common Errors to Avoid

❌ He don't know → ✅ He doesn't know

❌ More better → ✅ Better

❌ I seen him → ✅ I saw him

❌ Between you and I → ✅ Between you and me

❌ Less people → ✅ Fewer people

📝 After prepositions (between, for, with, to) → always use: me, him, her, us, them (NOT I, he, she, we, they).

3. Reading Comprehension Strategy

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How to approach RC in the exam

1. Read the questions FIRST, then read the passage looking for those answers.

2. The answer is always IN the passage. Don't use outside knowledge.

3. For "main idea" questions → usually in first or last paragraph.

4. For "tone/attitude" questions → look for feeling words (critical, optimistic, sarcastic).

5. Don't spend more than 4–5 minutes on one passage. Move on if stuck.

📝 If two answers seem correct, go with the one that is directly stated in the passage, not just implied.

1. Analogies

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How to solve analogies

Find the relationship in the first pair → apply same relationship to the second pair.

Example: Book : Library :: Painting : ?

→ Books are kept in Libraries → Paintings are kept in Galleries ✅

Common relationship types

TypeExample
Tool : UserScalpel : Surgeon
Part : WholePage : Book
Worker : WorkplaceChef : Kitchen
Animal : SoundLion : Roar
Word : OppositeDay : Night
Cause : EffectRain : Flood
Product : SourceWool : Sheep
🧠 Say the relationship as a sentence. "A is to B as C is to D" — both halves must make the same sentence.

2. Logical Reasoning

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Series Completion

Find the pattern. Could be +2, ×3, alternating, squares, etc.

Example: 2, 6, 12, 20, 30, ? → differences are 4, 6, 8, 10, 12 → answer = 42

Odd One Out

Find what's different — could be category, shape, number pattern.

Example: Apple, Mango, Carrot, Banana → Carrot is a vegetable, rest are fruits.

Blood Relations

Always draw a family tree. Don't try to solve in your head.

Example: "A is B's father's only son" → A is B's father → A is B's father.

🧠 For direction problems: always draw a compass. North=up, South=down, East=right, West=left.