🏛️ Tayarri.com · NUST Entry Test Preparation 2025

NUST Entry Test (NET)
Complete Study Guide

Comprehensive, exam-focused notes covering all five NET sections — Mathematics, Physics, Chemistry, English, and Intelligence. Master every concept tested at NUST with formulas, worked examples, and exam strategy.

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NET 2025 Format: 200 MCQs in 3 hours (180 min). Mathematics 80 Qs, Physics 60 Qs, Chemistry 40 Qs, English 10 Qs, Intelligence 10 Qs. Each correct answer = +1 mark. No negative marking. Score is merit-based for B.Eng admissions across NUST campuses.

Mathematics — 80 Questions (40%)

HIGH

🔢

Math · M1

Algebra & Number Systems

Quadratics, logs, sequences, binomial, partial fractions

Study now →

HIGH

∞

Math · M2

Functions, Limits & Continuity

Domain/range, limit laws, L'Hôpital, continuity

Study now →

HIGH

d/dx

Math · M3

Differentiation & Applications

All rules, maxima/minima, curve sketching, rates

Study now →

HIGH

∫

Math · M4

Integration

Indefinite, definite, techniques, area under curve

Study now →

MED

📐

Math · M5

Trigonometry

All ratios, identities, inverse trig, equations

Study now →

MED

📏

Math · M6

Coordinate Geometry

Lines, circles, conics, distance, tangents

Study now →

MED

⬛

Math · M7

Matrices, Vectors & Probability

Matrix ops, dot/cross products, probability rules

Study now →

Physics — 60 Questions (30%)

HIGH

🚀

Physics · P1

Mechanics

Kinematics, Newton's laws, work-energy, momentum, rotation

Study now →

HIGH

🌊

Physics · P2

Waves, Heat & Thermodynamics

SHM, wave equations, gas laws, thermodynamics laws

Study now →

HIGH

⚡

Physics · P3

Electricity & Magnetism

Coulomb, circuits, capacitors, magnetic force, induction

Study now →

MED

🔬

Physics · P4

Optics & Modern Physics

Reflection, refraction, interference, photoelectric, nuclear

Study now →

Chemistry — 40 Questions (20%)

HIGH

⚗️

Chemistry · C1

Physical Chemistry

Atomic structure, bonding, thermodynamics, equilibrium, kinetics

Study now →

MED

🧪

Chemistry · C2

Inorganic Chemistry

Periodic table, s/p/d-block, acids/bases, electrochemistry

Study now →

MED

🔗

Chemistry · C3

Organic Chemistry

Hydrocarbons, functional groups, reactions, isomerism

Study now →

English & Intelligence — 10+10 Questions (10%)

LOW

📝

English · E1

Grammar, Vocabulary & Writing

Sentence correction, synonyms, antonyms, comprehension

Study now →

LOW

🧠

Intelligence · I1

Analytical Reasoning & IQ

Number series, spatial, logical deduction, analogies

Study now →

NET 2025 — Full Structure at a Glance

📐 Mathematics80 Qs · 40%

⚡ Physics60 Qs · 30%

⚗️ Chemistry40 Qs · 20%

📝 English10 Qs · 5%

🧠 Intelligence10 Qs · 5%

⏱ Total Time200 Qs · 3 Hours

1. Merit Formula

NUST calculates aggregate merit for admission as follows:

Aggregate Formula

Merit = (NET Score × 50%) + (FSc/A-Level × 25%) + (Matric/O-Level × 15%) + (HAT/Interview × 10%)

Note: Exact weights may vary slightly by department. Verify from NUST's official prospectus.

2. Exam Strategy

1

Prioritize Mathematics (40%)

Math carries the most weight. Aim for 70+/80 correct. Strong calculus (differentiation + integration) alone gives you ~20 marks.

2

Secure Physics (30%)

Mechanics and Electromagnetism are highest-yield. Know formulas cold — most Physics MCQs are formula-plugging with one conceptual twist.

3

Attempt All Questions (No Negative Marking!)

NET 2025 has no negative marking. Never leave a blank. If stuck, eliminate 2 options and guess from remaining 2 — statistically gives +0.5 marks.

4

Time Allocation

5

Don't Over-invest in English & Intelligence

Together they are only 10%. Spend 3–4 days max on them. Use freed time to strengthen Math and Physics.

3. Key Subject-wise Tips

📐 Mathematics Tips

Learn all differentiation and integration formulas. Practice quadratic/cubic equations. Know Binomial theorem general term. Series (AP/GP) formulas are frequently tested.

⚡ Physics Tips

Memorize all unit conversions. Draw free body diagrams for mechanics. For EM problems, identify the law (Coulomb, Faraday, Lenz) first, then apply formula.

⚗️ Chemistry Tips

Focus on physical chemistry (equilibrium, kinetics, electrochemistry). Organic reaction mechanisms are frequently tested. Know periodic trends cold.

🧠 Intelligence Tips

For number series: find differences, ratios, or squares. For analogies: identify the relationship type (part-whole, category, function) first before picking answer.

💡 NET Focus

Quadratic equations, logarithms, sequences, binomial theorem and partial fractions together account for ~15–18 marks. Master all formulas and standard techniques cold.

1. Quadratic Equations

Quadratic Formula

x = (−b ± √(b²−4ac)) / 2a

Discriminant (Δ)

Δ = b²−4ac
Δ>0: 2 real roots; Δ=0: equal; Δ<0: complex

Vieta's Formulas

Sum of roots = −b/a
Product of roots = c/a

Sum of Squares

α²+β² = (α+β)²−2αβ

Sum of Cubes

α³+β³ = (α+β)³−3αβ(α+β)

New Equation (roots ×k)

Replace x with x/k in original equation

2. Laws of Logarithms

Product Rule

log_a(xy) = log_a x + log_a y

Quotient Rule

log_a(x/y) = log_a x − log_a y

Power Rule

log_a(xⁿ) = n·log_a x

Change of Base

log_a x = log x / log a = ln x / ln a

Special Values

log_a a=1; log_a 1=0; log_a(aⁿ)=n

Reciprocal

log_a b = 1 / log_b a

3. Sequences & Series

Type	nth Term	Sum of n terms	Key Condition
Arithmetic (AP)	`aₙ = a + (n−1)d`	`Sₙ = n/2 [2a + (n−1)d]`	Common difference d constant
Geometric (GP)	`aₙ = arⁿ⁻¹`	`Sₙ = a(1−rⁿ)/(1−r), r≠1`	Common ratio r constant
GP (Infinite, \|r\|<1)	—	`S∞ = a / (1−r)`	Converges only if \|r\| < 1
Harmonic (HP)	`1/aₙ is AP`	No simple closed form	Reciprocals form AP
Sum of natural numbers	—	`Σn = n(n+1)/2`	—
Sum of squares	—	`Σn² = n(n+1)(2n+1)/6`	—
Sum of cubes	—	`Σn³ = [n(n+1)/2]²`	—

4. Binomial Theorem

General Term

(a + b)ⁿ → Tᵣ₊₁ = ⁿCᵣ · aⁿ⁻ʳ · bʳ

Middle term: if n is even → T_(n/2 +1); if n is odd → T_((n+1)/2) and T_((n+3)/2)

Expansion

(a+b)ⁿ = Σ ⁿCᵣ aⁿ⁻ʳ bʳ (r = 0 to n)

nCr Formula

ⁿCᵣ = n! / [r!(n−r)!]

Pascal's Triangle Row n

Coefficients: ⁿC₀, ⁿC₁, … ⁿCₙ

Worked Example

Find the term independent of x in the expansion of (x − 1/x²)⁹

General term: T_(r+1) = ⁹Cᵣ · x^(9−r) · (−1/x²)^r = ⁹Cᵣ · (−1)^r · x^(9−r−2r)

For term independent of x: 9 − 3r = 0 → r = 3

T₄ = ⁹C₃ · (−1)³ = 84 × (−1) = −84

Answer: −84

5. Partial Fractions (4 Cases)

Denominator Type	Form	Example
Non-repeated linear	`A/(x−a) + B/(x−b)`	(3x+1)/[(x−1)(x+2)]
Repeated linear	`A/(x−a) + B/(x−a)²`	5/[(x+1)(x+1)²]
Irreducible quadratic	`A/(x−a) + (Bx+C)/(x²+bx+c)`	(x+2)/[(x−1)(x²+4)]
Improper fraction	Do polynomial long division first	(x³+1)/(x²−1)

💡 NET Focus

Limits (especially L'Hôpital's rule and standard forms) are heavily tested. Continuity conditions appear as MCQs. Know domain/range rules cold.

1. Standard Limit Results

Polynomial Limit

lim(x→a) f(x) = f(a) [direct sub]

0/0 Form — L'Hôpital

lim f/g = lim f'/g' (if 0/0 or ∞/∞)

sin x / x

lim(x→0) sin x / x = 1

tan x / x

lim(x→0) tan x / x = 1

eˣ − 1 / x

lim(x→0) (eˣ−1)/x = 1

ln(1+x) / x

lim(x→0) ln(1+x)/x = 1

Compound Interest Form

lim(n→∞) (1 + 1/n)ⁿ = e

aⁿ−bⁿ / (a−b) limit

lim(x→a) (xⁿ−aⁿ)/(x−a) = naⁿ⁻¹

2. Continuity & Differentiability

3 Conditions for Continuity at x = a

1. f(a) is defined 2. lim(x→a) f(x) exists 3. lim = f(a)

All three must hold. If any fails, f is discontinuous at x = a.

⚠️ Common Mistake

A function can be continuous but NOT differentiable (e.g., f(x)=|x| at x=0). But differentiability always implies continuity.

3. Domain Rules

Expression	Domain Restriction
√f(x)	f(x) ≥ 0
1/f(x)	f(x) ≠ 0
log f(x)	f(x) > 0
sin⁻¹(f(x))	−1 ≤ f(x) ≤ 1
Polynomial	All real numbers ℝ

💡 NET Focus

Differentiation rules (especially chain rule, product/quotient rules) and maxima/minima problems are NET favorites. Expect 10–14 marks from this topic.

1. Differentiation Rules

Power Rule

d/dx(xⁿ) = nxⁿ⁻¹

Product Rule

d/dx(uv) = u'v + uv'

Quotient Rule

d/dx(u/v) = (u'v − uv') / v²

Chain Rule

d/dx[f(g(x))] = f'(g(x)) · g'(x)

d/dx(eˣ)

eˣ

d/dx(aˣ)

aˣ · ln a

d/dx(ln x)

1/x

d/dx(log_a x)

1 / (x · ln a)

2. Trig & Inverse Trig Derivatives

Function	Derivative	Function	Derivative
sin x	cos x	sin⁻¹ x	1/√(1−x²)
cos x	−sin x	cos⁻¹ x	−1/√(1−x²)
tan x	sec² x	tan⁻¹ x	1/(1+x²)
cot x	−cosec² x	cot⁻¹ x	−1/(1+x²)
sec x	sec x tan x	sec⁻¹ x	1/(x√(x²−1))
cosec x	−cosec x cot x	cosec⁻¹ x	−1/(x√(x²−1))

3. Applications: Maxima & Minima

1

Find f'(x) and set f'(x) = 0

Solve for critical points (where slope is zero)

2

Apply Second Derivative Test

f''(x) < 0 → local maximum; f''(x) > 0 → local minimum; f''(x) = 0 → inconclusive (use first derivative test)

3

Check endpoints for absolute extrema

On a closed interval [a,b], evaluate f at all critical points AND at a and b

Worked Example — Maxima/Minima

Find the maximum and minimum values of f(x) = 2x³ − 9x² + 12x − 4

f'(x) = 6x² − 18x + 12 = 6(x² − 3x + 2) = 6(x−1)(x−2) = 0 → x = 1, 2

f''(x) = 12x − 18

At x=1: f''(1) = −6 < 0 → Local maximum. f(1) = 2−9+12−4 = 1

At x=2: f''(2) = 6 > 0 → Local minimum. f(2) = 16−36+24−4 = 0

Local Max = 1 at x=1 | Local Min = 0 at x=2

💡 NET Focus

Expect 8–12 integration questions. Know standard integrals, substitution, by-parts, and definite integral evaluation. Area between curves appears frequently.

1. Standard Integrals

Power Rule

∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n≠−1)

1/x

∫(1/x) dx = ln|x| + C

eˣ

∫eˣ dx = eˣ + C

aˣ

∫aˣ dx = aˣ/ln a + C

sin x

∫sin x dx = −cos x + C

cos x

∫cos x dx = sin x + C

sec² x

∫sec² x dx = tan x + C

1/√(1−x²)

∫1/√(1−x²) dx = sin⁻¹x + C

1/(1+x²)

∫1/(1+x²) dx = tan⁻¹x + C

2. Techniques of Integration

Integration by Substitution

Let u = g(x) → du = g'(x)dx → rewrite ∫f(g(x))g'(x)dx as ∫f(u)du

Example: ∫2x(x²+1)⁵dx → u=x²+1, du=2x dx → ∫u⁵du = u⁶/6 + C = (x²+1)⁶/6 + C

Integration by Parts

∫u·dv = uv − ∫v·du

Choose u using LIATE: Logarithm, Inverse trig, Algebraic, Trigonometric, Exponential (u = first type found)

3. Definite Integrals & Properties

Fundamental Theorem

∫ₐᵇ f(x)dx = F(b) − F(a)

Reversal of Limits

∫ₐᵇ = −∫ᵦₐ

Additive Property

∫ₐᵇ = ∫ₐᶜ + ∫ᶜᵦ

Even Function (sym. interval)

∫₋ₐᵃ f(x)dx = 2∫₀ᵃ f(x)dx

Odd Function (sym. interval)

∫₋ₐᵃ f(x)dx = 0

4. Area Between Curves

Formula

Area = ∫ₐᵇ |f(x) − g(x)| dx

Where f(x) is the upper curve and g(x) is the lower curve between x=a and x=b. If curves cross, split the integral at intersection points.

💡 NET Focus

Identity proofs, double angle, and solving trig equations are most tested. Know the unit circle, special angle values, and compound angle formulas.

1. Special Angle Values

Angle	0°	30°	45°	60°	90°
sin	0	1/2	1/√2	√3/2	1
cos	1	√3/2	1/√2	1/2	0
tan	0	1/√3	1	√3	∞

2. Key Identities

Pythagorean

sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ

Compound Angle

sin(A±B) = sinA cosB ± cosA sinB
cos(A±B) = cosA cosB ∓ sinA sinB

Double Angle

sin 2A = 2 sinA cosA
cos 2A = cos²A−sin²A = 1−2sin²A
tan 2A = 2tanA/(1−tan²A)

Half Angle

sin²A = (1−cos2A)/2
cos²A = (1+cos2A)/2

Sum to Product

sinA+sinB = 2sin((A+B)/2)cos((A−B)/2)

tan(A±B)

tan(A±B) = (tanA±tanB)/(1∓tanA tanB)

3. General Solutions of Trig Equations

Equation	General Solution
sin θ = sin α	θ = nπ + (−1)ⁿ α, n ∈ ℤ
cos θ = cos α	θ = 2nπ ± α, n ∈ ℤ
tan θ = tan α	θ = nπ + α, n ∈ ℤ

1. Straight Lines

Slope

m = (y₂−y₁)/(x₂−x₁) = −a/b (ax+by+c=0)

Distance

d = √[(x₂−x₁)²+(y₂−y₁)²]

Point to Line

d = |ax₁+by₁+c| / √(a²+b²)

Midpoint

((x₁+x₂)/2, (y₁+y₂)/2)

Parallel Lines

m₁ = m₂

Perpendicular Lines

m₁ × m₂ = −1

2. Circles

Standard Form

(x−h)²+(y−k)² = r²; center (h,k), radius r

General Form

x²+y²+2gx+2fy+c = 0
Center (−g,−f); r = √(g²+f²−c)

Tangent at Point

xx₁+yy₁+g(x+x₁)+f(y+y₁)+c = 0

Length of Tangent

√(x₁²+y₁²+2gx₁+2fy₁+c)

3. Conic Sections

Conic	Standard Equation	Key Features
Parabola	`y² = 4ax`	Focus (a,0), Directrix x=−a, Axis: x-axis
Parabola (vertical)	`x² = 4ay`	Focus (0,a), Directrix y=−a
Ellipse	`x²/a² + y²/b² = 1 (a>b)`	Foci (±ae,0), e = c/a < 1
Hyperbola	`x²/a² − y²/b² = 1`	Foci (±ae,0), e > 1, asymptotes y=±(b/a)x

1. Matrices & Determinants

Determinant (2×2)

|A| = ad − bc for [[a,b],[c,d]]

Inverse (2×2)

A⁻¹ = (1/|A|) · [[d,−b],[−c,a]]

Cramer's Rule

x = Dₓ/D, y = D_y/D, z = D_z/D

Rank

Rank = number of non-zero rows in row-echelon form

2. Vectors

Magnitude

|v| = √(a²+b²+c²)

Dot Product

a·b = |a||b|cosθ = a₁b₁+a₂b₂+a₃b₃

Cross Product Magnitude

|a×b| = |a||b|sinθ

Unit Vector

â = a / |a|

Angle Between Vectors

cosθ = (a·b) / (|a||b|)

Perpendicularity

a·b = 0 ⟺ a ⊥ b

3. Probability

Classical Probability

P(A) = n(A) / n(S)

Addition Rule

P(A∪B) = P(A)+P(B)−P(A∩B)

Conditional Probability

P(A|B) = P(A∩B) / P(B)

Bayes' Theorem

P(A|B) = P(B|A)·P(A) / P(B)

Independent Events

P(A∩B) = P(A)·P(B)

Binomial Distribution

P(X=r) = ⁿCᵣ pʳ qⁿ⁻ʳ; mean=np; σ²=npq

💡 NET Focus

Mechanics is the largest Physics topic (~18–20 marks). Kinematics equations, Newton's laws, and energy conservation problems appear most frequently. Always draw free body diagrams.

1. Kinematics Equations (Constant Acceleration)

v = u + at

Final velocity = initial + (accel × time)

s = ut + ½at²

Displacement from initial position

v² = u² + 2as

Velocity-displacement relationship (no time)

s = (u+v)t/2

Displacement using average velocity

Projectile: Range

R = u²sin2θ / g

Projectile: Max Height

H = u²sin²θ / 2g

2. Newton's Laws & Applications

Law	Statement	Formula
1st (Inertia)	Object stays at rest or constant velocity unless net force acts	ΣF = 0 → a = 0
2nd (Force)	Net force equals mass times acceleration	F = ma
3rd (Action-Reaction)	Every action has equal and opposite reaction	F₁₂ = −F₂₁
Friction	Opposing force at contact surface	f = μN (μ = coefficient)

3. Work, Energy & Power

Work

W = F·d·cosθ (J)

Kinetic Energy

KE = ½mv²

Potential Energy

PE = mgh

Work-Energy Theorem

W_net = ΔKE = KE_f − KE_i

Conservation of Energy

KE₁ + PE₁ = KE₂ + PE₂ (no friction)

Power

P = W/t = Fv (watts)

4. Momentum & Impulse

Momentum

p = mv (kg·m/s)

Impulse

J = FΔt = Δp

Conservation (Collision)

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Elastic Collision

KE conserved AND momentum conserved

5. Circular Motion & Gravitation

Centripetal Force

F_c = mv²/r = mω²r

Angular Velocity

ω = 2π/T = 2πf; v = ωr

Gravitational Force

F = Gm₁m₂/r² (G = 6.67×10⁻¹¹)

Orbital Velocity

v = √(GM/r); T² ∝ r³ (Kepler 3rd)

1. Simple Harmonic Motion (SHM)

Displacement

x = A sin(ωt + φ) or A cos(ωt + φ)

Velocity

v = ω√(A²−x²); max v = Aω at x=0

Acceleration

a = −ω²x (restoring; max at x=±A)

Period of Pendulum

T = 2π√(L/g)

Period of Spring-Mass

T = 2π√(m/k)

2. Wave Properties

Wave Speed

v = fλ

Wave Equation

y = A sin(2π/λ · x − 2πft)

Sound Speed (air, 0°C)

v = 331 m/s; increases 0.6 m/s per °C

Doppler Effect

f' = f·(v ± v_o)/(v ∓ v_s)

+ numerator: observer moves toward source; − denominator: source moves toward observer

3. Thermodynamics

1st Law of Thermodynamics

ΔU = Q − W (internal energy, heat, work)

Ideal Gas Law

PV = nRT (R = 8.314 J/mol·K)

Boyle's Law (const T)

P₁V₁ = P₂V₂

Charles's Law (const P)

V₁/T₁ = V₂/T₂

Gay-Lussac's Law (const V)

P₁/T₁ = P₂/T₂

Carnot Efficiency

η = 1 − T_cold/T_hot

💡 NET Focus

Ohm's law circuits, Kirchhoff's laws, capacitors, and magnetic force problems are very frequent. Know unit conversions: μF, mA, kΩ etc.

1. Electrostatics

Coulomb's Law

F = kq₁q₂/r² (k = 9×10⁹ N·m²/C²)

Electric Field

E = F/q = kq/r² (N/C or V/m)

Potential

V = kq/r (V); W = qV

Capacitance

C = Q/V = ε₀A/d (Farad, F)

Energy in Capacitor

U = ½CV² = Q²/2C

Capacitors in Parallel

C_total = C₁ + C₂ + ...

Capacitors in Series

1/C_total = 1/C₁ + 1/C₂ + ...

2. Current & Circuits

Ohm's Law

V = IR

Resistors in Series

R_total = R₁ + R₂ + ...

Resistors in Parallel

1/R_total = 1/R₁ + 1/R₂ + ...

Power

P = IV = I²R = V²/R (watts)

Kirchhoff's Current Law

ΣI_in = ΣI_out (at a node)

Kirchhoff's Voltage Law

ΣV = 0 around any closed loop

3. Magnetism & Electromagnetic Induction

Magnetic Force on Charge

F = qv × B = qvB sinθ

Force on Current

F = BIL sinθ

Faraday's Law

EMF = −dΦ/dt (Φ = BA cosθ)

Lenz's Law

Induced current opposes the change in flux

1. Optics

Snell's Law

n₁ sinθ₁ = n₂ sinθ₂

Refractive Index

n = c/v = sin i / sin r

Lens Formula

1/v − 1/u = 1/f

Magnification

m = v/u = h_i/h_o

Mirror Formula

1/v + 1/u = 1/f = 2/R

Young's Double Slit

fringe width β = λD/d

2. Modern Physics

Photoelectric Effect

E_photon = hf = hc/λ
KE_max = hf − φ

h = 6.626×10⁻³⁴ J·s; φ = work function

de Broglie Wavelength

λ = h/mv = h/p

Mass-Energy Equivalence

E = mc² (c = 3×10⁸ m/s)

Bohr's Model (H-atom)

E_n = −13.6/n² eV; r_n = 0.529n² Å

Radioactive Decay

N = N₀ e^(−λt); t_½ = 0.693/λ

💡 NET Focus

Physical chemistry (~50% of Chemistry marks) covers atomic structure, bonding, equilibrium, and electrochemistry. Know Kc/Kp expressions and how to apply Le Chatelier's principle.

1. Atomic Structure

Bohr's Radius

rₙ = 0.529 × n² / Z (Angstroms)

Energy Levels

Eₙ = −13.6 × Z² / n² (eV)

Quantum Numbers

n (shell), l (subshell), mₗ (orbital), mₛ (spin)

Max electrons in shell

2n² (n = 1,2,3…)

2. Chemical Bonding

Bond Type	Basis	Property
Ionic	Electron transfer between metals & nonmetals	High mp/bp, soluble in water, conducts when dissolved
Covalent	Shared electron pairs between nonmetals	Lower mp/bp, poor conductor
Metallic	Sea of delocalized electrons	Malleable, ductile, conducts electricity/heat
Hydrogen Bond	Electrostatic (N–H, O–H, F–H)	Explains high bp of H₂O, NH₃, HF
Van der Waals	Temporary dipole–dipole	Weakest; increases with molecular mass

3. Chemical Equilibrium

Equilibrium Constant Kc

Kc = [products]^coeff / [reactants]^coeff

Kp from Kc

Kp = Kc(RT)^Δn (Δn = mol gas products − reactants)

Le Chatelier's Principle

System shifts to counter imposed change (pressure, temp, concentration)

4. Electrochemistry

Faraday's 1st Law

m = ZIt (Z = electrochemical equivalent)

Faraday's 2nd Law

m₁/m₂ = E₁/E₂ (E = equivalent weight)

Cell EMF

E°cell = E°cathode − E°anode

Nernst Equation

E = E° − (RT/nF) ln Q

5. Chemical Kinetics

Rate Law

Rate = k[A]^m[B]^n

Arrhenius Equation

k = Ae^(−Ea/RT)

Half Life (1st order)

t_½ = 0.693/k

1. Periodic Table Trends

Property	Across Period (→)	Down Group (↓)
Atomic Radius	Decreases	Increases
Ionization Energy	Increases	Decreases
Electron Affinity	Increases (generally)	Decreases (generally)
Electronegativity	Increases (most electroneg: F)	Decreases
Metallic Character	Decreases	Increases
Non-metallic Character	Increases	Decreases

2. s-Block & p-Block Elements

Group 1 — Alkali Metals

Very reactive, soft metals. React violently with water: 2Na + 2H₂O → 2NaOH + H₂. Reactivity increases down group. Stored in oil (Na, K).

Group 17 — Halogens

Strong oxidizing agents. Reactivity decreases: F > Cl > Br > I. Form HX acids with hydrogen. F₂ is the most electronegative element.

Group 2 — Alkaline Earth Metals

Less reactive than Group 1. BeO is amphoteric. Mg burns in CO₂. Ca reacts with water slowly. Ba is most reactive in group.

Group 18 — Noble Gases

Unreactive due to full valence shells. Used in lasers, lighting. Xe forms compounds (XeF₂, XeF₄) with highly electronegative elements.

3. Acids, Bases & Salts

pH Definition

pH = −log[H⁺]; pOH = −log[OH⁻]

pH + pOH at 25°C

pH + pOH = 14

Strong Acid (HCl, HNO₃)

Fully ionizes; [H⁺] = initial concentration

Buffer pH (Henderson)

pH = pKa + log([A⁻]/[HA])

💡 NET Focus

Reaction mechanisms, IUPAC naming, and isomerism are most tested in organic chemistry. Know the distinction between substitution, addition, and elimination reactions.

1. Hydrocarbons

Class	General Formula	Bonds	Key Reaction
Alkanes (saturated)	CₙH₂ₙ₊₂	All single (C−C)	Substitution (halogenation, light)
Alkenes	CₙH₂ₙ	One C=C double bond	Addition (H₂, HX, X₂, H₂O)
Alkynes	CₙH₂ₙ₋₂	One C≡C triple bond	Addition (2 steps possible)
Benzene/Arenes	C₆H₆ + side chains	Delocalized π ring	Electrophilic Aromatic Substitution

2. Functional Groups & Key Reactions

Group	Formula	Class	Key Reaction
Hydroxyl	−OH	Alcohol	Oxidation → aldehyde/ketone; esterification with acids
Carbonyl (terminal)	−CHO	Aldehyde	Oxidation → carboxylic acid; Tollens'/Fehling's test
Carbonyl (internal)	C=O	Ketone	Reduction → secondary alcohol; NOT oxidized by Tollens'
Carboxyl	−COOH	Carboxylic Acid	Esterification; forms amides with amines
Amino	−NH₂	Amine	Basicity; reacts with acids; forms amides
Halo	−X (F,Cl,Br,I)	Alkyl Halide	Nucleophilic substitution (SN1/SN2)

3. Isomerism

Structural Isomers

Same molecular formula, different structural connectivity. Types: chain, position, functional group isomerism. e.g. C₄H₁₀ → n-butane and isobutane.

Stereoisomers

Same connectivity, different spatial arrangement. Types: geometric (cis/trans) around C=C; optical isomers (enantiomers) around a chiral center (4 different groups).

💡 NET Focus

10 MCQs on English. Expect: sentence correction (grammar), synonym/antonym vocabulary, one-word substitution, and a short comprehension passage. Scoring all 10 is achievable with 3–4 days of prep.

1. Common Grammar Rules Tested

Rule	Wrong	Correct
Subject-Verb Agreement	"The committee are meeting"	"The committee is meeting"
Pronoun Reference	"Everyone must bring their book" (ambiguous)	"Everyone must bring his/her book"
Parallel Structure	"She likes running, to swim, and dance"	"She likes running, swimming, and dancing"
Modifier Placement	"Running fast, the bus was missed"	"Running fast, she missed the bus"
Tense Consistency	"He walked in and sits down"	"He walked in and sat down"

2. High-Frequency Vocabulary

Aberrant — deviating from normal Benign — gentle, harmless Cacophony — harsh noise Dearth — scarcity, shortage Ephemeral — short-lived Furtive — secretive, stealthy Gregarious — sociable Harbinger — forerunner, sign Impetuous — hasty, reckless Juxtapose — place side by side Laconic — brief, concise Melancholy — sadness Nefarious — wicked, criminal Obstinate — stubborn Pragmatic — practical Querulous — complaining Rancor — bitterness, resentment Sagacious — wise, shrewd Taciturn — silent, reserved Ubiquitous — present everywhere Venerate — to respect deeply Wane — to decrease, diminish

3. One-Word Substitutions

Phrase	One Word
One who can use both hands equally well	Ambidextrous
Fear of heights	Acrophobia
Study of animals	Zoology
Words that sound the same but have different meanings	Homophones
Government by the people	Democracy
One who hates mankind	Misanthrope
Medicine that counteracts poison	Antidote
Speech given at a funeral	Eulogy

💡 NET Focus

10 IQ/reasoning MCQs. Categories: number series, letter series, analogies, odd one out, coding-decoding, and logical deduction. These are fully solvable with pattern recognition — no subject knowledge needed.

1. Number Series — Pattern Types

Pattern Type	Example Series	Rule
Arithmetic (add/sub)	3, 7, 11, 15, ?	+4 each time → 19
Geometric (multiply)	2, 6, 18, 54, ?	×3 each time → 162
Square pattern	1, 4, 9, 16, ?	n² → 25
Cube pattern	1, 8, 27, 64, ?	n³ → 125
Difference of differences	1, 2, 4, 7, 11, ?	Differences: 1,2,3,4,5 → 16
Alternating series	2, 5, 3, 6, 4, 7, ?	Two interleaved APs → 5

2. Analogies — How to Solve

1

Identify the Relationship

Part-whole? Cause-effect? Function? Category? Synonyms? Worker-tool? Action-result?

2

Form a Precise Sentence

e.g., "A pen is a tool used by a writer." Then apply: "A ___ is a tool used by a surgeon." → Scalpel.

3

Test All Options

Don't stop at first plausible answer. The best answer fits the relationship most precisely.

3. Coding-Decoding Tips

Letter Shift

If A=1, B=2 … Z=26, then reverse coding is Z=1, Y=2 etc. Count forward or backward in the alphabet. Always check if the shift is consistent.

Positional Coding

If MANGO = 13,1,14,7,15 (position in alphabet), then same logic applies. Reverse positions: A=26, B=25. Check both forward and reverse mappings.

4. Logical Deduction

Syllogism Method

Step 1: Convert both premises to standard form (All/Some/No A are B).

Step 2: Draw a Venn diagram quickly.

Step 3: Only accept a conclusion that is definitely true in all possible Venn diagrams — if it's only possibly true, it doesn't follow.

Key rule: "Some A are B" does NOT mean "Some B are A" is false — it may be true. But "All A are B" does imply "Some A are B".

Worked Example — Syllogism

All engineers are graduates. Some graduates are doctors. Conclusion: Some engineers are doctors?

Draw: Engineers ⊂ Graduates; Doctors ∩ Graduates ≠ ∅ (partial overlap)

The overlap of Graduates & Doctors may or may not include Engineers — not guaranteed

Conclusion does NOT follow — it is possible but not certain.

NUST Entry Test (NET)Complete Study Guide

NET Format, Marking & Exam Strategy

NET 2025 — Full Structure at a Glance

1. Merit Formula

2. Exam Strategy

3. Key Subject-wise Tips

Algebra & Number Systems

1. Quadratic Equations

2. Laws of Logarithms

3. Sequences & Series

4. Binomial Theorem

5. Partial Fractions (4 Cases)

Functions, Limits & Continuity

1. Standard Limit Results

2. Continuity & Differentiability

3. Domain Rules

Differentiation & Applications

1. Differentiation Rules

2. Trig & Inverse Trig Derivatives

3. Applications: Maxima & Minima

Integration

1. Standard Integrals

2. Techniques of Integration

3. Definite Integrals & Properties

4. Area Between Curves

Trigonometry

1. Special Angle Values

2. Key Identities

3. General Solutions of Trig Equations

Coordinate Geometry

1. Straight Lines

2. Circles

3. Conic Sections

Matrices, Vectors & Probability

1. Matrices & Determinants

2. Vectors

3. Probability

Mechanics

1. Kinematics Equations (Constant Acceleration)

2. Newton's Laws & Applications

3. Work, Energy & Power

4. Momentum & Impulse

5. Circular Motion & Gravitation

Waves, Heat & Thermodynamics

1. Simple Harmonic Motion (SHM)

2. Wave Properties

3. Thermodynamics

Electricity & Magnetism

1. Electrostatics

2. Current & Circuits

3. Magnetism & Electromagnetic Induction

Optics & Modern Physics

1. Optics

2. Modern Physics

Physical Chemistry

1. Atomic Structure

2. Chemical Bonding

3. Chemical Equilibrium

4. Electrochemistry

5. Chemical Kinetics

Inorganic Chemistry

1. Periodic Table Trends

2. s-Block & p-Block Elements

3. Acids, Bases & Salts

Organic Chemistry

1. Hydrocarbons

2. Functional Groups & Key Reactions

3. Isomerism

Grammar, Vocabulary & Writing

1. Common Grammar Rules Tested

2. High-Frequency Vocabulary

3. One-Word Substitutions

Analytical Reasoning & IQ

1. Number Series — Pattern Types

2. Analogies — How to Solve

3. Coding-Decoding Tips

4. Logical Deduction

NUST Entry Test (NET)
Complete Study Guide