Everyday Science, Reasoning & Social Science

Part V · General Awareness · Chapter Nineteen

Everyday Science, Reasoning & Social Science

Expect 14–18 questions from this chapter spanning three domains: everyday physics & chemistry facts (SI units, gas laws, optics, electricity), logical reasoning patterns (series, coding-decoding, analogies, blood relations), and 10th-standard social science (freedom struggle chronology, Indian states + capitals, Constitution basics, economic vocabulary). HP-specific items — Chandrayaan-3 landing, IMD monsoon zones, HP statehood, Shimla capital history — appear reliably.

Read · 90 min
Revise · 25 min
MCQs · 30

Syllabus Coverage

Everyday Physics: SI units, Newton’s laws, energy, heat & temperature, light, sound, electricity, magnetism, atomic & nuclear physics, astronomy & ISRO missions • Everyday Chemistry: periodic table, atomic models, bonds, acids & bases, common chemical compounds, allotropes, polymers • Verbal Reasoning: number & letter series, analogies, coding-decoding, blood relations, direction sense, syllogisms • Non-Verbal & Quantitative Reasoning: pattern completion, mirror images, percentages, ratio, time-work, simple & compound interest • Indian History recap (1857–1947), Indian Geography (states, capitals, climate), Civics & Economic Concepts (Constitution, GDP, inflation, RBI).

19.1 Everyday Physics & Astronomy

Physics underlies nearly every observable natural phenomenon — from the arc of a cricket ball to the glow of a tubelight. For competitive examinations the focus is on understanding principles rather than deriving equations from scratch. Master the seven SI base units, Newton’s three laws, the temperature-scale conversions, Ohm’s law, and the fundamentals of light and sound, and you will handle the bulk of everyday-science questions.

Newton — Principia Mathematica 1687 (laws of motion & gravitation) · Faraday — electromagnetic induction 1831 · Einstein — special relativity / E = mc² 1905 (annus mirabilis) · Rutherford — nuclear model 1911 · Bohr — orbital atomic model 1913 · Aryabhata — value of π, heliocentrism, 499 CE (Aryabhatīya)

19.1.1 SI System of Units

The Système International d’Unités (SI), adopted in 1960, defines seven independent base units from which all other physical units are derived. No two base units measure the same physical quantity; together they span mechanics, electromagnetism, thermodynamics, and photometry.

Scalar vs Vector

A scalar has only magnitude (e.g., mass, temperature, speed, energy). A vector has both magnitude and direction (e.g., velocity, force, acceleration, displacement). Speed is scalar; velocity is its vector counterpart. Work (force · displacement) is a scalar even though both inputs are vectors.

**Table 19.1** SI base units and selected derived units
Quantity	SI Unit	Symbol	Note / How derived
Length	metre	m	Base unit; 1 m = 100 cm
Mass	kilogram	kg	Only base unit with prefix in name
Time	second	s	Base unit; based on Cs-133 hyperfine transition
Electric current	ampere	A	Base unit
Temperature	kelvin	K	Base unit; 0 K = −273.15 °C (absolute zero)
Amount of substance	mole	mol	6.022 × 10²³ entities (Avogadro)
Luminous intensity	candela	cd	Base unit (light)
Derived Units (commonly tested)
Force	newton	N	kg · m / s²
Energy / Work	joule	J	N · m = kg · m² / s²
Power	watt	W	J / s = kg · m² / s³
Pressure	pascal	Pa	N / m²
Frequency	hertz	Hz	cycles / s (s¹)
Voltage	volt	V	J / C (energy per charge)
Resistance	ohm	Ω	V / A
Capacitance	farad	F	C / V
Magnetic flux density	tesla	T	kg / (A · s²)

Mnemonic — SI Base Units

Kindly Make Sure All Things Move Correctly

Kelvin · Metre · Second · Ampere · Temperature (already K, so think: Thermo-mole) · Mole · Candela. Alternatively: “my kilogram second ampere kelvin mole candela” → base quantities: length, mass, time, current, temp, amount, light.

19.1.2 Newton’s Laws of Motion

First law (Inertia): A body continues in its state of rest or uniform motion in a straight line unless acted upon by an external force. Inertia is a property of mass — heavier objects are harder to set in motion or stop.

Second law (F = ma): The net force on a body equals its mass multiplied by the acceleration produced. F is in newtons; m in kg; a in m/s². Weight W = mg where g ≈ 9.8 m/s² near Earth’s surface.

Third law (Action-Reaction): For every action there is an equal and opposite reaction. Rocket propulsion, walking, swimming — all governed by the third law. Note that action and reaction act on different bodies.

Momentum (p = mv) is conserved in every closed system. Impulse = change in momentum = F × t. Free-fall acceleration g ≈ 9.8 m/s² (on Moon g′ ≈ 1.63 m/s², roughly one-sixth of Earth’s).

19.1.3 Energy, Work and Power

**Table 19.2** Energy forms and key equations
Type	Formula	Unit	Example
Kinetic energy (KE)	KE = ½mv²	J	Moving cricket ball
Gravitational PE	PE = mgh	J	Water in a dam
Rest-mass energy	E = mc²	J	Nuclear reactions (Einstein 1905)
Work	W = F · d · cosθ	J	Lifting a box (θ = 0° → W = Fd)
Power	P = W / t = F × v	W	1 HP = 746 W

19.1.4 Heat, Temperature and Thermodynamics

Temperature measures the average kinetic energy of molecules, not the total heat. The three scales used in competitive papers are Celsius (°C), Fahrenheit (°F), and Kelvin (K).

Conversion formulae: K = °C + 273.15; °F = (°C × 9/5) + 32. Key benchmarks: ice melts at 0 °C = 32 °F = 273.15 K; water boils at 100 °C = 212 °F = 373.15 K. Both scales coincide at −40° (−40 °C = −40 °F).

Easy to confuse — Latent Heat vs Specific Heat Capacity

Latent Heat

Heat absorbed or released during a phase change at constant temperature. Latent heat of fusion (ice → water) = 80 cal/g (334 J/g). Latent heat of vaporisation (water → steam) = 540 cal/g (2260 J/g). Temperature does not change during the phase transition.

Specific Heat Capacity

Heat needed to raise 1 g of a substance by 1 °C, with no phase change. Water: 1 cal/g·°C = 4.2 J/g·°C (highest among common liquids — explains coastal climate moderation). Iron: ~0.11 cal/g·°C. Gold: ~0.03 cal/g·°C.

Heat transfer modes: Conduction (solids, molecule-to-molecule; metals best conductors), Convection (fluids, bulk movement; sea breeze, HP valley winds), Radiation (no medium needed; sun warms Earth through space; all bodies emit infrared radiation). Thermos flask eliminates all three: vacuum stops conduction + convection; silvered walls reflect radiation.

Easy to confuse — Boyle’s Law vs Charles’ Law vs Gay-Lussac’s Law

Boyle’s (1662)

At constant temperature: PV = constant. Pressure and volume are inversely proportional. Squeeze a syringe → P rises, V falls.

Charles’ (1787)

At constant pressure: V/T = constant. Volume and temperature are directly proportional. Hot-air balloon rises because heated air expands → density drops.

19.1.5 Light — Reflection, Refraction and Beyond

Light travels at c = 3 × 10&sup8; m/s in vacuum. It slows in denser media (water, glass); the ratio c/v is the refractive index (n). Light is an electromagnetic wave (transverse; no medium needed). The visible spectrum runs from violet (~400 nm) to red (~700 nm). VIBGYOR = Violet, Indigo, Blue, Green, Yellow, Orange, Red.

Easy to confuse — Reflection vs Refraction

Reflection

Light bounces back at the same angle. Angle of incidence = angle of reflection (measured from normal). Plane mirror, concave mirror (converging → real images), convex mirror (diverging → virtual, erect, diminished — used in rear-view mirrors).

Refraction

Light bends when crossing a medium of different density. Snell’s law: n₁ sinθ₁ = n₂ sinθ₂. Total internal reflection (TIR) occurs when light goes from dense to rare medium beyond the critical angle — basis of optical fibres and mirages. Prism disperses white light into spectrum; rainbow is atmospheric dispersion + internal reflection.

Lenses: Convex (converging) lens forms real inverted image when object is beyond focus (camera, projector, eye); forms virtual erect magnified image when object is within focus (magnifying glass). Concave (diverging) lens always forms virtual, erect, diminished image (used to correct myopia).

Eye defects and corrections: Myopia (short-sightedness) — image forms in front of retina; corrected by concave lens. Hypermetropia (long-sightedness) — image behind retina; corrected by convex lens. Presbyopia — age-related loss of near vision; corrected by bifocals. Astigmatism — irregular cornea curvature; corrected by cylindrical lens.

19.1.6 Sound

Sound is a longitudinal mechanical wave — particles vibrate along the direction of propagation. It requires a medium (cannot travel in vacuum). Speed in air at 20 °C ≈ 343 m/s; in water ≈ 1,500 m/s; in steel ≈ 5,100 m/s (solid > liquid > gas). Audible range for humans: 20 Hz – 20,000 Hz. Infrasound < 20 Hz (elephants, whales). Ultrasound > 20,000 Hz (bats, dolphins; medical sonography; sonar). Doppler effect: apparent frequency increases as source approaches, decreases as it recedes (ambulance siren pitch). Sonic boom when an aircraft exceeds speed of sound (Mach 1).

19.1.7 Electricity

Ohm’s Law: V = IR (voltage = current × resistance). Power P = VI = I²R = V²/R. SI unit: resistance in ohms (Ω), current in amperes (A), voltage in volts (V), power in watts (W).

Easy to confuse — AC vs DC

Alternating Current (AC)

Direction of current reverses periodically. Frequency: 50 Hz in India (50 cycles/s), 60 Hz in USA/Canada. Used in household supply because it can be stepped up/down by transformers, reducing transmission losses. RMS voltage in India: 230 V.

Direct Current (DC)

Current flows in one direction only. Used in batteries, electronics, mobile devices. Cannot be stepped up by ordinary transformers. Converted from AC by a rectifier. Edison promoted DC; Tesla/Westinghouse promoted AC (the “War of Currents” 1880s — AC won).

Circuits: In a series circuit, resistance adds (R_total = R₁+R₂+…); single break interrupts all. In a parallel circuit, 1/R_total = 1/R₁+1/R₂+…; total resistance is always less than the smallest individual resistor; household wiring uses parallel circuits so each appliance gets 230 V independently. Faraday’s law of electromagnetic induction: a changing magnetic flux induces an EMF — basis of generators, alternators, transformers. Transformer steps voltage up/down: V₁/V₂ = N₁/N₂ (N = number of turns).

Easy to confuse — LDR vs LED

LDR (Light Dependent Resistor)

Resistance decreases with increasing light intensity (made of semiconductor like CdS). Used in automatic street-lights (off during day, on at night) and alarm systems.

LED (Light Emitting Diode)

A p-n junction semiconductor that emits light when forward biased. Efficient, durable, no filament. OLED adds organic layer for flexible displays. Used in bulbs, screens, indicator lights.

19.1.8 Atomic and Nuclear Physics

Three types of radiation: α (alpha) particles = helium nuclei (2p + 2n); low penetration (stopped by paper); high ionisation. β (beta) = fast electrons; moderate penetration (stopped by thin metal). γ (gamma) = high-energy electromagnetic photons; highest penetration (needs lead/thick concrete to stop); lowest ionisation per unit path. Half-life is the time taken for half of a radioactive sample to decay — independent of temperature, pressure, or chemical state. Radioactive isotopes with uses: ¹⁴C (radiocarbon dating of organic materials up to ~50,000 years; basis: 5,730-year half-life), ¹³¹I (thyroid cancer therapy; half-life 8 days), ⁶⁰Co (cancer radiotherapy; gamma rays). Nuclear fission: heavy nucleus (²³⁵U or ²³⁹Pu) splits releasing enormous energy — basis of atomic bomb and nuclear reactors. Nuclear fusion: light nuclei (H isotopes) fuse — powers the Sun and H-bomb; being researched in ITER (toroidal fusion reactor).

19.1.9 Astronomy and the Solar System

Fig. 19.1 Schematic solar system (not to scale). The asteroid belt lies between Mars and Jupiter. Pluto was reclassified as a dwarf planet in 2006 by the IAU. Jupiter is the largest planet and has the most moons (95 confirmed). Venus is the hottest planet despite not being closest to the Sun — due to runaway CO₂ greenhouse effect. Earth is the densest planet.

Mnemonic — Planet Order

My Very Educated Mother Just Served Us Nachos

Mercury · Venus · Earth · Mars · Jupiter · Saturn · Uranus · Neptune. Pluto is no longer a planet (demoted 2006, IAU) — so “Nachos” ends the sequence.

19.1.10 India’s Space Programme (ISRO)

**Table 19.3** Key ISRO missions
Mission	Year	Achievement
Aryabhata (1st satellite)	1975	India’s 1st satellite; launched by USSR
INSAT-1B	1983	1st operational communication + met satellite
IRS-1A	1988	1st Indian remote-sensing satellite
PSLV-C1	1994	PSLV operational; workhorse launch vehicle
Chandrayaan-1	2008	Confirmed water molecules on Moon (M3 instrument)
Mangalyaan / MOM	2014	Mars orbit in 1st attempt; cheapest Mars mission ever
Chandrayaan-2	2019	Orbiter operational; Vikram lander crashed
Chandrayaan-3	2023	Soft landing on lunar south pole; 1st country to do so; Pragyan rover deployed
Aditya-L1	2023	India’s 1st solar observatory; Lagrange-1 point

HP Angle: ISRO was founded in 1969 by Vikram Sarabhai (father of India’s space programme) with headquarters in Bengaluru. The Chandrayaan-3 landing site (Shiv Shakti Point, 23 Aug 2023) is India’s proudest space milestone — a near-certain competitive-exam question. Gaganyaan (India’s 1st human spaceflight programme) is under development. GSLV-Mk III (now LVM3) is India’s heaviest operational rocket (GSAT-29, OneWeb launches).

19.2 Everyday Chemistry & Materials

Chemistry is the study of matter, its properties, and the changes it undergoes. For everyday-science questions the most tested topics are: the periodic table structure, key elements and their properties, atomic models (in historical order), acids and bases, and a short list of common chemical compounds with practical uses.

Dalton — atomic theory 1808 (indivisible atoms) · Mendeleev — periodic table 1869 (ordered by atomic mass; predicted missing elements) · Thomson — electron / plum-pudding 1897 · Rutherford — gold-foil / nuclear model 1911 · Moseley — modern table by atomic number 1913 · Bohr — orbital model 1913 · Marie Curie — radium & polonium discovered 1898 (Nobel ×2: Physics 1903, Chemistry 1911) · Schrödinger — wave-mechanical model 1926

19.2.1 The Periodic Table

The modern periodic table has 118 elements arranged in order of increasing atomic number (number of protons). There are 18 groups (vertical columns, same valence electrons) and 7 periods (horizontal rows, same number of electron shells). Mendeleev’s original 1869 table ordered by atomic mass, leaving gaps for undiscovered elements; Moseley’s 1913 revision ordered by atomic number — still the basis today.

Fig. 19.2 Simplified periodic table showing key elements with atomic numbers. Group 18 (noble gases, shaded green) are chemically inert. The d-block spans Groups 3–12 and contains all economically important metals (iron, copper, gold, etc.). Radioactive elements with atomic numbers ≥84 (Po) are unstable. Lanthanides (57–71) and actinides (89–103) form the f-block, shown separately at the bottom in the full table.

19.2.2 Acids, Bases and pH

pH is a measure of hydrogen-ion concentration: pH = −log[H³O¹]. Scale runs 0–14. pH < 7 = acidic; pH = 7 = neutral (pure water at 25 °C); pH > 7 = basic (alkaline). Every unit change = 10× change in [H³O¹].

Easy to confuse — Strong Acid vs Weak Acid

Strong Acid

Completely ionises in water. HCl, H₂SO₄, HNO₃. Very low pH (<1). HCl + H₂O → H₃O¹ + Cl¹. Concentrated H₂SO₄ used in car batteries, HNO₃ in fertilisers + explosives manufacturing.

Weak Acid

Partially ionises; equilibrium mixture. Acetic acid (CH₃COOH — vinegar; pH ~3), citric acid (lemons; pH ~2.2), carbonic acid (H₂CO₃ in soda water), lactic acid (curd). Formic acid (ant sting, pH ~3.4). The lower the pKa, the stronger.

Indicators: Litmus (natural dye from lichen Rocella tinctoria) turns red in acid and blue in base. Phenolphthalein: colourless in acid, pink/violet in base. Methyl orange: red in acid, yellow/orange in base. Universal indicator shows a range of colours matching the pH.

Easy to confuse — Oxidation vs Reduction (OIL RIG)

Oxidation

Loss of electrons (or gain of oxygen / loss of hydrogen). Fe → Fe²¹ + 2e¹. The substance that loses electrons is the reducing agent. Rusting of iron is slow oxidation; burning is fast oxidation (combustion).

Reduction

Gain of electrons (or gain of hydrogen / loss of oxygen). Cu²¹ + 2e¹ → Cu. The substance that gains electrons is the oxidising agent. Extraction of metals from ores (e.g., Fe from Fe₂O₃ using CO) is reduction. OIL RIG: Oxidation Is Loss, Reduction Is Gain.

Easy to confuse — Cation vs Anion

Cation

Positively charged ion (atom has lost electrons). Na¹, Ca²¹, Fe³¹, NH₄¹. Attracted to cathode (negative electrode) in electrolysis. Metals generally form cations.

Anion

Negatively charged ion (atom has gained electrons). Cl¹, O²¹, SO₄²¹, NO₃¹. Attracted to anode (positive electrode) in electrolysis. Non-metals generally form anions. HCl in water: H¹ (cation) + Cl¹ (anion).

19.2.3 Common Chemical Compounds and Their Uses

**Table 19.4** Everyday chemical compounds — names, formulae, and uses
Common Name	Chemical Name	Formula	Key Use / Fact
Baking soda	Sodium hydrogen carbonate	NaHCO₃	Antacid; baking (releases CO₂); fire extinguisher
Washing soda	Sodium carbonate decahydrate	Na₂CO₃·10H₂O	Laundry softener; glass manufacture
Plaster of Paris	Calcium sulphate hemihydrate	CaSO₄·½H₂O	Setting broken bones; wall finishing; sculpting
Gypsum	Calcium sulphate dihydrate	CaSO₄·2H₂O	Making PoP (heated to 120–130°C); fertiliser
Bleaching powder	Calcium hypochlorite + CaCl₂	Ca(OCl)Cl	Disinfection of water; bleaching cotton; oxidiser
Quick lime	Calcium oxide	CaO	Construction; neutralising acidic soil; manufacturing glass
Slaked lime	Calcium hydroxide	Ca(OH)₂	Mortar; whitewash; water treatment
Marble / chalk	Calcium carbonate	CaCO₃	Building stone; acid neutraliser; making lime
Table salt	Sodium chloride	NaCl	Food; electrolysis to make Cl₂ + NaOH
Epsom salt	Magnesium sulphate	MgSO₄·7H₂O	Laxative; bath salts; agriculture (Mg fertiliser)
Blue vitriol	Copper sulphate pentahydrate	CuSO₄·5H₂O	Fungicide (Bordeaux mixture); electroplating; algaecide
Green vitriol	Ferrous sulphate heptahydrate	FeSO₄·7H₂O	Iron tonic; ink manufacture; water purification
White vitriol	Zinc sulphate heptahydrate	ZnSO₄·7H₂O	Eye drops; wood preservation; galvanising
Vinegar	Dilute acetic acid	CH₃COOH (~5%)	Food preservative; condiment
Baking powder	NaHCO₃ + tartaric acid	Mixture	Leavening agent in baking (releases CO₂ when wet + hot)

19.2.4 Allotropes and Polymers

Allotropes are different structural forms of the same element. Carbon has the richest allotropy:

Diamond — sp³ hybridisation, tetrahedral network; hardest natural substance (10 on Mohs); electrical insulator (no free electrons); thermal conductor.
Graphite — sp² layers (hexagonal sheets) held by van der Waals forces; only non-metallic conductor of electricity (delocalised π electrons); lubricant; pencil “lead.”
Buckminsterfullerene (C₆₀) — soccer-ball shaped cage; discovered 1985 (Kroto, Curl, Smalley; Nobel 1996); used in drug delivery research.
Graphene — single atomic sheet of graphite; strongest material known; ultra-thin; excellent conductor.
Carbon nanotubes (CNTs) — rolled graphene cylinders; extremely high tensile strength.

Sulphur allotropes: Rhombic sulphur (stable below 96 °C) and monoclinic sulphur (stable 96–119 °C). Both convert to amorphous (plastic) sulphur on sudden cooling.

Phosphorus allotropes: White phosphorus (P₄; toxic, luminescent, very reactive; stored under water), red phosphorus (polymer chains; matchboxes), black phosphorus (stable, layered; semiconductor).

Polymers: Large molecules made of repeating monomer units. Natural polymers include cellulose (glucose monomers, plant cell walls), starch (glucose; energy storage), proteins (amino acids), natural rubber (isoprene). Synthetic polymers: polythene (ethylene monomer; packaging), PVC (vinyl chloride; pipes, cables), nylon (polyamide; fibres), polyester (PET; bottles, fabrics), Bakelite (phenol + formaldehyde; first fully synthetic plastic, 1907, Leo Baekeland; electrical fittings), Teflon (PTFE; non-stick coating).

Exam Tip: The vitriol colours are a classic MCQ: blue = copper sulphate; green = ferrous sulphate; white = zinc sulphate. Baking soda (NaHCO₃) and baking powder are often confused — baking powder is a mixture containing NaHCO₃ + an acid (cream of tartar / tartaric acid) + a filler; both produce CO₂ to leaven dough. Plaster of Paris loses water on setting (CaSO₄·½H₂O + &frac32;H₂O → CaSO₄·2H₂O = gypsum) — the reverse of how PoP is made from gypsum.

19.3 Verbal Reasoning Patterns

Verbal reasoning questions test your ability to identify patterns in sequences of numbers or letters, decode relationships between words, and draw logical conclusions from given statements. These questions appear in virtually every competitive examination from state TET/TGT/PGT to central CTET and SSC, and always account for 10–15 marks. Master the six core patterns and you will solve 80% of them in under 30 seconds each.

19.3.1 Number and Letter Series

A series question presents a sequence with a rule and asks you to find the missing or next term. Common underlying rules:

Arithmetic series — constant difference: 3, 7, 11, 15, ? → +4 each time → 19.
Geometric series — constant ratio: 2, 6, 18, 54, ? → ×3 each time → 162.
Squares / cubes — 1, 4, 9, 16, 25, ? → 1²,2²,3²… → 36. Or 1, 8, 27, 64, ? → 1³,2³… → 125.
Fibonacci — each term = sum of previous two: 1, 1, 2, 3, 5, 8, 13, ? → 21.
Prime number series — 2, 3, 5, 7, 11, 13, ? → 17.
Mixed-operation — alternating +/×: 2, 4, 3, 9, 4, 16, ? → pattern: even positions = previous × n, odd positions = +1 → 5.
Letter series — A, C, E, G, ? → every other letter → I. Or coded by position: A=1, B=2 etc.

Worked Example — Series with Two Interleaved Rules

Find the missing term: 4, 9, 25, 49, 121, 169, ?

Strategy: Check if these are perfect squares: 4=2², 9=3², 25=5², 49=7², 121=11², 169=13². The bases (2, 3, 5, 7, 11, 13) are consecutive prime numbers. Next prime = 17. Answer: 17² = 289.

19.3.2 Analogies

An analogy expresses a relationship: A : B :: C : ? (A is to B as C is to D). Identify the relationship type first, then apply it.

**Table 19.5** Types of analogy relationships
Relationship Type	Example	Answer
Animal → Young one	Cat : Kitten :: Cow : ?	Calf
Animal → Sound	Dog : Bark :: Cow : ?	Moo / Low
Tool → Worker	Scalpel : Surgeon :: Chisel : ?	Carpenter
Product → Source	Silk : Silkworm :: Wool : ?	Sheep
Part → Whole	Chapter : Book :: Scene : ?	Play / Film
Word → Antonym	Day : Night :: Joy : ?	Sorrow
Number → Square	4 : 16 :: 7 : ?	49
Country → Currency	India : Rupee :: Japan : ?	Yen
Planet → Satellite	Earth : Moon :: Mars : ?	Phobos (or Deimos)
Science → Study	Entomology : Insects :: Mycology : ?	Fungi

19.3.3 Coding-Decoding

A code substitutes letters, numbers, or symbols for words or letters according to a fixed rule. Common patterns:

Letter shift: If APPLE = DSSOH (each letter +3), then MANGO = ? → Each letter +3: M+3=P, A+3=D, N+3=Q, G+3=J, O+3=R → PDQJR.
Reverse alphabet: A=Z, B=Y, C=X… (mirror substitution). COLD = XLOW.
Number coding: If CAT = 3120 (C=3, A=1, T=20 positional values), then DOG = ? → D=4, O=15, G=7 → 41507.
Symbol substitution: ☆ = A, ♣ = B, ♥ = C … Each symbol represents a fixed letter.
Key-word based: In a coded language, “GIVEN” = “HIWFO” (each letter +1); decode the rule then apply.

Worked Example — Coding-Decoding

In a certain code: CLOUD = DNPWE. How is STORM coded?

Strategy: Check letter shifts: C+1=D, L+2=N, O+1=P, U+1=V?→ wait, U→W means +2. D→E means +1. Pattern alternates: odd position +1, even position +2? C(+1)=D; L(+2)=N; O(+1)=P; U(+2)=W; D(+1)=E → Yes. Apply to STORM: S(+1)=T; T(+2)=V; O(+1)=P; R(+2)=T; M(+1)=N → TVPTN.

19.3.4 Blood Relations

Draw a family tree for every blood-relation problem — it eliminates ambiguity. Standard conventions: boxes for males, circles for females, horizontal lines for marriage, vertical lines for parent–child.

Worked Example — Blood Relation

“Pointing to a man in a photograph, Meena says: ‘His mother is the only daughter of my father.’ How is Meena related to the man?”

Strategy: “Only daughter of my father” = Meena herself. So the man’s mother = Meena. Therefore Meena is the man’s mother.

19.3.5 Direction Sense

Use a compass rose (N/S/E/W) and track each turn. Left turn = anti-clockwise; right turn = clockwise. After completing the route, calculate displacement using the Pythagoras theorem if the path forms a right angle.

Worked Example — Direction Sense

Ravi walks 6 km north, then 8 km east. How far is he from his starting point, and in which direction?

Strategy: Two legs at right angles → distance = √(6² + 8²) = √(36+64) = √100 = 10 km. Direction: started south, walked north then east → he is now north-east of origin. Final direction from start = North-East.

19.3.6 Syllogisms and Logical Deduction

Syllogism is a form of deductive reasoning: two or more statements (premises) lead to a conclusion. The key rule is that conclusions must follow necessarily from the premises — never from assumed general knowledge. Use Venn diagrams to test validity.

Example: Statements: (1) All teachers are graduates. (2) Some graduates are scientists. Conclusions: I. Some teachers are scientists. II. Some scientists are teachers. III. All graduates are teachers. — None of these necessarily follows: statement 2 only says “some” graduates are scientists — they need not overlap with teachers at all. Neither I, II, nor III follows (assuming minimum possible overlap).

Easy to confuse — Deductive vs Inductive Reasoning

Deduction

Goes from general to specific. Conclusion is certain IF premises are true. “All mammals breathe air. A dolphin is a mammal. Therefore a dolphin breathes air.” Syllogisms are deductive. Used in mathematics and formal logic.

Induction

Goes from specific to general. Conclusion is probabilistic, not certain. “The sun rose every day for thousands of years, therefore it will rise tomorrow.” Science uses induction to build theories from observations. Inductive conclusions can be disproved by a single counter-example.

Easy to confuse — Fact vs Opinion (Statement-type questions)

Fact

An objective, verifiable statement. “The Ganges flows into the Bay of Bengal.” It can be confirmed or denied by evidence. In MCQs, a statement is factual if it can be definitively proved true or false.

Opinion

A subjective belief, judgment or preference. “Classical music is more soothing than pop.” Cannot be objectively proved. In analytical-reasoning questions, statements marked “assumptions” are often opinions or unstated presumptions.

19.4 Non-Verbal & Quantitative Reasoning

Non-verbal reasoning tests spatial and visual intelligence independently of language — pattern completion, mirror/water images, paper folding, embedded figures, cube nets, and figure series. Quantitative reasoning covers arithmetic applications: percentages, ratio and proportion, time-work, time-distance, and interest calculations. Together these make up approximately 20–25% of General Intelligence sections in state-level exams.

19.4.1 Non-Verbal Reasoning Types

Pattern completion: A 3×3 or 4×4 grid with one cell missing; find the cell that completes the pattern using row/column rules.
Mirror image: When a figure is placed in front of a vertical mirror, left and right are swapped; top and bottom remain the same. Clock at 3:00 has mirror image showing 9:00.
Water image: When a figure is reflected in a horizontal mirror (water surface), top and bottom are swapped; left and right remain the same.
Paper folding and cutting: Imagine folding a square sheet, punching a hole, then unfolding. The hole appears symmetrically at all folded layers.
Cube counting: Given a figure made of unit cubes, count total cubes (including hidden ones). Count by layer: top, middle, bottom.
Embedded figures: Find a smaller figure hidden within a complex larger figure.
Figure series: Like number series but with shapes; identify the rule governing changes in size, rotation, shading, or number of sides, then predict the next figure.

Fig. 19.3 Three sample reasoning-pattern diagrams: (A) geometric number series with constant ratio ×3; (B) analogy showing animal–young-one relationship; (C) figure series with 90° clockwise rotation rule. Identifying the underlying rule is the key skill — speed comes from pattern recognition, not calculation.

19.4.2 Quantitative Reasoning — Core Formulae

**Table 19.6** Quantitative reasoning formulae at a glance
Topic	Formula / Rule	Quick Example
Percentage	% = (part/whole) × 100	40 out of 200 = 20%
% change	[(New − Old)/Old] × 100	80 → 100 = +25%
Ratio & Proportion	a:b = c:d → ad = bc (cross-multiply)	2:5 = 8:? → ?=20
Average	Sum / Number of items	Avg of 3,5,7 = 15/3 = 5
Simple Interest	SI = P × R × T / 100; Amount = P+SI	P=1000, R=5%, T=2yr → SI=100
Compound Interest	A = P(1 + R/100)^T; CI = A − P	P=1000, R=10%, T=2 → A=1210; CI=210
Time & Work	If A does work in n days, A’s 1-day work = 1/n. Combined: 1/n₁ + 1/n₂	A:8d, B:12d → together: 1/8+1/12=5/24 → 24/5=4.8 days
Time & Distance	D = S × T; Avg speed (two equal dist.) = 2S₁S₂/(S₁+S₂)	60 km at 30 km/h = 2 hours
Profit & Loss	Profit % = (P/CP)×100; SP = CP(100+P%)/100	CP=200, SP=250 → Profit%=25%
Age problems	Let present age = x; set up equation from ratio/difference conditions	A is twice B now; in 5 yr A is 1.5×B → A=15, B=10 (check)

Worked Example — Time & Work (A-R type)

Assertion (A): If A can do a job in 10 days and B in 15 days, they will complete it together in 6 days.
Reason (R): Their combined work rate is the sum of individual rates.

Verification: A’s rate = 1/10; B’s rate = 1/15; combined = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6. Time = 6 days. Both A and R are correct, and R is the correct explanation. Answer: Both A and R are true, and R explains A.

Exam Tip: For compound interest MCQs, know that CI > SI for same P, R, T when T > 1 year. The difference between CI and SI for 2 years = P(R/100)². This formula lets you solve “find rate given CI and SI difference” problems in seconds without full expansion.

HP Angle — Verbal Reasoning in HP Exams: HPBOSE TGT/C&V and HPRCA papers typically include 10–12 reasoning questions. Blood-relation puzzles frequently use HP-relevant contexts (joint-family setups). Direction-sense problems sometimes use landmark-style references (temple → market → school). Series questions often mix prime numbers with squares — practice both simultaneously.

**Table 19.7** Freedom-struggle timeline — events, leaders, and significance
Year	Event	Key Figure(s)	Outcome / Significance
1857	Revolt of 1857 / Sepoy Mutiny	Mangal Pandey, Rani Lakshmibai, Bahadur Shah Zafar	First armed uprising; British Crown took over from East India Company (1858)
1885	Indian National Congress (INC) founded	A. O. Hume (British civil servant), W. C. Bonnerjee (1st President)	Platform for moderate constitutional demands; Lal-Bal-Pal era began 1905
1905	Partition of Bengal	Lord Curzon; opposed by Bal Gangadhar Tilak, Bipin Chandra Pal	Swadeshi movement; boycott of British goods; annulled 1911
1915	Gandhi returns from South Africa	M. K. Gandhi	Champaran (1917), Kheda (1918), Ahmedabad (1918) satyagrahas
1919	Jallianwala Bagh Massacre	General Dyer; Udham Singh (revenge, 1940)	Mass unarmed killing; national outrage; Rabindranath Tagore returned knighthood
1920	Non-Cooperation Movement	Gandhi, Motilal Nehru, Ali Brothers	Boycott of British schools, courts; suspended after Chauri Chaura violence 1922
1927	Simon Commission	Lord Simon; opposed by Lala Lajpat Rai (“Simon Go Back”)	Lajpat Rai died from baton blows; Bhagat Singh, Sukhdev, Rajguru avenged
1929	Lahore Congress; “Purna Swaraj” resolution	Jawaharlal Nehru (youngest Congress president)	Complete independence declared as goal; 26 Jan set as Independence Day
1930	Dandi Salt March / Civil Disobedience	Gandhi; 78 volunteers → thousands joined	Broke salt law; mass arrests; Gandhi-Irwin Pact 1931
1942	Quit India Movement	Gandhi (“Do or Die”), Aruna Asaf Ali, JP Narayan	Mass underground resistance; British promised post-war independence
1943–45	Indian National Army (INA) / Azad Hind Fauj	Subhas Chandra Bose, Shah Nawaz Khan	Armed resistance from South-East Asia; INA trials post-1945 galvanised public opinion
1946	Royal Indian Navy Mutiny	B. C. Dutt; 20,000 sailors	Showed armed forces were unreliable; accelerated British withdrawal decision
1947	Independence Day & Partition	Mountbatten, Nehru, Jinnah, Gandhi	India (15 Aug 1947) and Pakistan (14 Aug 1947) become independent; ~14 million displaced

Mnemonic — Freedom-Struggle Decades

1857, ‘85, ‘05, ‘19, ‘20, ‘30, ‘42, ‘47

“Revolt (1857) → Congress (1885) → Partition (1905) → Jallianwala (1919) → Non-coop (1920) → Dandi (1930) → Quit India (1942) → Independence (1947)” — R C P J N D Q I = Remember Congress Proclaimed Justice Now Do Quit India.

19.6 Indian Geography & Environment

India spans 3.28 million km² (7th largest country) from the Himalayan ranges in the north to Cape Comorin (Kanyakumari) in the south, and from Kutch in the west to Arunachal Pradesh in the east (easternmost tip: Kibithu). It shares borders with Pakistan (west), Afghanistan (brief, via PoK), China + Nepal + Bhutan (north), Myanmar + Bangladesh (east), and has a coastline of 7,516 km. The Tropic of Cancer (23.5° N) passes through Gujarat, Rajasthan, MP, Chhattisgarh, Jharkhand, West Bengal, Tripura, and Mizoram.

Fig. 19.4 India political outline map showing major states, capitals, and the North-East “Seven Sisters.” The Tropic of Cancer (23.5° N, dashed red line) passes through 8 states/UTs. India has 28 states and 8 Union Territories. Chandigarh is the shared capital of both Punjab and Haryana. Hyderabad serves as the joint capital of Telangana and Andhra Pradesh (until Amaravati is fully developed). HP capital: Shimla (summer); Dharamshala is winter capital / “Mini Switzerland.”

**Table 19.8** Indian states and capitals — complete list (28 states + 8 UTs)
State / UT	Capital	State / UT	Capital
Andhra Pradesh	Amaravati (+ Hyd. shared)	Arunachal Pradesh	Itanagar
Assam	Dispur (city: Guwahati)	Bihar	Patna
Chhattisgarh	Raipur	Goa	Panaji
Gujarat	Gandhinagar	Haryana	Chandigarh
Himachal Pradesh	Shimla	Jharkhand	Ranchi
Karnataka	Bengaluru	Kerala	Thiruvananthapuram
Madhya Pradesh	Bhopal	Maharashtra	Mumbai
Manipur	Imphal	Meghalaya	Shillong
Mizoram	Aizawl	Nagaland	Kohima
Odisha	Bhubaneswar	Punjab	Chandigarh
Rajasthan	Jaipur	Sikkim	Gangtok
Tamil Nadu	Chennai	Telangana	Hyderabad
Tripura	Agartala	Uttar Pradesh	Lucknow
Uttarakhand	Dehradun	West Bengal	Kolkata
Union Territories (8)
Delhi (NCT)	New Delhi	Jammu & Kashmir	Srinagar (summer) / Jammu (winter)
Ladakh	Leh	Chandigarh	Chandigarh (city itself)
Puducherry	Puducherry	Andaman & Nicobar Islands	Port Blair
Lakshadweep	Kavaratti	Dadra & Nagar Haveli + Daman & Diu (merged 2020)	Daman

19.6.1 Indian Climate and Monsoon

India has a tropical monsoon climate. The IMD divides the year into four seasons: Cold Weather (Dec–Feb), Hot Weather / Pre-monsoon (Mar–May), South-West Monsoon (June–September; brings ~80% of India’s annual rainfall; arrives at Kerala coast ~1 June; reaches HP/Punjab by ~1 July), Retreating Monsoon / North-East Monsoon (Oct–Nov; Tamil Nadu coast gets NE monsoon rains Oct–Dec).

Wettest place: Mawsynram, Meghalaya (~11,872 mm/year; displacing Cherrapunji/Sohra as the official wettest). Both are in the Khasi Hills, where moist Bay of Bengal air is deflected upward by hills (orographic rainfall).
Driest place: Jaisalmer, Rajasthan / Thar Desert (avg <200 mm/year).
Himachal Pradesh climate: Sub-tropical in Kangra/Hamirpur plains; temperate in Shimla/Manali; alpine/sub-alpine in Lahaul-Spiti. HP receives both western disturbances (winter, snow above 1,500 m) and SW monsoon (June–Sept). Average annual rainfall varies from 450 mm (Lahaul-Spiti, rain-shadow) to 2,800 mm (Dharamshala — receives extra orographic rainfall; sometimes called “Cherrapunji of HP”). HP has four major soil types: alluvial (lower valleys), red laterite, black cotton (limited), mountain/forest soils.

HP Angle — Geography: Himachal Pradesh became a full state on 25 January 1971 (prior: Union Territory from 1948, Part C state 1951). HP’s highest peak is Shilla (6,111 m) in Kinnaur; longest river entirely within HP is Uhl; the Beas, Sutlej, Ravi, Chenab, and Yamuna all flow through HP but originate elsewhere. Spiti valley is called the “Middle Land” and receives very little rain (rain shadow). The Pin Valley National Park (Spiti), Great Himalayan National Park (Kullu — UNESCO WHS 2014), and Kibber Wildlife Sanctuary are HP’s key protected areas.

19.7 Civics, Polity & Economic Concepts

For 10th-standard social science at the competitive level, focus on three clusters: (a) the Constitution of India — Preamble, Fundamental Rights, DPSP, structure of government; (b) elections and democracy — Election Commission, parliamentary vs presidential; (c) basic economics — GDP/GNP, inflation, monetary policy (RBI), fiscal policy (government), sectors of economy.

Fundamental Rights (Part III, Articles 12–35)

The six Fundamental Rights guaranteed to every citizen are: (1) Right to Equality (Art. 14–18), (2) Right to Freedom (Art. 19–22), (3) Right against Exploitation (Art. 23–24), (4) Right to Freedom of Religion (Art. 25–28), (5) Cultural & Educational Rights (Art. 29–30), (6) Right to Constitutional Remedies (Art. 32 — “Heart and Soul of the Constitution” per B. R. Ambedkar). Note: Right to Property was removed as an FR in 1978 (44th Amendment); it is now a legal right under Art. 300A.

19.7.1 Constitutional Highlights

Constituent Assembly: Formed 1946; adopted Constitution on 26 November 1949; came into force 26 January 1950 (Republic Day). Dr B. R. Ambedkar was chairman of the Drafting Committee.
Preamble declares India a Sovereign, Socialist, Secular, Democratic, Republic (SSSDR). “Socialist” and “Secular” added by 42nd Amendment, 1976.
Three pillars: Legislature (Parliament = Lok Sabha + Rajya Sabha), Executive (President + PM + Council of Ministers), Judiciary (Supreme Court + High Courts + subordinate courts).
Election Commission of India (ECI): Constitutional body (Art. 324); Chief Election Commissioner (CEC) cannot be removed except like a SC judge; oversees free and fair elections for Parliament, State Legislatures, President and VP.
Parliament: Lok Sabha = Lower House (People’s House); 543 elected + 2 Anglo-Indian (now removed by 104th Amendment 2020); max strength 552. Rajya Sabha = Upper House (Council of States); 238 + 12 nominated; not subject to dissolution. Joint sitting (Art. 108) for ordinary bills, presided over by Speaker of Lok Sabha.
DPSP (Directive Principles of State Policy, Part IV, Art. 36–51): Non-justiciable guidelines for the state for achieving socio-economic justice; borrowed from Ireland.
Amendments: Notable ones — 1st (restrictions on FR of free speech), 7th (reorganisation of states), 42nd (Emergency era, added Socialist+Secular, extended Lok Sabha to 5 yr), 44th (undid 42nd excesses, restored original tenure), 73rd/74th (Panchayati Raj + Urban Local Bodies), 86th (Right to Education 6–14 yr, Art. 21A), 101st (GST), 103rd (EWS reservation 10%), 104th (removed Anglo-Indian nomination).

19.7.2 Election-Related Timeline

**Table 19.9** Key election and constitutional milestones
Year	Event
1950	Constitution comes into force; ECI established
1952	First General Elections; INC wins majority; Nehru becomes PM
1975–77	Emergency imposed (25 Jun 1975 – 21 Mar 1977) by Indira Gandhi (Art. 352)
1977	First non-Congress government (Janata Party); Morarji Desai PM
1989	First hung Parliament; V. P. Singh PM; Mandal Commission recommendations accepted 1990
1993	73rd & 74th Amendments: Panchayati Raj and ULBs constitutionalised
2009	Decriminalisation of homosexuality — Delhi HC (Section 377 IPC)
2017	GST implemented (101st Amendment); one nation, one tax
2019	J&K bifurcated; Article 370 abrogated; Ladakh and J&K become UTs

19.7.3 Basic Economic Concepts

Easy to confuse — Macroeconomics vs Microeconomics

Macroeconomics

Studies the economy as a whole: GDP, GNP, national income, unemployment rate, inflation rate, monetary and fiscal policy. The “big picture”. RBI’s interest rate decisions are macroeconomic tools.

Microeconomics

Studies individual units: a firm’s pricing, a consumer’s choices, market equilibrium (supply = demand), monopoly vs competition. Price elasticity of demand is a microeconomic concept.

Easy to confuse — FDI vs FII

FDI (Foreign Direct Investment)

A foreign entity invests in and controls a business in India (e.g., setting up a factory, acquiring ≥10% stake). Long-term, stable. Regulated by DIPP (now DPIIT). Brings technology transfer and employment. Example: Apple manufacturing in India via Foxconn.

FII (Foreign Institutional Investment)

Foreign entities (mutual funds, banks, hedge funds) invest in stock markets / bonds without controlling interest. Short-term, volatile (“hot money”). Can be withdrawn rapidly causing market instability. Regulated by SEBI. Now called FPI (Foreign Portfolio Investment) officially.

**Table 19.10** Key economic terms and definitions
Term	Definition / Key Fact
GDP (Gross Domestic Product)	Total market value of all goods and services produced within India’s borders in a year, regardless of who produces them (Indian or foreign). India’s GDP (2024–25) ≈ $3.9 trillion (5th largest globally).
GNP (Gross National Product)	GDP + net income earned abroad by Indians − income earned in India by foreigners. GNP = GDP + NFA (Net Factor income from Abroad).
NDP / NNP	Net = Gross − Depreciation (capital consumption). NDP = GDP − depreciation.
Inflation	Sustained rise in general price level. Measured by CPI (Consumer Price Index — retail level; base year 2012) and WPI (Wholesale Price Index — wholesale level; base year 2011–12). RBI targets CPI inflation at 4% (±2%).
Repo Rate	Rate at which RBI lends to commercial banks. Increase → credit becomes costlier → controls inflation. (As of 2024: 6.5%).
Reverse Repo Rate	Rate at which RBI borrows from commercial banks. Increase → banks park money with RBI → liquidity reduced.
CRR (Cash Reserve Ratio)	% of deposits banks must keep as cash with RBI. Increase → less credit creation.
SLR (Statutory Liquidity Ratio)	% of deposits banks must keep in liquid assets (gold, govt securities). Currently 18%.
Fiscal Policy	Government tool: public spending and taxation. Expansionary (increase spending/cut tax) vs contractionary. Budget presented by Finance Minister (currently annually on 1 February). FRBM Act 2003 caps fiscal deficit.
Sectors of Economy	Primary (agriculture, mining, forestry); Secondary (manufacturing, industry); Tertiary (services — largest contributor to India’s GDP at ~55%). Quaternary = knowledge-based; Quinary = top decision-making.
Five-Year Plans	Planning Commission (est. 1950) ran 12 Five-Year Plans (1951–2017). Replaced by NITI Aayog (National Institution for Transforming India) in January 2015; PM Modi chairs it.
GST	Goods and Services Tax; implemented 1 July 2017; replaced >17 indirect taxes; dual structure (CGST + SGST or IGST for interstate); four slabs: 5%, 12%, 18%, 28%.

19.8 Quick-Reference Tables

**Table 19.11** Everyday physics constants (memorise these values)
Constant / Quantity	Symbol	Value
Speed of light in vacuum	c	3 × 10&sup8; m/s
Acceleration due to gravity (Earth)	g	9.8 m/s² (≈10 for quick calculation)
Avogadro’s number	N_A	6.022 × 10²³ mol¹
Planck’s constant	h	6.626 × 10³&sup4; J·s
Speed of sound in air (20°C)	—	~343 m/s
Absolute zero	0 K	−273.15 °C
Charge of electron	e	1.6 × 10¹&sup9; C
Latent heat of fusion of ice	L_f	80 cal/g = 334 J/g
Latent heat of vaporisation of water	L_v	540 cal/g = 2260 J/g
Atmospheric pressure (1 atm)	P₀	101,325 Pa = 1.013 × 10&sup5; Pa
1 kilowatt-hour (1 unit of electricity)	kWh	3.6 × 10&sup6; J

**Table 19.12** Types of reasoning patterns — quick-fire summary
Pattern Type	What to Identify	Common Trap
Arithmetic series	Constant difference (d)	Difference may alternate (e.g., +2,+4,+2,+4)
Geometric series	Constant ratio (r)	r < 1 gives decreasing sequence
Square/cube series	Perfect squares or cubes	May use primes as bases — check next prime
Fibonacci-type	Each = sum of previous two	May start with different seed values
Letter series	Position jump (+1, +2, alternating)	Reverse alphabet (Z=1) sometimes used
Analogy	Relationship type before solving	Superficial similarity ≠ correct relation
Coding-decoding	Rule: shift / reverse / positional	Rules may apply only to odd/even positions
Blood relations	Draw family tree; clarify gender	“My father’s only son” = me (not a sibling)
Direction sense	Use compass; track turns	Right facing South = West; not East
Syllogism	Use Venn diagrams; avoid knowledge	Conclusions must follow necessarily, not probably

Chapter Recap

SI has 7 base units (m, kg, s, A, K, mol, cd); all others are derived. Newton = kg·m/s²; Joule = N·m; Watt = J/s; Pascal = N/m².
Newton’s 3 laws: inertia · F=ma · action-reaction. g = 9.8 m/s²; Moon g′ = g/6.
Temperature: 0 K = −273.15°C; water boils at 100°C = 212°F = 373 K. Latent heat of fusion = 80 cal/g; vaporisation = 540 cal/g.
Light: c = 3×10&sup8; m/s. TIR → optical fibre & mirage. Myopia corrected by concave; hypermetropia by convex lens.
Sound: longitudinal wave; speed in air ~343 m/s. Ultrasound >20 kHz (bats, sonography).
Ohm’s law: V=IR; AC frequency in India = 50 Hz; India household voltage = 230 V.
Nuclear: α (helium nucleus), β (electron), γ (photon). Fission = U-235 (reactor/bomb); Fusion = Sun/H-bomb. ¹4C dating (T½ = 5,730 yr).
Solar system: 8 planets (MVEMJSUN); Pluto = dwarf (2006); Jupiter = largest + most moons; Venus = hottest; Earth = densest. Chandrayaan-3 = south pole soft landing, 23 Aug 2023.
Periodic table: 118 elements, 18 groups, 7 periods. Mendeleev (1869 by mass) → Moseley (1913 by atomic number). Atomic models: Dalton → Thomson (1897) → Rutherford (1911) → Bohr (1913) → Schrödinger (1926).
Acids: strong (HCl, H₂SO₄, HNO₃); weak (acetic, citric, lactic). OIL RIG: Oxidation Is Loss; Reduction Is Gain. Cation (+) to cathode; anion (−) to anode.
Reasoning: arithmetic → constant difference; geometric → constant ratio; Fibonacci → sum of previous two. Blood relations: draw family tree. Syllogism: use Venn, never general knowledge.
Freedom struggle: 1857 → 1885 INC → 1905 Bengal → 1919 Jallianwala → 1920 Non-coop → 1930 Dandi → 1942 Quit India → 1947 Independence.
India: 28 states + 8 UTs. HP capital = Shimla; full statehood = 25 Jan 1971. Seven Sisters + Sikkim = NE India. Wettest = Mawsynram (Meghalaya); driest = Jaisalmer.
Polity: Constitution adopted 26 Nov 1949; effective 26 Jan 1950. 6 FRs; Ambedkar = Drafting Committee chair. Preamble: SSSDR (“Socialist, Secular” added 42nd Amendment 1976).
Economics: GDP = value of goods/services within India. CPI inflation target = 4% (±2%). Repo rate = RBI lends to banks. NITI Aayog replaced Planning Commission 2015. GST = 1 Jul 2017.

Last-Night Cheatsheet

SI Base Units (7)

m (length), kg (mass), s (time)
A (current), K (temperature)
mol (amount), cd (luminosity)
Mnemonic: MKS-A-KMC

Energy / Power / Work

KE = ½mv²; PE = mgh
E = mc² (Einstein 1905)
Power W = J/s; 1 HP = 746 W
Work W = Fd cosθ

Electricity

V = IR; P = VI = I²R = V²/R
India: AC, 50 Hz, 230 V
Series: R adds. Parallel: R reduces
Faraday: changing flux → EMF

Chemical Compounds

Baking soda: NaHCO₃
Washing soda: Na₂CO₃·10H₂O
Plaster of Paris: CaSO₄·½H₂O
Blue vitriol: CuSO₄·5H₂O

Freedom Struggle Dates

1857 Revolt; 1885 INC founded
1919 Jallianwala; 1920 Non-coop
1930 Dandi; 1942 Quit India
15 Aug 1947 Independence

Indian Geography Highlights

28 states + 8 UTs; capital = New Delhi
Tropic of Cancer 23.5°N: 8 states
Wettest: Mawsynram (Meghalaya)
HP full state: 25 Jan 1971

Economics Quick-Fire

GDP vs GNP: +/− net factor income
Repo rate: RBI lends to banks
GST: 1 Jul 2017; 101st Amendment
NITI Aayog: Jan 2015 (replaced PC)

Nuclear Physics

α = He nucleus; stopped by paper
β = electron; stopped by thin metal
γ = photon; stopped by Pb / concrete
¹4C T½ = 5,730 yr (dating)

Practice Questions

Which of the following is NOT an SI base unit? HPRCA-pat.

Kelvin
Newton
Candela
Mole

Answer: B — Newton

Newton is a derived unit (kg·m/s²). The 7 base units are: m, kg, s, A, K, mol, cd. Kelvin, Candela, and Mole are all base units.

A man walks 8 km north, then turns right and walks 6 km east. What is the shortest distance from his starting point? HPRCA-pat.

10 km
14 km
12 km
7 km

Answer: A — 10 km

Two perpendicular sides 8 and 6: shortest distance = √(8²+6²) = √(64+36) = √100 = 10 km (classic 3-4-5 Pythagorean triple scaled by 2).

The chemical name of Plaster of Paris is: HPRCA-pat.

Calcium carbonate
Calcium sulphate dihydrate
Calcium sulphate hemihydrate
Calcium oxide

Answer: C — Calcium sulphate hemihydrate

CaSO₄·½H₂O. It is made by heating gypsum (CaSO₄·2H₂O) to 120–130°C. When PoP is set, it absorbs water and reforms gypsum (expansion).

Find the missing number in the series: 2, 6, 12, 20, 30, ?

Answer: B — 42

Differences: 4, 6, 8, 10, 12 → each difference increases by 2. So 30+12=42. Alternatively the series is n(n+1): 1×2=2, 2×3=6, 3×4=12, 4×5=20, 5×6=30, 6×7=42.

Assertion (A): Venus is the hottest planet in the solar system even though Mercury is closer to the Sun.
Reason (R): Venus has a thick atmosphere of carbon dioxide which traps heat via the greenhouse effect. HPRCA-pat.

Both A and R are true, and R is the correct explanation of A
Both A and R are true, but R is NOT the correct explanation of A
A is true but R is false
A is false but R is true

Answer: A

Venus surface temperature ≈ 465°C vs Mercury’s max ~430°C (day side) but −180°C at night. Venus has no day-night variation due to CO₂ greenhouse. Both A and R are true and R correctly explains A.

India’s Constitution came into effect on:

15 August 1947
26 November 1949
26 January 1950
1 October 1950

Answer: C — 26 January 1950

The Constitution was adopted on 26 Nov 1949 but came into force (effect) on 26 Jan 1950 — celebrated as Republic Day. 15 Aug 1947 is Independence Day.

Assertion (A): Graphite conducts electricity but diamond does not, although both are allotropes of carbon.
Reason (R): Graphite has delocalised π electrons in its sp² layered structure, while diamond’s sp³ tetrahedral bonds leave no free electrons. HPRCA-pat.

Both A and R are true, and R is the correct explanation of A
Both A and R are true, but R is NOT the correct explanation of A
A is true but R is false
A is false but R is true

Answer: A

Classic MCQ pairing graphite’s conductivity with its sp² structure. Both assertion and reason are precisely correct, and R explains A.

Match the chemical compound with its common name: HPRCA-pat.
I. NaHCO₃ — (a) Washing soda
II. Na₂CO₃·10H₂O — (b) Baking soda
III. CaSO₄·½H₂O — (c) Blue vitriol
IV. CuSO₄·5H₂O — (d) Plaster of Paris

I—a, II—b, III—c, IV—d
I—b, II—a, III—d, IV—c
I—b, II—d, III—a, IV—c
I—a, II—d, III—b, IV—c

Answer: B — I—b, II—a, III—d, IV—c

NaHCO₃ = baking soda; Na₂CO₃·10H₂O = washing soda; CaSO₄·½H₂O = Plaster of Paris; CuSO₄·5H₂O = blue vitriol. A standard match-the-column MCQ.

The Dandi Salt March of 1930 was initiated to protest against:

Rowlatt Act
Simon Commission
British monopoly on salt production and taxation
Partition of Bengal

Answer: C — British monopoly on salt production and taxation

Gandhi walked 241 miles from Sabarmati Ashram to Dandi (12 Mar – 6 Apr 1930) to break the Salt Law, launching the Civil Disobedience Movement. Rowlatt Act (1919) triggered Non-cooperation; Simon Commission (1927) protests; Bengal Partition = 1905.

In a certain code APPLE is written as DSSOH. How is MANGO coded? HPRCA-pat.

PDQJR
NBOHP
LZMFN
PCNJQ

Answer: A — PDQJR

Rule: each letter shifted +3. A+3=D, P+3=S, P+3=S, L+3=O, E+3=H → DSSOH. Apply to MANGO: M+3=P, A+3=D, N+3=Q, G+3=J, O+3=R → PDQJR.

Which of the following statements about the Fundamental Rights of India is/are CORRECT?
1. Right to Property is a Fundamental Right under Article 31.
2. Right to Constitutional Remedies is enshrined in Article 32.
3. Freedom of speech and expression is an absolute right with no restrictions.

1 and 2 only
2 only
2 and 3 only
1, 2, and 3

Answer: B — 2 only

Statement 1 is incorrect: Right to Property was removed as a Fundamental Right by the 44th Amendment 1978 — now a legal right (Art. 300A). Statement 3 is incorrect: Art. 19(1)(a) speech is subject to reasonable restrictions (Art. 19(2)) for sovereignty, security, public order, decency, etc. Only Statement 2 is correct.

The GDP of India is calculated at market prices and includes:

Income earned by Indian citizens abroad
Only income of Indian nationals regardless of location
Total value of goods and services produced within India’s borders by all residents
GDP minus depreciation of capital

Answer: C

GDP is territory-based: all production within India regardless of producer nationality. Option A describes GNP’s additional component (NFA). Option D describes NDP (Net Domestic Product).

Match the state with its capital: HPRCA-pat.
I. Himachal Pradesh — (a) Shillong
II. Meghalaya — (b) Panaji
III. Goa — (c) Shimla
IV. Sikkim — (d) Gangtok

I—c, II—a, III—b, IV—d
I—a, II—c, III—d, IV—b
I—c, II—b, III—a, IV—d
I—b, II—d, III—c, IV—a

Answer: A — I—c, II—a, III—b, IV—d

HP → Shimla; Meghalaya → Shillong; Goa → Panaji; Sikkim → Gangtok. Note that Goa’s capital is often mistakenly given as “Panjim” (old name of Panaji).

Assertion (A): India’s household mains electricity supply is alternating current (AC) at 50 Hz.
Reason (R): AC can be stepped up/down by transformers, reducing transmission losses over long distances compared to DC.

Both A and R are true, and R is the correct explanation of A
Both A and R are true, but R is NOT the correct explanation of A
A is true but R is false
A is false but R is true

Answer: A

India uses 230 V AC at 50 Hz. The advantage of AC over DC for transmission is transformer compatibility — this is why Westinghouse/Tesla’s AC system won the “War of Currents” over Edison’s DC.

Pointing to a photograph, Ravi says: “She is the daughter of the only son of my grandfather.” How is Ravi related to the person in the photograph? HPRCA-pat.

Nephew
Uncle
Brother
Sister

Answer: C — Brother (or D — Sister if genders permit)

“Only son of my grandfather” = Ravi’s father. “Daughter of my father” = Ravi’s sister. So Ravi is the photograph person’s brother. (Best answer: C.)

Chandrayaan-3 successfully soft-landed on the Moon on: HPRCA-pat.

14 July 2023
23 August 2023
5 September 2019
11 October 2023

Answer: B — 23 August 2023

Chandrayaan-3’s Vikram lander soft-landed on the lunar south pole on 23 Aug 2023 — making India the first country to achieve this. The rover Pragyan was deployed. Launch date was 14 Jul 2023 (GSLV-MkIII from Sriharikota).

Assertion (A): Sound cannot travel in a vacuum.
Reason (R): Sound is a transverse electromagnetic wave that requires a medium of charged particles.

Both A and R are true, and R is the correct explanation of A
Both A and R are true, but R is NOT the correct explanation of A
A is true but R is false
A is false but R is true

Answer: C — A is true but R is false

Sound is a longitudinal mechanical wave (not transverse, not electromagnetic). It requires a medium because it propagates through compression and rarefaction of matter. In vacuum there is no medium, so sound cannot travel. Assertion is correct; Reason is incorrect in description.

Match the discovery with the scientist: HPRCA-pat.
I. Periodic table (atomic mass order) — (a) Moseley
II. Nuclear model of atom — (b) Thomson
III. Electron discovered — (c) Mendeleev
IV. Periodic table (atomic number order) — (d) Rutherford

I—c, II—d, III—b, IV—a
I—a, II—b, III—c, IV—d
I—c, II—b, III—d, IV—a
I—d, II—c, III—a, IV—b

Answer: A — I—c, II—d, III—b, IV—a

Mendeleev 1869 (atomic mass); Rutherford 1911 (nuclear model, gold-foil); Thomson 1897 (electron, plum-pudding); Moseley 1913 (atomic number basis for periodic table).

Himachal Pradesh attained full statehood on: HPRCA-pat.

15 August 1947
1 November 1956
25 January 1971
26 January 1950

Answer: C — 25 January 1971

HP became a Union Territory in 1948; a “Part C state” in 1951; then a full state on 25 January 1971 (18th state of India) under the HP Statehood Act. Y. S. Parmar was its first Chief Minister.

Find the odd one out: HPRCA-pat.

Echoes
Sonar
Rainbow
Ultrasound imaging

Answer: C — Rainbow

Echoes, Sonar, and Ultrasound imaging are all based on sound (or ultrasound) principles. Rainbow is a phenomenon of light (dispersion, internal reflection, refraction by water droplets). Hence Rainbow is the odd one out.

Arrange the following events in correct chronological order:
1. Quit India Movement
2. Jallianwala Bagh Massacre
3. Dandi Salt March
4. Indian National Congress founded

4 → 2 → 3 → 1
2 → 4 → 3 → 1
4 → 3 → 2 → 1
2 → 3 → 1 → 4

Answer: A — 4 → 2 → 3 → 1

INC founded 1885 → Jallianwala Bagh 1919 → Dandi Salt March 1930 → Quit India Movement 1942.

The wettest place in India is:

Cherrapunji, Meghalaya
Mawsynram, Meghalaya
Agumbe, Karnataka
Mahabaleshwar, Maharashtra

Answer: B — Mawsynram, Meghalaya

Mawsynram (avg ~11,872 mm/yr) officially displaced Cherrapunji as the world’s wettest place. Both are in the Khasi Hills, Meghalaya, receiving Bay of Bengal moisture forced upward by the hills. Many older texts still cite Cherrapunji; current standard answer is Mawsynram.

Assertion (A): A person with myopia (short-sightedness) is prescribed concave (diverging) lenses.
Reason (R): In myopia, the eye’s focal point falls in front of the retina; a concave lens diverges incoming light to shift the focus back onto the retina.

Both A and R are true, and R is the correct explanation of A
Both A and R are true, but R is NOT the correct explanation of A
A is true but R is false
A is false but R is true

Answer: A

Myopia = eyeball too long / lens too curved; parallel rays from distant objects converge before the retina. Concave lens pre-diverges rays so the eye can focus them on the retina. Both A and R are correct, and R explains A perfectly.

Consider the following statements about India’s monetary policy:
1. RBI sets the Repo Rate at which it lends to commercial banks.
2. Increasing the Repo Rate typically reduces inflation by making credit more expensive.
3. The CRR is the percentage of deposits banks must keep as liquid government securities.

1 and 2 only
2 and 3 only
1 and 3 only
1, 2 and 3

Answer: A — 1 and 2 only

Statement 3 is incorrect: CRR is cash that banks keep with RBI (not “liquid government securities” — that describes SLR). CRR = Cash Reserve Ratio (cash); SLR = Statutory Liquidity Ratio (liquid assets incl. govt securities). Statements 1 and 2 are correct.

If A can complete a work in 12 days and B can complete it in 18 days, how many days will they take together?

7.2 days
6 days
8 days
9 days

Answer: A — 7.2 days

A’s rate = 1/12; B’s rate = 1/18; combined = 3/36 + 2/36 = 5/36. Time = 36/5 = 7.2 days. Check: in 7.2 days A does 7.2/12 = 0.6; B does 7.2/18 = 0.4; total = 1.0 ✓.

Match the radiation type with its penetration ability (increasing order): HPRCA-pat.
I. Alpha (α) — (a) Highest penetration; stopped by lead
II. Beta (β) — (b) Lowest penetration; stopped by paper
III. Gamma (γ) — (c) Moderate penetration; stopped by thin metal

I—a, II—b, III—c
I—b, II—c, III—a
I—c, II—a, III—b
I—b, II—a, III—c

Answer: B — I—b, II—c, III—a

α = least penetrating (stopped by paper or 5 cm air); β = moderate (stopped by 3 mm aluminium); γ = most penetrating (stopped only by thick lead or concrete). Inverse relationship with ionising power: α ionises most, γ least per unit path.

Which of the following statements about the Directive Principles of State Policy (DPSP) is INCORRECT?

DPSPs are contained in Part IV of the Constitution (Articles 36–51)
DPSPs are justiciable — courts can enforce them directly
DPSPs were borrowed from the Irish Constitution
DPSPs aim at establishing a welfare state

Answer: B — DPSPs are justiciable

DPSPs are explicitly non-justiciable (Art. 37: shall not be enforceable by any court). They are guidelines to the state; courts cannot order the government to implement them, unlike Fundamental Rights which are enforceable. Options A, C, and D are all correct.

The NITI Aayog replaced which body in January 2015? HPRCA-pat.

Finance Commission
Planning Commission
Election Commission
National Development Council

Answer: B — Planning Commission

The Planning Commission (established 1950 by PM Nehru) was dissolved on 1 January 2015 and replaced by NITI Aayog (National Institution for Transforming India). The PM chairs NITI Aayog; it functions as a policy think-tank rather than a plan-allocating body.

In the series 1, 4, 9, 16, 25, the next term is 36. What rule generates this series? HPRCA-pat.

Each term = previous + 3
Each term = previous × 2
Each term = n² where n = position
Each term = previous + consecutive even numbers

Answer: C — Each term = n²

1=1², 4=2², 9=3², 16=4², 25=5², 36=6². Option D is also true: differences are 3,5,7,9,11 (consecutive odd numbers) — but option C is the defining rule. For MCQ purposes, C is the expected answer.

Which article of the Constitution gives the right to move the Supreme Court for enforcement of Fundamental Rights, and was described by B. R. Ambedkar as the “heart and soul” of the Constitution? HPRCA-pat.

Article 14
Article 19
Article 21
Article 32

Answer: D — Article 32

Art. 32 is the Right to Constitutional Remedies — one of the six Fundamental Rights. It empowers citizens to directly approach the Supreme Court to enforce FRs. Ambedkar called it the “heart and soul of the Constitution.” Art. 226 gives similar power to High Courts. Art. 21 = right to life and personal liberty; Art. 19 = freedom of speech etc.; Art. 14 = equality before law.

End of Chapter 19 · Everyday Science, Reasoning & Social Science. HPRCA-pat. indicates HPRCA / state-TGT pattern questions; literal past-paper items will be flagged with year when official papers are sourced.

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