Quantitative Aptitude
Arithmetic, Algebra, Geometry, Mensuration, Trigonometry & DI1
Number System
βΌ
Types of Numbers
- Natural Numbers: 1, 2, 3β¦ | Whole: 0, 1, 2β¦ | Integers: β¦β2,β1,0,1,2β¦
- Rational: p/q form (qβ 0) | Irrational: β2, Ο β non-terminating, non-repeating
- Prime: divisible only by 1 and itself; only even prime = 2
Divisibility Rules
| Divisor | Rule | Example |
|---|---|---|
| 2 | Last digit even | 128 β |
| 3 | Sum of digits Γ· 3 | 123 β 6 β |
| 4 | Last 2 digits Γ· 4 | 1124 β 24 β |
| 9 | Sum of digits Γ· 9 | 729 β 18 β |
| 11 | Alt. sum = 0 or Β±11 | 121 β (1+1)β2=0 β |
π‘ HCF Γ LCM = Product of two numbers (valid only for TWO numbers)
2
Simplification & Approximation
βΌ
BODMAS Rule
- Brackets β Order (powers/roots) β Division β Multiplication β Addition β Subtraction
- For approximation: round to nearest easy number, compute, then adjust
Fraction β Decimal β Percent
| Fraction | Decimal | % |
|---|---|---|
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333β¦ | 33.33% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
π In SSC approximation: never deviate more than Β±2% from the actual answer
3
Percentage
βΌ
Core Formulas
- % = (Value / Total) Γ 100
- % Change = [(New β Old) / Old] Γ 100
- Successive % change A then B β Net = A + B + AB/100
- x% of y = y% of x (cross trick)
β
If price β by r%, consumption must β by [r/(100+r)]Γ100 to keep expenditure constant
4
Profit and Loss
βΌ
Key Formulas
- Profit = SP β CP | Loss = CP β SP
- Profit% = (Profit / CP) Γ 100 | SP = CP Γ (100 + P%) / 100
- Successive Discounts x% & y%: Net = x + y β xy/100
- Dishonest dealer gain% = (Error / True weight β Error) Γ 100
π‘ Two items sold at same SP, one at X% profit, other at X% loss β always a net loss of (XΒ²/100)%
5
Simple Interest
βΌ
Formula
- SI = (P Γ R Γ T) / 100 | Amount = P + SI
- P = (SI Γ 100) / (R Γ T) | R = (SI Γ 100) / (P Γ T)
- Money doubles in SI β T = 100/R years
π If SI for n years is given and you need SI for m years β simply scale: SIβ = SIβ Γ (m/n)
6
Compound Interest
βΌ
Formulas
- A = P Γ (1 + R/100)βΏ | CI = A β P
- Half-yearly: Rate = R/2, Time = 2n | Quarterly: Rate = R/4, Time = 4n
- CI β SI (2 yrs) = P Γ (R/100)Β² | CI β SI (3 yrs) = P(R/100)Β²(3 + R/100)
π‘ Rule of 72: Years to double = 72 Γ· Rate%. Money triples β 114 Γ· Rate%
7
Ratio and Proportion
βΌ
Key Rules
- a:b = c:d β ad = bc (cross-multiplication / componendo-dividendo)
- Duplicate ratio of a:b = aΒ²:bΒ² | Sub-duplicate = βa:βb
- Mean proportional of a & b = β(ab) | Third proportional of a,b = bΒ²/a
- Compounded ratio of a:b and c:d = ac:bd
β
Componendo: (a+b):(aβb) = (c+d):(cβd)
8
Partnership
βΌ
Profit Sharing
- Simple Partnership: Profit β Capital (equal time)
- Compound Partnership: Profit β Capital Γ Time
- A invests βΉPβ for tβ, B invests βΉPβ for tβ β Ratio = Pβtβ : Pβtβ
π Working partner may receive salary/commission before profit split β deduct first, then divide remaining
9
Average
βΌ
Formulas
- Average = Sum / Count
- Avg of first n naturals = (n+1)/2 | First n even = n+1 | First n odd = n
- If a new member joins and average changes by x β new sum = new count Γ new avg
- Weighted average = (wβaβ + wβaβ) / (wβ + wβ)
10
Mixture and Alligation
βΌ
Alligation Rule
- Ratio = (Dearer β Mean) : (Mean β Cheaper)
- Repeated withdrawal & replacement: Final conc. = C Γ (1 β x/V)βΏ
π‘ Alligation works for price, speed, % concentration, age β any average-type mix problem
11
Time and Work
βΌ
Key Concepts
- A completes in n days β 1-day work = 1/n
- A + B together: T = AB / (A+B)
- Efficiency method: Total work = LCM of all days; find units/day per person
- MβDβHβ/Wβ = MβDβHβ/Wβ (work equivalence formula)
β
If A is twice as efficient as B, and B takes n days β A takes n/2 days; together = n/3 days
12
Pipes and Cisterns
βΌ
Rules
- Inlet pipe fills in x hrs β rate = +1/x | Outlet empties in y hrs β rate = β1/y
- Net rate when both open = 1/x β 1/y | Time to fill = xy/(yβx)
- With leak: Time = FL/(LβF) where F = fill time, L = leak empty time
13
Time, Speed and Distance
βΌ
Formulas
- Speed = Distance / Time | 1 km/h = 5/18 m/s | 1 m/s = 3.6 km/h
- Average speed (equal distance) = 2xy/(x+y)
- Relative speed: same direction = |SββSβ|; opposite = Sβ+Sβ
Trains
- Cross a pole: Time = Train length / Speed
- Cross a platform: Time = (Train + Platform length) / Speed
π£ Boats & Streams: Downstream = B+S | Upstream = BβS | B = (D+U)/2 | S = (DβU)/2
14
Boats and Streams
βΌ
Key Formulas
- Downstream speed (D) = Boat speed (B) + Stream speed (S)
- Upstream speed (U) = B β S
- B = (D + U) / 2 | S = (D β U) / 2
- Time downstream vs upstream: tβ/tβ = U/D (inverse ratio)
π If man can row x km/h in still water and stream flows y km/h β speed ratio: (x+y):(xβy)
15
Algebraic Identities
βΌ
Must-Know Identities
- (a+b)Β² = aΒ² + 2ab + bΒ² | (aβb)Β² = aΒ² β 2ab + bΒ²
- aΒ² β bΒ² = (a+b)(aβb)
- (a+b)Β³ = aΒ³ + 3aΒ²b + 3abΒ² + bΒ³
- aΒ³ + bΒ³ = (a+b)(aΒ² β ab + bΒ²) | aΒ³ β bΒ³ = (aβb)(aΒ² + ab + bΒ²)
- If a + b + c = 0 β aΒ³ + bΒ³ + cΒ³ = 3abc
π‘ SSC CGL frequently tests: if x + 1/x = k, find xΒ² + 1/xΒ² = kΒ²β2; xΒ³+1/xΒ³ = kΒ³β3k
16
Linear Equations
βΌ
Methods to Solve
- Substitution: Express one variable in terms of other, substitute
- Elimination: Multiply equations to match coefficients, then add/subtract
- Cross-multiplication: For aβx+bβy=cβ and aβx+bβy=cβ: x = (bβcββbβcβ)/(aβbββaβbβ)
π No solution (parallel lines): aβ/aβ = bβ/bβ β cβ/cβ | Infinite solutions: aβ/aβ = bβ/bβ = cβ/cβ
17
Quadratic Equations
βΌ
axΒ² + bx + c = 0
- Roots: x = [βb Β± β(bΒ²β4ac)] / 2a
- Sum of roots = βb/a | Product of roots = c/a
- Discriminant D = bΒ²β4ac: D>0 β real distinct; D=0 β equal; D<0 β imaginary
β
SSC trick: for integer roots, factorise by splitting middle term β faster than formula
18
Lines and Angles
βΌ
Key Angle Pairs
- Complementary = 90Β° | Supplementary = 180Β° | Vertically opposite = equal
- Corresponding angles (parallel lines + transversal) = equal
- Alternate interior angles = equal | Co-interior (same-side) = supplementary
π Sum of all angles around a point = 360Β°. Linear pair = 180Β°
19
Triangles
βΌ
Important Properties
- Sum of angles = 180Β° | Exterior angle = sum of two non-adjacent interior angles
- Pythagoras: aΒ² + bΒ² = cΒ² (right triangle) | Common triples: 3-4-5, 5-12-13, 8-15-17
- Equilateral triangle area = (β3/4)aΒ² | Altitude = (β3/2)a
Similarity & Congruence
- Similar triangles: AA, SAS, SSS similarity criteria
- Ratio of areas of similar triangles = (ratio of sides)Β²
- Mid-point theorem: line joining midpoints of two sides is parallel to third and half its length
π‘ Centres: Centroid (medians), Incentre (angle bisectors), Circumcentre (perpendicular bisectors), Orthocentre (altitudes)
20
Quadrilaterals
βΌ
| Shape | Area | Key Property |
|---|---|---|
| Square | aΒ² | All sides equal, all angles 90Β° |
| Rectangle | l Γ b | Opposite sides equal, all angles 90Β° |
| Parallelogram | base Γ height | Opposite sides parallel & equal |
| Rhombus | Β½ Γ dβ Γ dβ | All sides equal; diagonals bisect perpendicularly |
| Trapezium | Β½(a+b)Γh | One pair of parallel sides |
π Sum of all angles of any quadrilateral = 360Β°
21
Circles
βΌ
Key Theorems
- Angle in semicircle = 90Β° (Thales' theorem)
- Angles in same segment = equal
- Angle at centre = 2 Γ angle at circumference (same arc)
- Tangent β₯ radius at point of contact
- Two tangents from external point = equal length
Formulas
- Area = ΟrΒ² | Circumference = 2Οr | Arc length = (ΞΈ/360) Γ 2Οr
- Sector area = (ΞΈ/360) Γ ΟrΒ²
22
2D Mensuration
βΌ
| Shape | Area | Perimeter |
|---|---|---|
| Circle | ΟrΒ² | 2Οr |
| Triangle | Β½ Γ b Γ h | β[s(sβa)(sβb)(sβc)] | a+b+c |
| Rectangle | l Γ b | 2(l+b) |
| Square | aΒ² | 4a |
| Parallelogram | b Γ h | 2(a+b) |
| Rhombus | Β½dβdβ | 4a |
| Trapezium | Β½(a+b)h | a+b+c+d |
β
Equilateral triangle: Area = (β3/4)aΒ² | s = (a+a+a)/2 in Heron's formula
23
3D Mensuration
βΌ
| Shape | Volume | Total Surface Area |
|---|---|---|
| Cube (side a) | aΒ³ | 6aΒ² |
| Cuboid (l,b,h) | lbh | 2(lb+bh+lh) |
| Cylinder | ΟrΒ²h | 2Οr(r+h) |
| Cone | β ΟrΒ²h | Οr(r+l), l=β(rΒ²+hΒ²) |
| Sphere | 4/3ΟrΒ³ | 4ΟrΒ² |
| Hemisphere | 2/3ΟrΒ³ | 3ΟrΒ² |
π‘ Diagonal of cube = aβ3 | Diagonal of cuboid = β(lΒ²+bΒ²+hΒ²)
24
Trigonometric Ratios
βΌ
Ratios (SOH-CAH-TOA)
- sin ΞΈ = P/H | cos ΞΈ = B/H | tan ΞΈ = P/B
- cosec ΞΈ = 1/sin | sec ΞΈ = 1/cos | cot ΞΈ = 1/tan
| Angle | 0Β° | 30Β° | 45Β° | 60Β° | 90Β° |
|---|---|---|---|---|---|
| sin | 0 | 1/2 | 1/β2 | β3/2 | 1 |
| cos | 1 | β3/2 | 1/β2 | 1/2 | 0 |
| tan | 0 | 1/β3 | 1 | β3 | β |
25
Trigonometric Identities
βΌ
Fundamental Identities
- sinΒ²ΞΈ + cosΒ²ΞΈ = 1
- 1 + tanΒ²ΞΈ = secΒ²ΞΈ β secΒ²ΞΈ β tanΒ²ΞΈ = 1
- 1 + cotΒ²ΞΈ = cosecΒ²ΞΈ β cosecΒ²ΞΈ β cotΒ²ΞΈ = 1
Complementary Angles
- sin(90Β°βΞΈ) = cosΞΈ | cos(90Β°βΞΈ) = sinΞΈ | tan(90Β°βΞΈ) = cotΞΈ
π SSC tip: Use complementary angle pairs to simplify long expressions quickly
26
Heights and Distances
βΌ
Concepts
- Angle of Elevation: angle formed looking upward from horizontal to object
- Angle of Depression: angle formed looking downward from horizontal
- tan ΞΈ = Height / Base β Height = Base Γ tan ΞΈ
β
30Β° β multiply base by 1/β3 | 45Β° β height = base | 60Β° β multiply base by β3
27
Data Interpretation (Bar, Pie, Line, Table)
βΌ
General Strategy
- Read all headings and units before solving any question
- Identify the unit (βΉ crore, thousands, %) upfront to avoid scaling errors
Type-wise Tips
- Bar Graph: Compare bar heights visually before calculating
- Pie Chart: Value = (Angle/360Β°) Γ Total or (% /100) Γ Total
- Line Graph: Focus on slope direction (increasing/decreasing trends)
- Table: Row totals and column totals β verify given totals before trusting values
π‘ In SSC CGL Tier-2, DI sets have 5 questions β attempt all from same set for time efficiency
Reasoning Ability
Verbal & Non-Verbal Reasoning for SSC1
Analogy
βΌ
Types
- Word Analogy: Doctor : Hospital :: Teacher : School (place of work)
- Number Analogy: 4 : 16 :: 5 : 25 (squares)
- Letter Analogy: AB : DC :: EF : HG (reverse adjacent pair)
| Relationship | Example |
|---|---|
| Tool : User | Pen : Writer |
| Part : Whole | Chapter : Book |
| Product : Raw Material | Butter : Milk |
| Cause : Effect | Fire : Smoke |
| Animal : Young one | Cow : Calf |
π‘ Always identify the EXACT relationship in the given pair first, then apply to unknown
2
Classification (Odd One Out)
βΌ
Types
- Word classification: category (animals, fruits, metals), usage, properties
- Number classification: odd/even, prime, square, cube β identify the outlier
- Letter classification: number of letters, vowel pattern, position sum
π Check multiple angles β the obvious grouping may be a distractor. Think laterally.
3
Coding-Decoding
βΌ
EJOTY Trick
Every 5th letter: E=5, J=10, O=15, T=20, Y=25 β use as anchors to find positions quickly.
Types of Coding
- Letter shift: +3 β A=D, B=E, C=F
- Skip coding: Skip 1 β AβC, BβD; Skip 2 β AβD
- Word coding: Each word replaced by another given word
- Number coding: Letters replaced by numbers per rule
- Reverse coding (ATBASH): A=Z, B=Y, C=Xβ¦
β
In exams: write AβZ with 1β26 below before solving β saves time per question
4
Number Series
βΌ
Common Patterns
- Arithmetic (AP): constant difference β 2, 5, 8, 11 (+3)
- Geometric (GP): constant ratio β 2, 6, 18, 54 (Γ3)
- Squares/Cubes: 1, 4, 9, 16, 25 or 1, 8, 27, 64
- Difference of differences (2nd order AP): 1, 3, 7, 13, 21 (diff: 2,4,6,8)
- Mixed: Fibonacci-like, alternating, prime series
π Always compute first-order differences first; if not constant, compute second-order differences
5
Alphabet Series
βΌ
Key Concepts
- Write AβZ with positions 1β26 and reverse ZβA with 1β26 for quick lookup
- Opposite letter pairs (sum = 27): AβZ, BβY, CβX, DβWβ¦
- Common patterns: skip 1, skip 2, reverse order, alternating pairs
π‘ EJOTY rule: E=5, J=10, O=15, T=20, Y=25 β memorise for instant position recall
6
Blood Relations
βΌ
| Term | Meaning |
|---|---|
| Maternal | From mother's side |
| Paternal | From father's side |
| Sibling | Brother or Sister |
| Spouse | Husband or Wife |
| Cousin | Uncle's or Aunt's child |
Strategy
- Draw a family tree immediately; use M/F labels for gender clarity
- Start from reference person, work outward step by step
π‘ "Son of B's father's only son" β B's father's only son = B himself β that person is B's son
7
Direction Test
βΌ
Key Tips
- Always draw a map; fix starting point, mark North upward
- Right turn (clockwise): NβEβSβWβN
- Left turn (anti-clockwise): NβWβSβEβN
- Final displacement (straight-line distance) = Pythagoras theorem
π Shadow direction: Morning sun is in East β shadow falls West. Evening sun West β shadow East
8
Order and Ranking
βΌ
Formula
- Position from left + Position from right = Total + 1
- Minimum total when two persons swap: find the overlap or gap
β
"If A ranks 5th from top and 8th from bottom β Total = 5+8β1 = 12"
9
Syllogism
βΌ
Venn Diagram Rules
- All A are B + All B are C β All A are C β
- No A are B + All B are C β No A are C β
- Some A are B + Some B are C β No definite conclusion β
- "Definitely" = true in ALL possible diagrams | "Possibility" = true in at least one
β οΈ Either-or: both conclusions individually wrong but together exhaustive β "Either I or II follows"
10
Venn Diagram
βΌ
Formula
- n(AβͺB) = n(A) + n(B) β n(Aβ©B)
- n(AβͺBβͺC) = n(A)+n(B)+n(C) β n(Aβ©B) β n(Bβ©C) β n(Aβ©C) + n(Aβ©Bβ©C)
π "Only A" = n(A) β n(Aβ©B) β n(Aβ©C) + n(Aβ©Bβ©C)
11
Statement and Conclusion
βΌ
Rules
- Conclusion must follow directly from the statement β no external assumptions
- Broad/general conclusions from specific statements = NOT valid
- Comparative conclusions need comparative data in the statement
β
Test: "Does the conclusion HAVE to be true if the statement is true?" β if yes, it follows
12
Mirror Image
βΌ
Rules
- Vertical mirror (left-right flip): Left β Right, Top/Bottom unchanged
- Horizontal mirror (top-bottom flip): Top β Bottom, Left/Right unchanged
- Letters unchanged in vertical mirror: A, H, I, M, O, T, U, V, W, X, Y
π Time in mirror: subtract clock time from 11:60 (for 12-hr clock without seconds)
13
Water Image
βΌ
Rules
- Water image = horizontal flip (Top β Bottom, Left/Right unchanged)
- Letters unchanged in water image: B, C, D, E, H, I, K, O, X
- Combination: Mirror + Water image = 180Β° rotation of original
14
Paper Folding
βΌ
Strategy
- Mentally "unfold" the paper step by step from last fold to first
- Holes made after folding appear symmetrically on both layers when unfolded
- Fold axis = line of symmetry; holes mirror across each fold axis
π‘ Practice by actually folding paper and punching β muscle memory helps in exams
15
Paper Cutting
βΌ
Approach
- Track fold lines carefully β cuts on folded paper create symmetric cuts when opened
- Number of pieces from n straight cuts through folded paper can increase exponentially
- Always unfold mentally from last fold backward
16
Embedded Figures
βΌ
Strategy
- Look for the given small figure hidden inside the larger complex figure
- Match line count, angles, and relative proportions β not just general shape
- The embedded figure must use the same lines as the complex figure (no extra lines)
π Rotate the answer options mentally if the figure might appear at an angle inside the complex figure
17
Figure Counting
βΌ
Types & Method
- Counting triangles: Count small + medium + large; use formula for standard grids
- Counting squares/rectangles: For nΓn grid: squares = nΒ²+(nβ1)Β²+β¦+1Β² | rectangles = βΏβΊΒΉCβ Γ βΏβΊΒΉCβ
- Counting straight lines: identify all possible paths along grid lines
β
Triangles in a triangle divided by n lines from apex: n(n+2)(2n+1)/8 β memorise for common patterns
18
Non-Verbal Series
βΌ
Pattern Types
- Rotation: figure rotated 45Β°, 90Β°, 180Β° in each step
- Size change: figure grows or shrinks progressively
- Addition/deletion: elements added or removed each step
- Movement: shading or elements move along a fixed path
π‘ Check changes in: shape, size, shading, number of elements, rotation β systematically
English Language
Grammar, Vocabulary & Practice Topics1
Noun
βΌ
Types of Nouns
- Proper: Names of specific people/places (Ram, India)
- Common: General names (boy, city)
- Collective: Group names (team, herd, flock)
- Abstract: Ideas/feelings (love, freedom, courage)
- Material: Substances (gold, water, wood)
π Countable nouns take a/an; uncountable nouns (water, advice, information) take no article and no plural 's'
2
Pronoun
βΌ
Types & Rules
- Personal: I/me, he/him, she/her, they/them, we/us, you
- Reflexive: myself, himself, themselves β used when subject = object
- Everyone/someone/nobody β singular pronoun (his/her, NOT their in formal English)
- Between two β each other | Among 3+ β one another
β οΈ "Between you and I" β β "Between you and me" β
(object form after preposition)
3
Verb
βΌ
Types
- Transitive: Requires an object (She reads a book)
- Intransitive: No object needed (He sleeps)
- Auxiliary: is/am/are/was/were/has/have/do/will/shall/can/may/must
- Modal: can, could, may, might, shall, should, will, would, must, ought to
π "Used to" = past habit (no longer true) | "Be used to" = accustomed to (present habit)
4
Adjective
βΌ
Degrees of Comparison
| Positive | Comparative | Superlative |
|---|---|---|
| good | better | best |
| bad | worse | worst |
| far | farther/further | farthest/furthest |
| many/much | more | most |
β οΈ Don't double compare: "more better" β | "more smarter" β
5
Adverb
βΌ
Types
- Manner (how): quickly, carefully | Place (where): here, there, away
- Time (when): now, soon, yesterday | Frequency: always, never, often
- Degree: very, quite, almost, enough (always placed before the word it modifies)
β
"Enough" comes after adjective/adverb: "good enough" β
| "enough good" β
6
Preposition
βΌ
Common Rules
- at (point): at noon, at the corner | in (enclosed space/period): in March, in India
- on (surface/day): on Monday, on the table | by (not later than): by 5 PM
- since (point of time): since 2010 | for (duration): for 3 years
- between (two) vs among (three or more)
β οΈ Never end a preposition sentence in formal writing: "With whom did she go?" β
7
Conjunction
βΌ
Types & Pairs
- Coordinating: FANBOYS β For, And, Nor, But, Or, Yet, So
- Correlative pairs: eitherβ¦or | neitherβ¦nor | bothβ¦and | not onlyβ¦but also | whetherβ¦or
- Subordinating: although, because, since, unless, until, if, when, while
π "Although" and "but" cannot be used together in same clause: "Although he tried, he failed" β
NOT "Although he tried but he failed" β
8
Articles
βΌ
Usage Rules
- A: before consonant sound (a university, a one-way)
- An: before vowel sound (an hour, an MBA, an honest man)
- The: specific/known noun, superlatives, unique things (the Sun), rivers, oceans, mountain ranges
- No article: languages, meals, sports, proper nouns (generally)
β
"The" before: the Ganges, the Himalayas, the Pacific β but NOT before India, America, Delhi
9
Tenses
βΌ
| Tense | Structure | Signal Words |
|---|---|---|
| Simple Present | V1 / V1+s/es | always, usually, every day |
| Present Continuous | am/is/are + V-ing | now, at present, currently |
| Present Perfect | has/have + V3 | just, already, yet, ever, never |
| Present Perfect Cont. | has/have been + V-ing | since, for (ongoing) |
| Simple Past | V2 | yesterday, ago, last year |
| Past Continuous | was/were + V-ing | while, when (background) |
| Past Perfect | had + V3 | before, after, by the time |
| Simple Future | will/shall + V1 | tomorrow, soon, next week |
10
Subject-Verb Agreement
βΌ
Key Rules
- Each / every / either / neither β always singular verb
- "A number of" β plural verb | "The number of" β singular verb
- Neitherβ¦nor / Eitherβ¦or β verb agrees with the nearer subject
- Collective nouns (team, jury) β singular when acting as one; plural when divided
β οΈ "The news is" β
| "The data are" β
(data is plural of datum) | "The police are" β
11
Active and Passive Voice
βΌ
Conversion Rule
- Object of active β Subject of passive
- Passive verb = is/am/are/was/were/be/been/being + V3
- Subject of active β "by + object" (optional if unknown/obvious)
| Active Tense | Passive Form |
|---|---|
| Simple Present | is/am/are + V3 |
| Simple Past | was/were + V3 |
| Present Perfect | has/have been + V3 |
| Simple Future | will be + V3 |
12
Direct and Indirect Speech
βΌ
Tense Backshift
| Direct (inside quotes) | Indirect |
|---|---|
| Simple Present | Simple Past |
| Present Continuous | Past Continuous |
| Present Perfect | Past Perfect |
| Simple Past | Past Perfect |
| will | would |
| can | could |
π "today" β "that day" | "tomorrow" β "the next day" | "yesterday" β "the previous day" | "here" β "there"
13
Synonyms
βΌ
Strategy
- Learn word roots: "bene" (good), "mal" (bad), "dict" (say), "rupt" (break), "port" (carry)
- Use context of surrounding sentence to infer meaning
- Eliminate options that are clearly opposite or unrelated first
| Word | Synonym |
|---|---|
| Abate | Reduce, Diminish |
| Acrimony | Bitterness, Hostility |
| Candid | Frank, Outspoken |
| Eloquent | Fluent, Expressive |
| Prudent | Wise, Careful |
14
Antonyms
βΌ
| Word | Antonym |
|---|---|
| Benevolent | Malevolent |
| Prolific | Barren |
| Verbose | Terse / Concise |
| Turbulent | Calm / Tranquil |
| Obsolete | Current / Modern |
π Build vocabulary from editorial sections of newspapers β target 10 new words daily with antonym pairs
15
One Word Substitution
βΌ
| Phrase | One Word |
|---|---|
| One who eats both plants and animals | Omnivore |
| One who does not believe in God | Atheist |
| Murder of one's own mother | Matricide |
| Fear of closed spaces | Claustrophobia |
| One who can use both hands equally | Ambidextrous |
| Government by the people | Democracy |
| Study of birds | Ornithology |
| Unable to pay debts | Insolvent |
16
Idioms and Phrases
βΌ
| Idiom | Meaning |
|---|---|
| Beat around the bush | Avoid the main topic |
| Break the ice | Initiate conversation |
| Bite the bullet | Endure a painful situation |
| Hit the nail on the head | Say exactly the right thing |
| Spill the beans | Reveal a secret |
| Under the weather | Feeling sick |
| Cost an arm and a leg | Very expensive |
| Once in a blue moon | Very rarely |
17
Spelling Correction
βΌ
Common Misspellings
| Wrong | Correct |
|---|---|
| Accomodation | Accommodation |
| Beleive | Believe |
| Definately | Definitely |
| Occurance | Occurrence |
| Seperate | Separate |
| Neccessary | Necessary |
β
Rule: "i before e except after c" β believe, achieve, receive, deceive
18
Error Detection
βΌ
Common Error Areas
- Subject-Verb agreement (Each, neither, either β singular)
- Tense consistency within a sentence
- Misuse of articles and prepositions
- Dangling modifiers and parallelism
- Double negatives ("didn't do nothing" β)
- Comparative errors ("more better" β)
π‘ Read each sentence part aloud mentally β your ear often catches errors faster than your eye
19
Sentence Improvement
βΌ
Approach
- Read the underlined part and identify what sounds wrong (tense, grammar, word choice)
- Check each option against the full sentence context
- "No improvement" is a valid answer β don't change correct sentences
π Common fixes: wrong preposition, wrong tense, incorrect article, wrong comparative form
20
Fill in the Blanks
βΌ
Approach
- Single blank: check grammar fit first (noun/verb/adj/adv), then meaning
- Double blank: eliminate options where either word fails β both must fit
- Connector words signal contrast (although, however) or cause (because, since)
21
Cloze Test
βΌ
Strategy
- Read the entire passage once for overall context before filling any blank
- Check grammatical category needed: noun/verb/adjective/adverb
- Eliminate options that break the logical/grammatical flow
β
The theme of the passage is your biggest clue β all blanks follow the same tone/idea
22
Reading Comprehension
βΌ
Strategy
- Read questions first, then skim passage for relevant paragraphs
- Main idea β check first and last paragraphs
- Inference questions β answer must be implied, not directly stated
- Tone/attitude β look for positive/negative/neutral language
β οΈ Never bring outside knowledge β answer ONLY from the passage
23
Para Jumbles
βΌ
Strategy
- Opening sentence: introduces topic, no pronoun reference back, no connector word at start
- Closing sentence: concluding tone (hence, thus, therefore), no further follow-up needed
- Look for pronounβnoun pairs and connector words (however, moreover, therefore)
- Use elimination to narrow down answer choices
General Awareness
History, Geography, Polity, Economics, Science & Current Affairs1
Ancient History
βΌ
Key Periods
- Indus Valley Civilisation: 2600β1900 BCE; major cities: Harappa, Mohenjo-daro, Lothal
- Vedic Age: Rigveda β oldest; Upanishads, Mahabharata, Ramayana
- Maurya Empire: Chandragupta Maurya (founded), Ashoka (greatest ruler); capital Pataliputra
- Gupta Empire: "Golden Age" of India β Chandragupta II; Aryabhata, Kalidasa
π Ashoka's Dhamma: non-violence, tolerance, respect for all religions β spread via rock/pillar edicts
2
Medieval History
βΌ
Key Dynasties & Events
- Delhi Sultanate (1206β1526): Slave, Khilji, Tughlaq, Sayyid, Lodi dynasties
- Mughal Empire (1526β1707): Babur (founder), Akbar (greatest), Aurangzeb (last powerful)
- Vijayanagara Empire: Hampi; Krishnadevaraya was greatest ruler
- Battle of Panipat: 1st (1526) Babur vs Ibrahim Lodi | 2nd (1556) Akbar vs Hemu | 3rd (1761) Marathas vs Afghans
3
Modern History
βΌ
Key Events
- Battle of Plassey (1757) β British East India Company victory; effective start of British rule
- Sepoy Mutiny / 1857 Revolt β first war of Independence; Mangal Pandey, Rani Laxmibai
- Indian National Congress founded: 1885 (A.O. Hume)
- Partition of Bengal: 1905 (Curzon) β sparked Swadeshi movement
- Montagu-Chelmsford Reforms: 1919 | Government of India Act: 1935
4
Freedom Movement
βΌ
Major Movements
- Non-Cooperation Movement (1920β22): Gandhi; withdrew from British institutions
- Civil Disobedience (1930): Dandi March β Salt Satyagraha; March 12, 1930
- Quit India Movement (1942): "Do or Die" β August 8, 1942
- INA: Subhas Chandra Bose; "Give me blood, I will give you freedom"
- Independence: August 15, 1947 | Constitution adopted: November 26, 1949 | Republic Day: January 26, 1950
5
Physical Geography
βΌ
Key Concepts
- Layers of Earth: Crust β Mantle β Outer Core (liquid) β Inner Core (solid)
- Plate tectonics: movement of tectonic plates causes earthquakes and volcanic activity
- Climate zones: Tropical, Subtropical, Temperate, Polar
- Atmosphere layers: Troposphere (weather), Stratosphere (ozone), Mesosphere, Thermosphere, Exosphere
6
Indian Geography
βΌ
Key Facts
- Area: 3.29 million kmΒ² (7th largest) | Population: ~1.4 billion (2nd largest)
- Longest river: Ganga | Largest state (area): Rajasthan | Smallest state: Goa
- Highest peak: Kangchenjunga (K2 is in Pakistan-administered territory)
- Major soil types: Alluvial (most fertile), Black (cotton), Red, Laterite, Desert
- Tropic of Cancer passes through: Gujarat, Rajasthan, MP, Chhattisgarh, Jharkhand, WB, Tripura, Mizoram
7
World Geography
βΌ
Quick Facts
- Largest country (area): Russia | Smallest: Vatican City
- Longest river: Nile (Africa) | Amazon (South America β largest by volume)
- Highest mountain: Mt. Everest (8,849 m) β Nepal/China border
- Largest ocean: Pacific | Largest continent: Asia | Smallest: Australia
- Deserts: Sahara (largest hot desert) | Antarctic (largest cold desert)
8
Constitution of India
βΌ
Key Facts
- Adopted: November 26, 1949 | Enforced: January 26, 1950
- Drafted by: Constituent Assembly (Chair: B.R. Ambedkar)
- Longest written constitution in the world
- Originally: 395 Articles, 8 Schedules | Now: 448 Articles, 12 Schedules, 25 Parts
- Preamble: Sovereign, Socialist, Secular, Democratic Republic
π "Socialist" and "Secular" were added by the 42nd Amendment (1976)
9
Fundamental Rights & Duties
βΌ
6 Fundamental Rights (Articles 12β35)
- Right to Equality (14β18) | Right to Freedom (19β22)
- Right Against Exploitation (23β24) | Right to Freedom of Religion (25β28)
- Cultural & Educational Rights (29β30) | Right to Constitutional Remedies (32)
Fundamental Duties (Article 51-A)
- Added by 42nd Amendment (1976) β originally 10 duties; 11th added by 86th Amendment (2002)
- Includes: respecting Constitution, national flag & anthem, protecting environment
10
Parliament & Judiciary
βΌ
Parliament
- Bicameral: Lok Sabha (Lower House, max 552) + Rajya Sabha (Upper House, max 250)
- Lok Sabha term: 5 years | Rajya Sabha: permanent; 1/3 retire every 2 years
- Money Bill can only be introduced in Lok Sabha
Judiciary
- Supreme Court: highest court; original + appellate + advisory jurisdiction
- Chief Justice of India appointed by President
- High Courts at state level | District Courts at district level
11
Basic Economics
βΌ
Key Concepts
- GDP: Gross Domestic Product β total value of goods/services in a country in a year
- GNP: GDP + Net factor income from abroad
- Inflation: CPI measures retail inflation | WPI measures wholesale inflation
- Fiscal Deficit: Total expenditure β Total receipts (excl. borrowings)
- Current Account Deficit: Imports of goods+services > Exports
12
Banking Basics
βΌ
- RBI: established 1935; nationalized 1949; HQ Mumbai; Governor heads RBI
- Repo Rate: RBI lends to banks | Reverse Repo: banks park money with RBI
- CRR: cash reserve kept with RBI | SLR: investment in govt securities
- NEFT (batch) | RTGS (real-time, min βΉ2L) | IMPS (24Γ7) | UPI (instant)
13
Budget & Economic Survey
βΌ
Union Budget
- Presented by Finance Minister | Article 112 (Annual Financial Statement)
- Revenue Budget: Revenue receipts + Revenue expenditure
- Capital Budget: Capital receipts + Capital expenditure (assets/liabilities)
Economic Survey
- Released before Union Budget by Ministry of Finance (Chief Economic Adviser)
- Covers: GDP growth, inflation, external trade, social sector analysis
14
Physics
βΌ
Key Topics for SSC
- Newton's Laws: Inertia, F=ma, Action-Reaction
- Light: reflection, refraction, total internal reflection, lenses (convex = converging, concave = diverging)
- Sound: travels fastest in solids; cannot travel in vacuum; speed β 343 m/s in air
- Electricity: Ohm's Law V=IR | Series: R = Rβ+Rβ | Parallel: 1/R = 1/Rβ + 1/Rβ
- SI units: Force = Newton | Energy = Joule | Power = Watt | Pressure = Pascal
15
Chemistry
βΌ
Key Topics for SSC
- Acids: pH < 7; taste sour (HCl, HβSOβ, HNOβ) | Bases: pH > 7; taste bitter (NaOH)
- pH scale: 0β14; pure water pH = 7 (neutral)
- Important compounds: NaCl (table salt), HβO (water), COβ (carbon dioxide), HβOβ (hydrogen peroxide)
- Rusting: Fe + Oβ + HβO β FeβOβ (iron oxide) β prevented by galvanisation (zinc coating)
- Radioactivity discovered by: Henri Becquerel | Marie Curie (Radium, Polonium)
16
Biology
βΌ
Key Topics for SSC
- Cell: basic unit of life; discovered by Robert Hooke (1665)
- DNA: Deoxyribonucleic acid β carries genetic information; double helix (Watson & Crick, 1953)
- Vitamins: A (vision), B (metabolism), C (immunity/scurvy), D (bones/rickets), K (clotting)
- Blood groups: A, B, AB (universal recipient), O (universal donor)
- Diseases: Malaria (Plasmodium, mosquito), TB (Mycobacterium), COVID-19 (SARS-CoV-2 virus)
17
National Affairs
βΌ
What to Track
- Government schemes and their ministries
- Cabinet reshuffles, new ministers and their portfolios
- State elections and new Chief Ministers
- Important bills passed in Parliament
π Read one quality newspaper daily or use a monthly current affairs digest β revise last 6 months before exam
18
International Affairs
βΌ
What to Track
- Heads of international organizations (UN, IMF, World Bank, WTO, WHO)
- India's bilateral and multilateral agreements
- G20, BRICS, SCO, ASEAN summits and outcomes
- Major international conflicts and peace agreements
19
Sports & Awards
βΌ
Sports
- Cricket: ICC tournament results, ICC rankings, Player of the Series awards
- Olympics & Commonwealth Games: Indian medal winners
- Grand Slams (Tennis): Australian Open, French Open, Wimbledon, US Open β winners
Awards
- Bharat Ratna, Padma Vibhushan, Bhushan, Shri (civilian awards)
- Arjuna Award (sport) | Khel Ratna (highest sports honour) | Dronacharya (coaches)
- Nobel Prize: Peace β Oslo; Literature, Science β Stockholm
20
Government Schemes
βΌ
| Scheme | Focus Area | Ministry |
|---|---|---|
| PM Awas Yojana | Housing for all | Housing & Urban Affairs |
| Swachh Bharat Mission | Sanitation & cleanliness | Jal Shakti / Housing |
| PM Kisan Samman | βΉ6000/year to farmers | Agriculture |
| Skill India | Vocational training | Skill Development |
| Make in India | Manufacturing growth | Commerce & Industry |
| Beti Bachao Beti Padhao | Girl child education | Women & Child Dev. |
| Ayushman Bharat | Health insurance βΉ5L/family | Health |
Computer Knowledge
Basics, Hardware, Software, Networking & Advanced Topics1
Basics of Computer
βΌ
Definition & Characteristics
- Electronic device: accepts data β processes β produces output
- Key traits: Speed, Accuracy, Storage, Automation, Versatility, Diligence
- IPO Cycle: Input β Process β Output
Number Systems
| System | Base | Digits Used |
|---|---|---|
| Binary | 2 | 0, 1 |
| Octal | 8 | 0β7 |
| Decimal | 10 | 0β9 |
| Hexadecimal | 16 | 0β9, AβF |
π 1 Byte = 8 bits | 1 KB = 1024 Bytes | 1 MB = 1024 KB | 1 GB = 1024 MB | 1 TB = 1024 GB
2
History & Generations of Computers
βΌ
| Generation | Technology | Era | Example |
|---|---|---|---|
| 1st | Vacuum Tubes | 1940sβ50s | ENIAC, UNIVAC |
| 2nd | Transistors | 1950sβ60s | IBM 7094 |
| 3rd | Integrated Circuits | 1960sβ70s | IBM 360 |
| 4th | Microprocessors (VLSI) | 1970sβpresent | Intel PCs |
| 5th | Artificial Intelligence | Present & future | AI systems |
Types of Computers
- Supercomputer (fastest) | Mainframe | Minicomputer | Microcomputer (Personal Computer)
3
Input Devices
βΌ
Common Input Devices
- Keyboard β primary text input device
- Mouse β pointing device; scroll, click, drag
- Scanner β converts physical document to digital image
- Microphone β captures audio input
- Webcam β captures video input
- Barcode Reader / OMR / OCR β specialized input devices
- Touchscreen β both input and output (I/O device)
- Joystick / Gamepad β for gaming/simulation
π‘ OMR = Optical Mark Recognition (MCQ sheets) | OCR = Optical Character Recognition (printed text)
4
Output Devices
βΌ
Common Output Devices
- Monitor (VDU) β visual display unit; soft copy output
- Printer β hard copy output; types: Inkjet, Laser, Dot Matrix, 3D
- Speaker β audio output
- Projector β displays enlarged image on screen
- Plotter β draws precise lines/diagrams (engineering/architecture)
| Printer Type | Technology | Best For |
|---|---|---|
| Laser | Toner + drum | High-volume text |
| Inkjet | Liquid ink | Photo quality color |
| Dot Matrix | Impact pins | Carbon copies |
5
Memory (RAM, ROM & Storage)
βΌ
| Type | Full Form | Volatile? | Use |
|---|---|---|---|
| RAM | Random Access Memory | Yes (lost on shutdown) | Working memory |
| ROM | Read Only Memory | No | Stores BIOS/firmware |
| Cache | β | Yes | Fastest memory, between CPU & RAM |
| HDD | Hard Disk Drive | No | Secondary storage |
| SSD | Solid State Drive | No | Faster secondary storage |
| Flash/USB | β | No | Portable storage |
β
Memory speed hierarchy (fastest to slowest): Registers β Cache (L1,L2,L3) β RAM β SSD β HDD β Cloud
6
Operating System
βΌ
Functions of OS
- Acts as interface between user and hardware
- Process management | Memory management | File management | Device management | Security
Types of OS
- Single-user (Windows) | Multi-user (Linux/Unix) | Real-time (RTOS) | Batch | Distributed
Popular OS
- Desktop: Windows, macOS, Linux | Mobile: Android (Google), iOS (Apple)
- Server: Linux, Windows Server | Embedded: RTOS, Android (IoT)
7
MS Word
βΌ
Key Shortcuts
| Shortcut | Action |
|---|---|
| Ctrl+S | Save |
| Ctrl+Z / Ctrl+Y | Undo / Redo |
| Ctrl+B / I / U | Bold / Italic / Underline |
| Ctrl+F | Find |
| Ctrl+H | Find & Replace |
| Ctrl+P | |
| Ctrl+A | Select All |
| F7 | Spell Check |
| Ctrl+Home / End | Go to beginning / end of document |
π Default extension: .docx | Earlier versions: .doc | Template: .dotx | Mail merge: bulk personalized letters
8
MS Excel
βΌ
Key Functions
- =SUM(A1:A10) | =AVERAGE(B1:B5) | =MAX() | =MIN() | =COUNT() | =COUNTA()
- =IF(condition, value_if_true, value_if_false)
- =VLOOKUP(value, table, col_index, [range]) | =HLOOKUP() (horizontal version)
- =CONCATENATE(A1, " ", B1) | =LEN(A1) | =LEFT/RIGHT/MID()
Key Facts
- Max rows: 1,048,576 | Max columns: 16,384 (XFD)
- Extension: .xlsx | Macro-enabled: .xlsm | Template: .xltx
β
Cell reference: A1 (relative), $A$1 (absolute), A$1 or $A1 (mixed)
9
MS PowerPoint
βΌ
Key Facts
- Extension: .pptx | Older: .ppt | Template: .potx
- Views: Normal, Slide Sorter, Notes Page, Reading View, Slide Show
- F5 = Start slide show from beginning | Shift+F5 = Start from current slide
- Transitions: animations between slides | Animations: effects on objects within slides
Common Office Shortcuts
- Ctrl+C/V/X β Copy/Paste/Cut | Ctrl+N β New | Ctrl+O β Open | F12 β Save As
10
Internet Basics
βΌ
Key Terms
- Internet: Global network of interconnected computers
- WWW: World Wide Web β system of interlinked web pages; invented by Tim Berners-Lee (1989)
- HTTP / HTTPS: Protocol for web; S = Secure (uses SSL/TLS encryption)
- IP Address: Unique identifier for each device; IPv4 = 32-bit; IPv6 = 128-bit
- Browser: Chrome, Firefox, Edge, Safari, Opera
- URL: Uniform Resource Locator β web address format: https://domain.com/path
- Email protocols: SMTP (send) | POP3 / IMAP (receive)
11
Networking
βΌ
| Term | Full Form / Meaning |
|---|---|
| LAN | Local Area Network β small area (office/home) |
| WAN | Wide Area Network β large geographic area; Internet = largest WAN |
| MAN | Metropolitan Area Network β city-wide |
| Router | Connects different networks; assigns/manages IP addresses |
| Switch | Connects devices within same LAN |
| Hub | Like switch but broadcasts to all ports (older, less efficient) |
| Modem | Modulator-Demodulator β converts digital β analog signals |
| DNS | Domain Name System β maps domain names to IP addresses |
| Firewall | Security system monitoring/filtering network traffic |
Network Topology
- Star (most common), Bus, Ring, Mesh, Tree, Hybrid
12
Cyber Security
βΌ
Common Threats
- Virus: Self-replicating malicious program; attaches to files
- Worm: Spreads across networks without user action; no host file needed
- Trojan Horse: Disguises as legitimate software; creates backdoor
- Ransomware: Encrypts data; demands ransom to restore (e.g., WannaCry)
- Spyware: Secretly monitors user activity; steals data
- Phishing: Fraudulent emails/sites to steal login credentials
- DDoS: Distributed Denial of Service β overwhelms server with traffic
Protection Tools
- Antivirus software | Firewall | VPN | Two-Factor Authentication (2FA) | Encryption
π‘ CERT-In (Computer Emergency Response Team β India) is the national agency for cyber incident response
13
Database Basics
βΌ
Key Concepts
- Database: Organised collection of structured data
- DBMS: Database Management System β software that manages databases (MySQL, Oracle, MS Access, PostgreSQL)
- RDBMS: Relational DBMS β data stored in tables with rows and columns; relationships between tables
- Table: Collection of rows (records/tuples) and columns (fields/attributes)
- Primary Key: Uniquely identifies each record; cannot be NULL or duplicate
- Foreign Key: Column in one table that references the primary key of another table
- Index: Speeds up data retrieval without changing table structure
SQL β Structured Query Language
| Command | Type | Purpose |
|---|---|---|
| SELECT | DQL | Retrieve data from table |
| INSERT | DML | Add new records |
| UPDATE | DML | Modify existing records |
| DELETE | DML | Remove records |
| CREATE | DDL | Create table/database |
| DROP | DDL | Delete table/database |
| ALTER | DDL | Modify table structure |
| GRANT/REVOKE | DCL | Set permissions |
Important SQL Clauses
- WHERE β filter records | ORDER BY β sort results | GROUP BY β group records
- HAVING β filter after GROUP BY | JOIN β combine rows from two or more tables
- DISTINCT β remove duplicate rows | LIMIT β restrict number of rows returned
Types of Joins
- INNER JOIN: Returns rows matching in both tables
- LEFT JOIN: All rows from left table + matching from right
- RIGHT JOIN: All rows from right table + matching from left
- FULL OUTER JOIN: All rows from both tables
Normalisation
- Process of organising database to reduce redundancy and improve integrity
- 1NF: No repeating groups | 2NF: No partial dependencies | 3NF: No transitive dependencies
β
SELECT * FROM Students WHERE marks > 90 ORDER BY name ASC; β retrieves top scorers alphabetically
π ACID properties: Atomicity, Consistency, Isolation, Durability β ensures reliable DB transactions