OPERATION SELECTION 🎯 | SSC CGL AIR 1 Master Revision & Prep Portal

Math 📐

1. Percentage Mastery (Complete Fraction Table, Successive & TCS Traps)

Percentage is the Backbone of SSC CGL Math. It directly powers Profit & Loss, Simple & Compound Interest, Ratio & Proportion, Mixture & Alligation, and Data Interpretation. AIR 1 speed requires instant fraction-percentage conversion without paper-pencil calculation.

1.1 Standard Fraction ↔ Percentage Master Table (Must Memorize)

Fraction	Percentage %	Decimal Value	SSC TCS Speed Trick / Memory Shortcut
$\frac{1}{2}$	$50\%$	0.50	Half value
$\frac{1}{3}$	$33.33\% / 33\frac{1}{3}\%$	0.333	$\frac{2}{3} = 66.66\% / 66\frac{2}{3}\%$
$\frac{1}{4}$	$25\%$	0.25	$\frac{3}{4} = 75\%$
$\frac{1}{5}$	$20\%$	0.20	$\frac{2}{5} = 40\%, \frac{3}{5} = 60\%, \frac{4}{5} = 80\%$
$\frac{1}{6}$	$16.66\% / 16\frac{2}{3}\%$	0.166	$\frac{5}{6} = 83.33\% \ (100\% - 16.66\%)$
$\frac{1}{7}$	$14.2857\% / 14\frac{2}{7}\%$	0.1428	Table of 14: $\frac{1}{7} = 14.28\%, \frac{2}{7} = 28.57\%, \frac{3}{7} = 42.85\%$
$\frac{1}{8}$	$12.5\% / 12\frac{1}{2}\%$	0.125	$\frac{3}{8} = 37.5\%, \frac{5}{8} = 62.5\%, \frac{7}{8} = 87.5\%$ (TCS Favorite)
$\frac{1}{9}$	$11.11\% / 11\frac{1}{9}\%$	0.111	Multiple of 11: $\frac{4}{9} = 44.44\%, \frac{7}{9} = 77.77\%$
$\frac{1}{10}$	$10\%$	0.10	Base multiplier
$\frac{1}{11}$	$9.09\% / 9\frac{1}{11}\%$	0.0909	Multiple of 9: $\frac{3}{11} = 27.27\%, \frac{7}{11} = 63.63\%$
$\frac{1}{12}$	$8.33\% / 8\frac{1}{3}\%$	0.0833	$\frac{5}{12} = 41.66\%, \frac{7}{12} = 58.33\%$
$\frac{1}{13}$	$7.69\% / 7\frac{9}{13}\%$	0.0769	$13 \times 7.69 \approx 100$
$\frac{1}{14}$	$7.14\% / 7\frac{1}{7}\%$	0.0714	Half of $\frac{1}{7}$ ($14.28 / 2 = 7.14\%$)
$\frac{1}{15}$	$6.66\% / 6\frac{2}{3}\%$	0.0666	TCS tests $66.66\%$ ($\frac{2}{3}$) vs $6.66\%$ ($\frac{1}{15}$)
$\frac{1}{16}$	$6.25\% / 6\frac{1}{4}\%$	0.0625	Half of $\frac{1}{8}$ ($12.5 / 2 = 6.25\%$). $\frac{3}{16} = 18.75\%$
$\frac{1}{17}$	$5.88\% / 5\frac{15}{17}\%$	0.0588	TCS Mains special fraction
$\frac{1}{18}$	$5.55\% / 5\frac{5}{9}\%$	0.0555	Half of $\frac{1}{9}$ ($11.11 / 2 = 5.55\%$)
$\frac{1}{19}$	$5.26\% / 5\frac{5}{19}\%$	0.0526	$19 \times 5.26 \approx 100$
$\frac{1}{20}$	$5\%$	0.050	Standard
$\frac{1}{24}$	$4.16\% / 4\frac{1}{6}\%$	0.0416	Half of $\frac{1}{12}$ ($8.33 / 2 = 4.16\%$)
$\frac{1}{25}$	$4\%$	0.040	Standard

1.2 Core Formulas & Quick Calculators

Successive Percentage Change (2 Vars)

$\text{Net \%} = a + b + \frac{a \cdot b}{100}$

For increase use $(+)$, for decrease use $(-)$. E.g., $+20\%$ and $-10\% \implies 20 - 10 - \frac{200}{100} = +8\%$.

Reverse Percentage Rule

$\text{\% Less} = \left[ \frac{x}{100 + x} \right] \times 100$

If A is $x\%$ more than B, then B is $\left[\frac{x}{100+x}\right]\%$ less than A. If A is $x\%$ less, B is $\left[\frac{x}{100-x}\right]\%$ more.

Income - Expenditure - Savings

$\text{Income} = \text{Expenditure} + \text{Savings}$

Use Ratio Method: If Exp increases by $x\%$, Savings by $y\%$, Net Income $\%$ = Weighted Average (Allegation).

Population Growth / Depreciation

$P_{\text{final}} = P_{\text{initial}} \times \left(1 \pm \frac{r}{100}\right)^n$

For $n$ years. Ratio method (Initial : Final) is 3x faster than exponent expansion.

Figure 1.1: Visualizing Reverse Percentage & Equilibrium (e.g. +25% followed by -20% returns to 100).

SSC TCS EXAMINER TRAP ALERT #1 (Percentage)

Voting / Election Trap: Examiners give: "10% voters didn't cast vote, 10% cast votes were invalid, winner got 60% of VALID votes and won by 3240 votes." Students mistake "60% of total" vs "60% of valid". TCS Trap Rule: Always draw the Tree Diagram starting from $100x$!
Total = $100x \implies$ Cast = $90x \implies$ Valid = $90x \times 0.9 = 81x$. Winner = $60\%$ of $81x$, Loser = $40\%$ of $81x$. Diff = $20\%$ of $81x = 16.2x = 3240 \implies x = 200 \implies$ Total = $20,000$.
Consumption-Price Trap: If price of sugar increases by $33\frac{1}{3}\%\ (\frac{1}{3})$, consumption must decrease by $25\%\ (\frac{1}{4})$ to keep expenditure constant! $\left[\frac{1}{n+1}\right]$ decrease for $\left[\frac{1}{n}\right]$ increase.
Percentage DI Calculation Trap: In Mains Pie Charts, don't compute exact absolute values for ratio or percentage questions! Cancel out the total base value directly.

Math 📐

2. Triangles & Geometry AIR 1 Blueprint (Centroid, Medians & Important Theorems)

Geometry carries the maximum weightage in SSC CGL Mains (4 to 6 questions). Master Centroid 2:1 division, Euler line, BPT / Thales theorem, Midpoint theorem, Apollonius theorem, and Excircle geometry with vector diagrams below.

2.1 Centroid ($G$) & Median Division Master Diagrams

The 3 medians of a triangle intersect at the Centroid ($G$). Understand the two fundamental median properties tested by TCS:

Diagram A: Centroid Divides Medians in 2:1 Ratio

Centroid Ratio Rule: Centroid $G$ divides each median in the ratio $2 : 1$ from vertex to midpoint.
$$\mathbf{\frac{AG}{GD} = \frac{BG}{GE} = \frac{CG}{GF} = \frac{2}{1}}$$

Diagram B: 3 Medians Divide Triangle into 6 Equal Areas

Area Division Property: The 3 medians divide $\triangle ABC$ into 6 small triangles of EXACTLY EQUAL AREA ($\text{Area} = \frac{1}{6} \Delta$).

2.2 Important Geometry Theorems: BPT, Midpoint, Apollonius & Excircle

Below are the 4 core geometry theorems with dedicated vector diagrams, TCS speed shortcuts, and candidate confusion alerts.

Theorem 1: Basic Proportionality Theorem (BPT / Thales Theorem)

BPT Statement: If a line $DE$ is drawn parallel to side $BC$ intersecting $AB$ at $D$ and $AC$ at $E$, then: $$\mathbf{\frac{AD}{DB} = \frac{AE}{EC}} \iff \mathbf{\frac{AD}{AB} = \frac{AE}{AC} = \frac{DE}{BC}}$$

TCS CONFUSION TRAP #1: BPT Parallel Line Ratio Error

❌ Fatal Student Mistake: Students write $\frac{AD}{DB} = \frac{DE}{BC}$. This is completely WRONG!
✔ Correct Rule: The parallel side ratio $\frac{DE}{BC}$ requires the TOTAL SIDE $AB$ of the large triangle $\triangle ABC$ ($\triangle ADE \sim \triangle ABC$): $$\mathbf{\frac{AD}{AB} = \frac{DE}{BC}}, \quad \text{NOT } \frac{AD}{DB}!$$

Theorem 2: Midpoint Theorem & Area Ratio ($1 : 3$)

Midpoint Theorem Statement: Segment joining midpoints $D$ and $E$ is **parallel to $BC$** and **half its length**: $$\mathbf{DE \parallel BC} \quad \text{and} \quad \mathbf{DE = \frac{1}{2} BC}$$

Theorem 3: Apollonius Theorem (Median Length Calculation)

Apollonius Theorem Formula: In any triangle $\triangle ABC$ with median $AD$ to side $BC$: $$\mathbf{AB^2 + AC^2 = 2\left(AD^2 + BD^2\right)}$$

Theorem 4: Excircle & Exradii Geometry ($r_a, r_b, r_c$)

Exradii Formulas: $r_a = \frac{\Delta}{s - a}, \ r_b = \frac{\Delta}{s - b}, \ r_c = \frac{\Delta}{s - c}$. Master relation: $\mathbf{\frac{1}{r} = \frac{1}{r_a} + \frac{1}{r_b} + \frac{1}{r_c}}$.

SSC TCS EXAMINER TRAP ALERT #2 (Triangles & Geometry - Visual Breakdown)

Trap 1: Angle Bisector Ratio ($\frac{BD}{DC} = \frac{AB}{AC}$) vs Median ($BM = MC$)

Angle Bisector Theorem: Angle bisector $AD$ divides base $BC$ in ratio of adjacent sides: $$\mathbf{\frac{BD}{DC} = \frac{AB}{AC} = \frac{10}{18} = \frac{5}{9}}$$ ⚠️ TCS Trap: Bisector $D$ is NOT the midpoint of $BC$! Since $AB < AC$, point $D$ lies closer to $B$ (smaller side pulls $D$ towards it). Median $M$ always bisects base equally ($BM = MC$).

Trap 2: Circumradius ($R$) vs Inradius ($r$) of Equilateral Triangle ($R : r = 2 : 1$)

Radius & Area Ratios for Equilateral Triangle: $$\mathbf{R : r = 2 : 1} \quad \text{and} \quad \mathbf{\text{Area of Circumcircle} : \text{Area of Incircle} = R^2 : r^2 = 4 : 1}$$

Trap 3: Orthocentre ($H$) at $90^\circ$ Vertex vs Circumcentre ($O$) at Hypotenuse Midpoint

Right Triangle Centers Rule: Orthocentre $H$ lies at the $90^\circ$ vertex $A$. Circumcentre $O$ lies at the midpoint of hypotenuse $BC$.
$$\mathbf{\text{Distance } HO = R = \frac{\text{Hypotenuse}}{2} = \frac{c}{2}}$$

Trap 4: Euler Line Collinear Ratio ($HG : GO = 2 : 1$) & Nine-Point Center ($N$)

Euler Line Ratio: $\mathbf{HG : GO = 2 : 1}$ (Orthocentre to Centroid $= 2$ parts, Centroid to Circumcentre $= 1$ part). Nine-point center $N$ is the exact midpoint of $HO$, making $\mathbf{HN : NG : GO = 3 : 1 : 2}$.

GS 🌍

3. Ancient History: Indus Valley Civilization (IVC / Harappan Civilization)

IVC is a guaranteed 1 to 2 question topic in SSC CGL Tier 1 and Tier 2. SSC questions focus strictly on Site-River mapping, Excavators, Unique Discoveries, and Town Planning features.

Timeline

2600 BCE - 1900 BCE (Mature Phase)

Bronze Age Civilization. Radiocarbon dating confirmation (C-14). Total area $\approx 1.3 \text{ million sq km}$ (Triangular shape).

Geographical Boundaries

N: Manda | S: Daimabad | E: Alamgirpur | W: Sutkagen Dor

North: Manda (Chenab, J&K), South: Daimabad (Pravara/Godavari, MH), East: Alamgirpur (Hindon, UP), West: Sutkagen Dor (Dasht, Pak-Iran border).

3.1 IVC Master Site - River - Excavator - Key Discoveries Table

Site Name	River	Location / State	Excavator & Year	Unique SSC TCS Discoveries
Harappa	Ravi	Sahiwal, Punjab (Pakistan)	Daya Ram Sahni (1921)	6 Granaries in a row, Coffin burial (R-37 cemetery), Bronze sex-identified figurines, Red sandstone torso.
Mohenjo-daro ("Mound of the Dead")	Indus	Larkana, Sindh (Pakistan)	R.D. Banerji (1922)	Great Bath, Great Granary (largest structure), Bronze Dancing Girl (Lost-Wax technique), Pashupati Seal, Steatite Bearded Priest.
Lothal	Bhogava	Ahmedabad, Gujarat	S.R. Rao (1954)	Artificial Tidal Dockyard (World's earliest), Rice husk remains, Fire altars, Persian seal, Chess board.
Kalibangan ("Black Bangles")	Ghaggar	Hanumangarh, Rajasthan	Amalananda Ghosh (1953), B.B. Lal & B.K. Thapar	Ploughed field surface (earliest evidence), Wooden drainage, Fire altars, Camel bones.
Chanhudaro	Indus	Nawabshah, Sindh (Pakistan)	N.G. Majumdar (1931), E.J.H. Mackay	Only IVC city WITHOUT a Citadel! Bead-making factory, Lipstick/Cosmetics, Footprint of dog chasing cat on brick.
Dholavira	Luni	Kutch, Gujarat	J.P. Joshi (1967), R.S. Bisht (1990)	3-Tier Town Planning (Citadel, Middle Town, Lower Town), Unique Water Harvesting Reservoir, 10-letter Signboard. (UNESCO World Heritage 2021).
Banawali	Rangoi / Saraswati	Fatehabad, Haryana	R.S. Bisht (1974)	Clay model of plough, High quality Barley seeds, Lack of systematic drainage.
Rakhigarhi	Ghaggar	Hisar, Haryana	Amarendra Nath (1997-2000)	Largest IVC Site in India (and overall largest site). DNA study of skeletal remains.
Surkotada	-	Kutch, Gujarat	J.P. Joshi (1964)	Remains of Horse bones (only site with horse bone evidence), Pot burials.

3.2 Town Planning, Trade, Seals & Religion

Town Planning & Bricks

Grid System | Brick Ratio $1 : 2 : 4$

Underground covered drainage system with inspection manholes. Burnt bricks used in housing. Main streets intersected at $90^\circ$ angles.

Seals & Script

Steatite Material | Boustrophedon Script

Script was pictographic, written right to left then left to right (Undeciphered). Most common seal motif: Unicorn.

Agriculture & Crops

Wheat, Barley, Cotton (Sindon)

First in the world to produce Cotton! Mesopotamians called Harappan region "Meluha".

Religion & Worship

Mother Goddess | Pashupati Mahadeva

No temples found! Worshipped Mother Goddess (Fertility), Pashupati (surrounded by Elephant, Tiger, Rhino, Buffalo & 2 Deer), Peepal tree, Humped Bull.

Figure 3.1: Geographical Boundaries of Indus Valley Civilization.

SSC TCS EXAMINER TRAP ALERT #3 (Indus Valley Civilization)

Iron vs Bronze Trap: IVC people were NOT AWARE OF IRON! Iron was discovered in India during Later Vedic Period (around 1000 BCE at Atranjikhera). IVC was a Bronze Age civilization (Copper + Tin).
Horse Evidence Trap: IVC was NOT a horse-centered civilization. Only Surkotada (Gujarat) yielded bone remains of horse.
Citadel Trap: Chanhudaro is the ONLY city without a Citadel. Dholavira is divided into 3 parts (Citadel, Middle Town, Lower Town) unlike standard 2-part cities.
Lothal Dockyard vs Dholavira Reservoir: Artificial Dockyard = Lothal; Water Reservoir system = Dholavira.

GS 🌍

4. Polity: Making of Constitution, Preamble & Schedules

Indian Polity is the highest scoring area in GS. Questions on Assembly dates, Drafting committee members, Preamble amendments, and Schedules are asked in almost every shift.

Cabinet Mission Plan (1946)

3 Members: Pethick-Lawrence, Cripps, Alexander

Formulated the scheme for Constituent Assembly. Total initial strength: 389 (296 British India + 93 Princely States). Reduced to 299 after partition.

Key Dates & Key Personalities

Dec 9 (1st Mtg) | Dec 11 (President) | Dec 13 (Objective Res)

Temporary Chairman: Dr. Sachchidananda Sinha. Permanent President: Dr. Rajendra Prasad. Constitutional Advisor: Sir B.N. Rau.

Drafting Committee (Aug 29, 1947)

Chairman: Dr. B.R. Ambedkar (7 Members)

Members: Ambedkar, N. Gopalaswami Ayyangar, Alladi Krishnaswami Ayyar, Dr. K.M. Munshi, Syed Mohammad Saadullah, N. Madhava Rau (replacing B.L. Mitter), T.T. Krishnamachari (replacing D.P. Khaitan).

Time, Cost & Adoption

2 Yrs, 11 Mos, 18 Days | ₹64 Lakh Cost

Adopted: 26 November 1949 (Constitution Day). Enforced: 26 January 1950 (Republic Day - to mark 1930 Lahore Session Poorna Swaraj declaration).

Feature	Original Constitution (26 Jan 1950)	Present Constitution (2026)	SSC TCS Exam Context
Preamble	1 Preamble	1 Preamble (Amended ONCE)	42nd Amendment 1976 added: Socialist, Secular, Integrity.
Parts	22 Parts	25 Parts	Added: IVA (Fundamental Duties), IXA (Municipalities), IXB (Cooperatives), XIVA (Tribunals). Deleted: Part VII.
Articles	395 Articles	448+ Articles	Numbered up to 395 structurally, but with sub-articles (e.g. 21A, 51A).
Schedules	8 Schedules	12 Schedules	9th (1st Amend 1951), 10th (52nd Amend 1985), 11th (73rd Amend 1992), 12th (74th Amend 1992).
Calligrapher	Prem Behari Narain Raizada	-	Handwritten in italic style. Decorated by Nandalal Bose & Beohar Rammanohar Sinha.

4.2 Borrowed Features of the Indian Constitution

Country / Source	Borrowed Features (Frequently Asked in SSC CGL)
British Constitution (UK)	Parliamentary Form of Govt, Rule of Law, Cabinet System, Single Citizenship, Bicameralism, Prerogative Writs, Speaker's office.
US Constitution (USA)	Fundamental Rights, Judicial Review, Independence of Judiciary, Impeachment of President, Removal of SC/HC Judges, Preamble.
Irish Constitution (Ireland)	Directive Principles of State Policy (DPSP), Nomination of members to Rajya Sabha, Method of election of President.
USSR / Russia	Fundamental Duties (Article 51A), Ideals of Justice (Social, Economic, Political) in Preamble, 5-Year Plans.
Canadian Constitution	Federation with a strong Centre, Residuary powers with Centre, Appointment of State Governors by Centre, Advisory jurisdiction of SC.
Australian Constitution	Concurrent List, Freedom of Trade & Commerce, Joint Sitting of two Houses of Parliament (Art 108).
Weimar Constitution (Germany)	Suspension of Fundamental Rights during Emergency.
South Africa	Procedure for Amendment of Constitution (Art 368), Election of members of Rajya Sabha.

4.3 Preamble & 12 Schedules (Trick: TEARS OF OLD PM)

AIR 1 Memory Trick for 12 Schedules: "TEARS OF OLD PM"

T - Territories & States (Schedule 1)
E - Emoluments, Salaries & Allowances (Schedule 2)
A - Affirmations & Oaths (Schedule 3)
R - Rajya Sabha Seat Allocation (Schedule 4)
S - Scheduled Areas Administration (Schedule 5)
O - Other Tribal Areas (ATM-M: Assam, Tripura, Meghalaya, Mizoram) (Schedule 6)
F - Federal Lists (Union, State, Concurrent) (Schedule 7)
O - Official Languages (22 Languages) (Schedule 8)
L - Land Reforms (1st Amendment 1951) (Schedule 9)
D - Anti-Defection Law (52nd Amendment 1985) (Schedule 10)
P - Panchayats (73rd Amendment 1992 - 29 Subjects) (Schedule 11)
M - Municipalities (74th Amendment 1992 - 18 Subjects) (Schedule 12)

SSC TCS EXAMINER TRAP ALERT #4 (Polity)

Berubari vs Kesavananda Bharati Case Trap: In Berubari Union Case (1960), SC held Preamble is NOT a part of Constitution. But in Kesavananda Bharati Case (1973), SC overruled and declared Preamble IS a part of the Constitution and can be amended under Art 368 without altering Basic Structure.
Adoption vs Enforcement Date Trap: Adoption = 26 November 1949. Enforcement = 26 January 1950. Don't confuse the two in TCS MCQs!
Schedule 6 ATM-M Exception Trap: Schedule 6 covers Assam, Meghalaya, Tripura, Mizoram. Manipur is NOT included! (SSC repeatedly tests this trap).

GS 🌍

5. Static GK: Important Mountain Passes of India (State-Wise & Strategic Mapping)

Mountain Passes of India is one of the most favorite static GK topics of TCS. Examiners ask questions on Pass - State mapping, Connectivity between cities, and River entries.

Pass Name	State / UT	Connects / Strategic Importance	SSC TCS High-Yield Fact
Zoji La	Ladakh / J&K	Srinagar to Leh (NH 1)	Crucial pass across Zaskar Range. Extremely frequent in PYQs.
Banihal Pass	Jammu & Kashmir	Jammu to Srinagar	Houses the famous Jawahar Tunnel across Pir Panjal Range.
Rohtang Pass	Himachal Pradesh	Kullu Valley to Lahaul & Spiti	Houses Atal Tunnel (9.02 km long - World's longest highway single-tube tunnel above 10,000 ft).
Shipki La	Himachal Pradesh	Himachal to Tibet	Sutlej River enters India through this pass!
Nathu La	Sikkim	Sikkim (Gangtok) to Lhasa (Tibet)	Ancient Silk Route branch. Reopened for trade in 2006. Used for Kailash Mansarovar Yatra.
Jelep La	Sikkim	Sikkim to Lhasa (Tibet)	Passes through Chumbi Valley.
Lipulekh Pass	Uttarakhand	Uttarakhand to Tibet	Tri-junction of India, China & Nepal. Main route for Kailash Mansarovar Yatra.
Bomdi La	Arunachal Pradesh	Arunachal to Lhasa (Tibet)	Located in Greater Himalayas east of Bhutan.
Thal Ghat	Maharashtra	Mumbai to Nashik / North India	Western Ghats (Sahyadri) pass.
Bhor Ghat	Maharashtra	Mumbai to Pune / South India	Western Ghats pass (NH 48).
Pal Ghat	Kerala / TN	Palakkad (Kerala) to Coimbatore (TN)	Major gap in Western Ghats between Nilgiri Hills & Anaimalai Hills.

Figure 5.1: Key Strategic Mountain Passes across Himalayas & Western Ghats.

SSC TCS EXAMINER TRAP ALERT #5 (Mountain Passes)

River Entry Trap: Sutlej river enters India through Shipki La (Himachal Pradesh). Indus flows between Ladakh & Zaskar ranges.
Kailash Mansarovar Yatra Routes: Main traditional route = Lipulekh Pass (Uttarakhand). Reopened motorable route = Nathu La Pass (Sikkim).
Nilgiri Separator Trap: Pal Ghat gap separates Nilgiri Hills to the north from Anaimalai Hills to the south.

English 📜

6. English Grammar: 20 Most High-Yield Rules for Spotting Errors & Improvement

In SSC CGL Mains, English carries 135 marks (45 questions × 3 marks). Error Spotting and Sentence Improvement depend 100% on mastering these core grammar rules.

#	Grammar Rule Title	Rule Explanation	SSC TCS Incorrect vs Correct Example
1	Subject Joined by 'As well as', 'With', 'Along with'	When two subjects are joined by as well as, along with, with, together with, in addition to, accompanied by, the verb agrees with the FIRST SUBJECT.	❌ The Captain along with his sailors were drowned. ✔ The Captain along with his sailors was drowned.
2	Either...Or / Neither...Nor Agreement	When two subjects are joined by either...or, neither...nor, not only...but also, the verb agrees with the NEAREST SUBJECT.	❌ Neither the teacher nor the students was present. ✔ Neither the teacher nor the students were present.
3	Scarcely / Hardly...When	Scarcely and Hardly are followed by WHEN (not than), and take inverted auxiliary verb order (`Hardly + had + S + V3... when`).	❌ Hardly had I reached the station than the train left. ✔ Hardly had I reached the station when the train left.
4	No Sooner...Than	No sooner is followed by THAN (not when/then), with inversion (`No sooner + did/had + S... than`).	❌ No sooner did he see the police when he ran away. ✔ No sooner did he see the police than he ran away.
5	Lest...Should	Lest means "for fear that" and is ALWAYS followed by SHOULD or base verb. It is inherently negative, so NO 'NOT' after lest!	❌ Work hard lest you will not fail. ✔ Work hard lest you should fail.
6	Conditional Type 3 (Past Unfulfilled)	`If + Subject + HAD + V3, Subject + WOULD HAVE + V3`.	❌ If he would have worked hard, he would pass. ✔ If he had worked hard, he would have passed.
7	Hyphenated Nouns / Compound Adjectives	A compound noun functioning as an adjective NEVER takes a plural 's'.	❌ He gave me a five-rupees note. ✔ He gave me a five-rupee note.
8	Each / Every + Singular Verb	Each, Every, Everyone, Someone, Nobody, Either, Neither always take a SINGULAR VERB and SINGULAR PRONOUN (his/her).	❌ Every student must submit their project. ✔ Every student must submit his/her project.
9	Prefer / Preferable + TO	Prefer, preferable, superior, inferior, senior, junior, prior take preposition TO (never 'than'). Do not use 'more' with preferable!	❌ Coffee is more preferable than tea. ✔ Coffee is preferable to tea.
10	One of the + Plural Noun + Singular Verb	`One of + Plural Noun + Singular Verb`. BUT if relative pronoun (who/which/that) comes, verb agrees with antecedent (Plural)!	❌ One of my friends are a doctor. ✔ One of my friends is a doctor.
11	Uncountable Nouns (No Plural 's')	Nouns like furniture, advice, information, poetry, luggage, equipment, hair, mischief are uncountable. They never take 'a/an' or plural 's'.	❌ He gave me many advices and furnitures. ✔ He gave me much advice and items of furniture.
12	Order of Personal Pronouns (231 & 123 Rule)	Normal/Good sense: 2nd → 3rd → 1st person (231). Confession/Mistake/Plural: 1st → 2nd → 3rd person (123).	❌ I, you and he will study together. ✔ You, he and I will study together.
13	Gerund after Prepositions & Specific Phrases	Phrases like look forward to, used to, prone to, addicted to, with a view to take V1 + ing (Gerund), not base V1!	❌ I am looking forward to meet you. ✔ I am looking forward to meeting you.
14	Comparative Degree Double Use Trap	Never use double comparatives or double superlatives together (e.g. more better, most smartest).	❌ She is more wiser than her sister. ✔ She is wiser than her sister.
15	Between vs Among	Between is used for TWO persons/things or mutual relationship among distinct entities. Among is used for MORE THAN TWO.	❌ Divide the sweets between all five children. ✔ Divide the sweets among all five children.
16	Since vs For (Time Prepositions)	Since for a specific point in time (since 1999, since 8 AM). For for a period/duration of time (for 5 hours, for 3 years).	❌ He has been living here since 5 years. ✔ He has been living here for 5 years.
17	Subjective vs Objective Pronoun after 'Than'	When comparing subjects, use nominative (subjective) case pronoun after than / as.	❌ He is taller than me. ✔ He is taller than I (am).
18	Nouns Plural in Form but Singular in Meaning	Mathematics, Physics, News, Politics, Economics, Ethics, Innings, Gallows take a Singular Verb.	❌ Mathematics are a difficult subject. ✔ Mathematics is a difficult subject.
19	Nouns Always Plural in Form & Verb	Trousers, Scissors, Spectacles, Pliers, Alms, Assets, Surroundings, Savings take a Plural Verb.	❌ My spectacles is broken. ✔ My spectacles are broken. (A pair of spectacles IS...)
20	Die OF vs Die FROM	Die OF a disease/illness (malaria, cancer). Die FROM a cause/overwork/snakebite/loss of blood.	❌ He died from cholera. ✔ He died of cholera.

Math 📐

1. Ratio & Proportion, Partnership, Mixture & Alligation (Day 2 Masterclass)

Ratio & Proportion powers almost 40% of SSC CGL Math (Ages, Income-Expenditure, Partnerships, Mixtures, DI). Master these core formulas, Alligation diagrams, and replacement rules.

1.1 Types of Ratio & Proportion Definitions

Ratio Concept	Formula / Relation	Example / TCS Quick Shortcut
Compound Ratio	$\frac{a}{b} \times \frac{c}{d} = \mathbf{\frac{ac}{bd}}$	Compound ratio of $2:3$ and $5:7 = (2 \times 5) : (3 \times 7) = \mathbf{10 : 21}$.
Duplicate Ratio	$\mathbf{a^2 : b^2}$	Duplicate ratio of $3:4 = 3^2 : 4^2 = \mathbf{9 : 16}$.
Sub-duplicate Ratio	$\mathbf{\sqrt{a} : \sqrt{b}}$	Sub-duplicate ratio of $25:36 = \sqrt{25} : \sqrt{36} = \mathbf{5 : 6}$.
Triplicate Ratio	$\mathbf{a^3 : b^3}$	Triplicate ratio of $2:3 = 2^3 : 3^3 = \mathbf{8 : 27}$.
Sub-triplicate Ratio	$\mathbf{\sqrt[3]{a} : \sqrt[3]{b}}$	Sub-triplicate ratio of $27:64 = \mathbf{3 : 4}$.
Mean Proportional	$x = \mathbf{\sqrt{ab}}$	Mean proportional of 4 and 16 $= \sqrt{4 \times 16} = \sqrt{64} = \mathbf{8}$.
Third Proportional	$c = \mathbf{\frac{b^2}{a}}$	Third proportional to $a, b$ ($a:b = b:c \implies c = b^2/a$). To 4 and 12 $= 12^2 / 4 = \mathbf{36}$.
Fourth Proportional	$d = \mathbf{\frac{bc}{a}}$	Fourth proportional to $a, b, c$ ($a:b = c:d \implies d = bc/a$). To 3, 6, 9 $= (6 \times 9)/3 = \mathbf{18}$.
Componendo & Dividendo	If $\frac{a}{b} = \frac{c}{d} \implies \mathbf{\frac{a+b}{a-b} = \frac{c+d}{c-d}}$	Crucial for solving fraction equations instantly in Algebra & Trigonometry!

1.2 Partnership Basics & Profit Division

General Profit Division Rule

$\text{Profit Ratio} = (C_1 \times T_1) : (C_2 \times T_2) : (C_3 \times T_3)$

Profit is directly proportional to the product of Capital Investment ($C$) and Time Period ($T$).

Working vs Sleeping Partner

$\text{Divisible Profit} = \text{Total Profit} - \text{Working Salary}$

Working partner salary/commission must be deducted from Total Profit FIRST before dividing remaining profit in capital-time ratio!

1.3 Rule of Alligation & Replacement Formula

Diagram 2.1: The Rule of Alligation Cross Diagram

Rule of Alligation Formula: $$\mathbf{\frac{\text{Quantity of Cheaper } (Q_C)}{\text{Quantity of Dearer } (Q_D)} = \frac{\text{Dearer Price } (d) - \text{Mean Price } (m)}{\text{Mean Price } (m) - \text{Cheaper Price } (c)} = \frac{d - m}{m - c}}$$

Master Formula: Liquid Removal & Replacement

If a container holds $V$ litres of liquid (e.g. pure milk), and $x$ litres are drawn out and replaced with water, and this operation is repeated $n$ times, then: $$\mathbf{\text{Final Quantity of Pure Milk Remaining} = V \times \left(1 - \frac{x}{V}\right)^n}$$ $$\mathbf{\frac{\text{Final Milk Quantity}}{\text{Initial Milk Quantity}} = \left(1 - \frac{x}{V}\right)^n}$$

SSC TCS EXAMINER TRAP ALERT #6 (Ratio & Alligation)

Alligation Base Unit Trap: When applying Alligation to Speed (km/h), the resulting ratio is of TIME (not distance)! When applying Alligation to Profit % (on Cost Price), resulting ratio is of COST PRICE (not Selling Price!). Always look at the denominator of the unit!
Replacement Ratio Trap: TCS gives: "Milk and water ratio in final mixture is 64:17 after 2 operations." Students take final milk = 64. Correct: Total volume $V = 64 + 17 = 81$. So $\frac{\text{Milk}}{\text{Total}} = \frac{64}{81} = \left(1 - \frac{x}{V}\right)^2 \implies 1 - \frac{x}{V} = \frac{8}{9} \implies \frac{x}{V} = \frac{1}{9}$!

Math 📐

2. Algebra Masterclass (Cubic Identities, $x + \frac{1}{x}$ Shortcuts & Quadratics)

Algebra is 100% formula and pattern recognition. Master the master cubic identity, power expansion rules for $x + \frac{1}{x}$, and quadratic maximum/minimum values.

2.1 The Master Cubic Identity & TCS Special Cases

The Master Cubic Expansion

$$\mathbf{a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)}$$ $$\mathbf{= \frac{1}{2}(a+b+c)\left[(a-b)^2 + (b-c)^2 + (c-a)^2\right]}$$

Key Identity: $a^2+b^2+c^2-ab-bc-ca = \mathbf{\frac{1}{2}\left[(a-b)^2+(b-c)^2+(c-a)^2\right]}$.
💡 TCS Speed Rule: Use Form 2 when $a, b, c$ are large consecutive numbers or have a constant common difference!

Special Case 1: If $a+b+c = 0$

$$\mathbf{a^3+b^3+c^3 = 3abc}$$

If $a+b+c=0 \implies a^3+b^3+c^3 - 3abc = 0$.
E.g. $(x-y)^3 + (y-z)^3 + (z-x)^3 = \mathbf{3(x-y)(y-z)(z-x)}$.

Special Case 2: AP Consecutive Numbers

$$\mathbf{a^3+b^3+c^3-3abc = 9 \cdot b \cdot d^2}$$

If $a, b, c$ are in AP with middle term $b$ and common diff $d$:
E.g., $a=99, b=100, c=101 \implies 9 \times 100 \times 1^2 = \mathbf{900}$ in 2 seconds!

2.2 $x + \frac{1}{x} = k$ Power Expansion Master Table

Given Condition	Target Expression	Direct Shortcut Formula	Numerical Example ($k = 3$)
$x + \frac{1}{x} = k$	$x^2 + \frac{1}{x^2}$	$\mathbf{k^2 - 2}$	$3^2 - 2 = \mathbf{7}$
$x + \frac{1}{x} = k$	$x^3 + \frac{1}{x^3}$	$\mathbf{k^3 - 3k}$	$3^3 - 3(3) = 27 - 9 = \mathbf{18}$
$x + \frac{1}{x} = k$	$x^4 + \frac{1}{x^4}$	$\mathbf{(k^2 - 2)^2 - 2}$	$7^2 - 2 = \mathbf{47}$
$x + \frac{1}{x} = k$	$x^5 + \frac{1}{x^5}$	$\mathbf{\left(x^2+\frac{1}{x^2}\right)\left(x^3+\frac{1}{x^3}\right) - \left(x+\frac{1}{x}\right)}$	$(7 \times 18) - 3 = 126 - 3 = \mathbf{123}$
$x - \frac{1}{x} = k$	$x^2 + \frac{1}{x^2}$	$\mathbf{k^2 + 2}$	If $k=3 \implies 3^2 + 2 = \mathbf{11}$
$x - \frac{1}{x} = k$	$x^3 - \frac{1}{x^3}$	$\mathbf{k^3 + 3k}$	If $k=3 \implies 3^3 + 3(3) = 27 + 9 = \mathbf{36}$

2.3 Special Symmetry Constants (Instant 1-Second Solvers)

If $x + \frac{1}{x} = 1$

$\mathbf{x^3 = -1} \iff \mathbf{x^3 + 1 = 0}$

Power difference of 3 evaluates to 0! E.g. $x^{15} + x^{12} = x^{12}(x^3 + 1) = \mathbf{0}$.

If $x + \frac{1}{x} = -1$

$\mathbf{x^3 = +1} \iff \mathbf{x^3 - 1 = 0}$

Substitute $x^3 = 1$ everywhere in high power terms!

If $x + \frac{1}{x} = \sqrt{3}$

$\mathbf{x^6 = -1} \iff \mathbf{x^6 + 1 = 0}$

Power difference of 6 evaluates to 0! E.g. $x^{72} + x^{66} + x^{54} + x^{48} = \mathbf{0}$.

If $x + \frac{1}{x} = 2$ or $-2$

If $+2 \implies \mathbf{x = 1}$; If $-2 \implies \mathbf{x = -1}$

Direct value substitution! $x^{100} + \frac{1}{x^{100}} = 1 + 1 = \mathbf{2}$.

2.4 Quadratic Maximum/Minimum & Polynomial Theorems

Max/Min of $ax^2 + bx + c$

$\text{Extremum Value} = \mathbf{\frac{4ac - b^2}{4a}} \quad \text{at } x = \mathbf{-\frac{b}{2a}}$

If $a > 0 \implies$ MINIMUM value.
If $a < 0 \implies$ MAXIMUM value.

Remainder & Factor Theorem

$\text{Remainder} = P(a) \quad \text{when } P(x) \div (x-a)$

If $P(a) = 0$, then $(x-a)$ is an exact FACTOR of polynomial $P(x)$.

SSC TCS EXAMINER TRAP ALERT #7 (Algebra)

Power Difference of 6 Trap: If $x + \frac{1}{x} = \sqrt{3}$, examiners ask: "Find $x^{200} + x^{194} + x^{100} + x^{94} + x^6 + 5$."
Notice power pairs with diff 6: $(200 - 194 = 6 \implies 0)$, $(100 - 94 = 6 \implies 0)$, and $x^6 = -1$.
Expression becomes $0 + 0 + (-1) + 5 = \mathbf{4}$! Solved in 3 seconds without expanding.
Sign Error Trap: Remember: $x - \frac{1}{x} = k \implies x^3 - \frac{1}{x^3} = k^3 \mathbf{+} 3k$ (PLUS $3k$, not minus!).

GS 🌍

3. Ancient History: Vedic Civilization (Rigvedic vs Later Vedic Era)

Vedic Age spans 1500 BCE to 600 BCE. TCS questions focus on Early vs Later Vedic political assemblies, Varna emergence, Vedic literature (4 Vedas, Upanishads), and Iron discovery.

3.1 Early Vedic (Rigvedic) vs Later Vedic Comparison

Feature	Early Vedic Period (~1500 BCE – 1000 BCE)	Later Vedic Period (~1000 BCE – 600 BCE)
Primary Region	Sapta Sindhu (Land of 7 rivers: Indus, 5 Punjab rivers, Saraswati)	Gangetic Plains (Western UP, Bihar) - Expansion eastward
Economy	Pastoral (Cattle / Cows primary wealth). Gavishti = search for cows / war.	Agrarian (Agriculture primary). Discovery of Iron (Syama Ayas ~1000 BCE at Atranjikhera). Painted Grey Ware (PGW).
Political Assemblies	Sabha, Samiti, Vidatha, Gana held strong democratic control over King (Rajan). Women attended Sabha & Vidatha.	Assemblies lost power; King became autocratic with grand titles (Samrat, Ekrat). Women excluded from Sabha.
Social Structure	Flexible, occupational mobility. No child marriage. Women enjoyed high status (Gargi, Maitreyi scholars).	Hereditary Varna System solidified. Emergence of Gotra system. Status of women declined.
Main Deities	Indra / Purandara (250 hymns), Agni (200 hymns), Varuna (Moral order / Rta), Soma (Plant god - 9th Mandal).	Trinity emerged: Prajapati (Creator), Vishnu (Preserver), Rudra (Destroyer). Ritual sacrifices grew complex.

3.2 Master 4 Vedas & Vedic Literature Table

Veda / Literature	Priest / Key Feature	Upaveda	High-Yield SSC TCS Exam Facts
Rig Veda	Hotri	Ayurveda (Medicine)	Oldest religious text in world. 1028 Hymns, 10 Mandalas. Gayatri Mantra in 3rd Mandal (by Vishwamitra). 7th Mandal: Battle of Ten Kings (Dasrajan War) on Parushni (Ravi) river. 10th Mandal: Purusha Sukta (origin of 4 Varnas).
Sama Veda	Udgatri	Gandharvaveda (Music)	Book of Chants. Root of Indian classical music & melody (Saman).
Yajur Veda	Adhvaryu	Dhanurveda (Archery/War)	Book of Sacrificial Prayers & Rituals. Only Veda written in both Prose & Poetry! Divided into Shukla (White) & Krishna (Black).
Atharva Veda	Brahma	Shilpaveda (Architecture)	Book of Magic, Spells, Charms & Treatment of Diseases. Non-Aryan origin elements.
Upanishads	Philosophers / Sages	Vedanta (End of Vedas)	108 Upanishads total. Focus on Atman & Brahman. "Satyameva Jayate" is taken from Mundaka Upanishad. Satyakam Jabala story in Chhandogya Upanishad.

SSC TCS EXAMINER TRAP ALERT #8 (Vedic Civilization)

Gayatri Mantra Mandal Trap: Gayatri Mantra is in the 3rd Mandal of Rig Veda (dedicated to Goddess Savitri / Sun), NOT the 10th Mandal!
Dasrajan War River Trap: Battle of 10 Kings was fought on the banks of Parushni (Ravi) river, where King Sudas won.
Mundaka vs Mandukya Trap: "Satyameva Jayate" is taken from Mundaka Upanishad (NOT Mandukya Upanishad!).

GS 🌍

4. Polity: Fundamental Rights (Articles 12–35) & 5 Master Writs

Fundamental Rights (Part III, Art 12-35) is the most heavily tested Polity topic in SSC CGL. Master the 6 Fundamental Rights, the 5 Writs under Art 32/226, and Emergency exceptions.

4.1 Summary of 6 Fundamental Rights (Articles 14–32)

Category	Articles	Key Provisions & High-Yield Facts
Right to Equality	Art 14 – 18	• Art 14: Equality before law (UK) & Equal protection of laws (USA). • Art 15: No discrimination on grounds ONLY of religion, race, caste, sex, place of birth. • Art 16: Equality of opportunity in public employment. • Art 17: Abolition of Untouchability (Absolute right). • Art 18: Abolition of Titles (except Military & Academic).
Right to Freedom	Art 19 – 22	• Art 19: 6 Freedoms (Speech, Assembly, Association, Movement, Residence, Profession). • Art 20: Protection against conviction (No ex-post facto, No double jeopardy, No self-incrimination). • Art 21: Right to Life & Personal Liberty (includes Privacy, Clean Air, Livelihood). • Art 21A: Right to Education (6-14 yrs) — Added by 86th Amend 2002. • Art 22: Protection against arrest (24 hrs magistrate production).
Right against Exploitation	Art 23 – 24	• Art 23: Prohibition of traffic in human beings & forced labor (Begar). • Art 24: Prohibition of child labor in factories/mines (<14 yrs).
Freedom of Religion	Art 25 – 28	• Art 25: Conscience, practice & propagation of religion. • Art 26: Manage religious affairs. • Art 27: Freedom from taxation for religious promotion. • Art 28: Freedom from religious instruction in state educational institutes.
Cultural & Educational Rights	Art 29 – 30	• Art 29: Protection of interests of minorities (language, script, culture). • Art 30: Right of minorities to establish & administer educational institutions.
Right to Constitutional Remedies	Art 32	Dr. Ambedkar called it the "Heart and Soul of the Constitution". Empowers Supreme Court (Art 32) and High Courts (Art 226) to issue 5 Writs.

4.2 The 5 Master Writs under Article 32 (SC) & Article 226 (HC)

Writ Name	Literal Meaning	Issued Against Whom?	Purpose / Exam Trigger
Habeas Corpus	"To have the body of"	Both Public Authorities & Private Individuals	To release a person who has been detained illegally/unlawfully.
Mandamus	"We command"	Public Officials, Lower Courts, Corporations	To direct a public authority to perform an official duty they failed/refused to perform. Cannot be issued against President, Governors or Private Individuals!
Prohibition	"To forbid"	Judicial & Quasi-Judicial Authorities only	Issued by higher court to lower court to prevent it from exceeding jurisdiction. (Preventive only - BEFORE order).
Certiorari	"To be certified / informed"	Judicial, Quasi-Judicial & Administrative Authorities	Issued by higher court to lower court to quash an order already passed in excess of jurisdiction. (Both Preventive & Curative - AFTER order).
Quo-Warranto	"By what authority?"	Public Offices / Officials	To prevent illegal usurpation of a public office by an unqualified person. Can be sought by ANY interested person (not just aggrieved).

Right to Property (44th Amendment 1978)

Art 31 Removed $\to$ Now Legal Right under Art 300A

Right to Property was deleted from Fundamental Rights list by 44th Amendment in 1978 during Morarji Desai govt.

Non-Suspensible FRs in Emergency

Articles 20 & 21 CAN NEVER BE SUSPENDED

Under 44th Amendment 1978, enforcement of Articles 20 & 21 cannot be suspended even during National Emergency! Art 19 suspended only during external war.

SSC TCS EXAMINER TRAP ALERT #9 (Fundamental Rights & Writs)

Articles 20 & 21 Emergency Trap: Examiners ask: "Which Articles remain active during National Emergency?" Answer: Articles 20 and 21 can NEVER be suspended!
Mandamus Exceptions Trap: Mandamus CANNOT be issued against the President of India, State Governors, or Private Persons/Entities!
Art 32 vs Art 226 Scope Trap: High Court writ jurisdiction under Art 226 is WIDER than Supreme Court under Art 32! SC can issue writs ONLY for Fundamental Rights; HC can issue writs for FRs as well as ordinary legal rights!

GS 🌍

5. Static GK: Important Lakes of India (State-Wise Mapping & SVG Diagram)

Lakes of India is a guaranteed 1-question static GK topic. TCS tests Lake-State mapping, freshwater vs saltwater rank, and unique ecological features.

5.1 Master Lakes of India Table

Lake Name	State / UT	Type / Origin	SSC TCS High-Yield Fact
Wular Lake	Jammu & Kashmir	Freshwater (Tectonic)	Largest Freshwater Lake in India! Fed by Jhelum River. Houses Tulbul Navigation Project.
Dal Lake	Jammu & Kashmir	Freshwater	"Jewel in the crown of Kashmir". Famous for Shikaras & floating vegetable markets (Radh).
Chilika Lake	Odisha	Brackish Lagoon	Largest Coastal Lagoon in India (2nd largest in world). 1st Ramsar Site of India (1981). Famous for Irrawaddy Dolphins.
Sambhar Lake	Rajasthan	Saline (Inland)	Largest Inland Saltwater Lake in India! Produces ~9% of India's salt.
Pulicat Lake	AP - TN Border	Brackish Lagoon	2nd largest brackish water lagoon. Separated from Bay of Bengal by Sriharikota Island (ISRO Space Centre).
Loktak Lake	Manipur	Freshwater	Famous for floating islands called Phumdis! Houses Keibul Lamjao National Park (World's ONLY floating national park & home to Sangai deer).
Vembanad Lake	Kerala	Brackish / Freshwater	Longest Lake in India (96.5 km)! Hosts Nehru Trophy Boat Race (Vallam Kali) at Punnamada. Willington Island inside it.
Lonar Lake	Maharashtra	Crater Lake	Formed by Meteorite Impact in basalt rock during Pleistocene epoch. Turned pink due to haloarchaea microbes.
Pangong Tso	Ladakh	Saline (Endorheic)	High altitude lake (4,225 m). 60% lies in Tibet (China). Changes colors from blue to green.
Bhojtal (Upper Lake)	Madhya Pradesh	Freshwater (Man-made)	Built by King Raja Bhoja of Paramara dynasty. Ramsar site.

Diagram 5.1: Key Strategic Lakes Map of India

Figure 5.1: Strategic Geographical Distribution of Important Lakes of India.

SSC TCS EXAMINER TRAP ALERT #10 (Lakes of India)

Largest Freshwater vs Saltwater Trap: Largest Freshwater Lake = Wular Lake (J&K); Largest Inland Saltwater Lake = Sambhar Lake (Rajasthan); Largest Coastal Lagoon = Chilika Lake (Odisha).
Loktak Phumdis & Deer Trap: World's ONLY floating national park is Keibul Lamjao on Loktak Lake (Manipur), home to the endangered Sangai (Brow-antlered deer).
Longest vs Largest Lake: Longest lake in India is Vembanad Lake (Kerala) (96.5 km), NOT Chilika!

English 📜

6. English Grammar: Master Rules 21 to 40 for SSC CGL Error Spotting

Master Rules 21 to 40 of High-Yield English Grammar. TCS frequently tests Parallelism, Subjunctive Mood, Little vs Few, Inversion after Negative Adverbs, and Plural Noun Meaning changes.

#	Grammar Rule Title	Rule Explanation	SSC TCS Incorrect vs Correct Example
21	Parallelism in Conjunctions	Correlative conjunctions (Not only... but also, Either... or, Both... and) must join identical parts of speech (verb-verb, noun-noun).	❌ He not only lost his ticket but also his luggage. ✔ He lost not only his ticket but also his luggage.
22	Unfulfilled Wish / Subjunctive Mood	Imaginary or unreal conditions (If I were, I wish, As if) ALWAYS take WERE regardless of whether subject is singular or plural!	❌ If I was a bird, I would fly. ✔ If I were a bird, I would fly.
23	Elder / Eldest vs Older / Oldest	Elder / Eldest is used ONLY for family members (followed by to or no preposition). Older / Oldest is used for unrelated persons and things (followed by than).	❌ He is elder than me. ✔ He is older than I am. / He is my elder brother.
24	Little / A Little / The Little	Little = Almost none (Negative). A little = Some quantity (Positive). The little = Specific small quantity present. (Used for Uncountable).	❌ He has little knowledge, so he passed. ✔ He has a little knowledge, so he passed.
25	Few / A Few / The Few	Few = Negligible (Negative). A few = Some (Positive). The few = All of the small number available. (Used for Countable Nouns).	❌ Few students were present, so class continued. ✔ A few students were present, so class continued.
26	Too... To Transformation	`Too + Adjective + To + V1` conveys negative meaning equivalent to `So + Adjective + That + Cannot`.	❌ He is too weak that he cannot walk. ✔ He is too weak to walk. / He is so weak that he cannot walk.
27	Dangling Modifier / Unattached Participle	A participle clause must clearly refer to the subject of the main clause. Otherwise it creates a ridiculous dangling modifier!	❌ Walking in the garden, a snake bit him. ✔ While he was walking in the garden, a snake bit him.
28	Inversion with Negative Adverbs	When a sentence starts with negative adverbs (Seldom, Never, Barely, Hardly, Rarely, Scarcely), use Auxiliary Verb before Subject!	❌ Seldom he comes here. ✔ Seldom does he come here.
29	Beside vs Besides	Beside means "by the side of / next to". Besides means "in addition to / apart from".	❌ Beside Hindi, he knows English. ✔ Besides Hindi, he knows English.
30	Nouns Changing Meaning in Plural	Good (virtue) vs Goods (property/cargo); Custom (habit) vs Customs (duties/tax); Wood (timber) vs Woods (forest); Iron (metal) vs Irons (chains).	❌ The train carried heavy good. ✔ The train carried heavy goods.
31	It is High Time + V2 (Past Simple)	Phrases like It is time / It is high time / It is about time followed by a subject take V2 (Past Simple Tense)!	❌ It is high time we start preparing for CGL. ✔ It is high time we started preparing for CGL.
32	As if / As though + Past Subjunctive	As if and As though take past subjunctive verb (were or had + V3) to show unreal comparison.	❌ He talks as if he knows everything. ✔ He talks as if he knew / were knowing everything.
33	Double Negatives Avoidance	Words like Hardly, Scarcely, Barely, Unless, Until, Lest, Forbid, Deny ALREADY contain negative meaning. Never add 'not'!	❌ Unless you do not work hard, you will fail. ✔ Unless you work hard, you will fail.
34	Collective Noun Verb Agreement	Collective nouns (Jury, Committee, Team, Audience) take Singular Verb when unanimous, and Plural Verb when divided!	❌ The jury is divided in their opinions. ✔ The jury are divided in their opinions.
35	Many a + Singular Noun + Singular Verb	`Many a + Singular Noun + Singular Verb` (whereas `Many + Plural Noun + Plural Verb`).	❌ Many a man have succumbed to temptation. ✔ Many a man has succumbed to temptation.
36	The Number of vs A Number of	`The number of + Plural Noun + SINGULAR Verb`. `A number of + Plural Noun + PLURAL Verb`.	❌ The number of candidates are increasing. ✔ The number of candidates is increasing.
37	One and a Half + Plural Noun + Singular Verb	`One and a half + Plural Noun + Singular Verb`. E.g. One and a half hours is allowed.	❌ One and a half hour are allowed. ✔ One and a half hours is allowed.
38	No sooner... Than Inversion Syntax	`No sooner + did/had + Subject + V1/V3... THAN`. Never use 'when' or 'then'!	❌ No sooner had I arrived when it started raining. ✔ No sooner had I arrived than it started raining.
39	Emphatic vs Reflexive Pronoun Placement	Emphatic pronouns immediately follow the noun/pronoun they emphasize (e.g. I myself saw him). Reflexive pronouns act as object.	❌ Myself am Suresh. ✔ I am Suresh. / I myself am Suresh.
40	Die OF vs Die FROM vs Die FOR	Die OF (disease/hunger/thirst); Die FROM (wound/overwork/poison); Die FOR (a cause/country).	❌ He died from cancer. ✔ He died of cancer.