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Study Center & Notes

Access fundamental rules, key formulas, and comprehensive topic-wise study modules structured specifically for the CHSLRE and Matriculation Level syllabi.

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English Language General Intelligence Numerical Aptitude General Awareness

English Language

Core Grammar Principles

Subject-Verb Agreement
  • Rule 1: Words like Everyone, Each, Nobody, Anyone always take a singular verb. (e.g., Everyone is here.)
  • Rule 2: If subjects are joined by "as well as" or "along with", the verb agrees with the first subject.
  • Rule 3: "Neither/Nor" and "Either/Or" — the verb agrees with the subject closest to it.
Active vs. Passive Voice
  • Golden Rule: The Tense NEVER changes when converting voice.
  • Active: "The dog bit the boy." (Past Simple)
  • Passive: "The boy was bitten by the dog." (Still Past Simple)
  • Continuous Tenses: Always add "being". (e.g., "is writing" becomes "is being written").

CHSLRE: Grammar & Structure

Spot Error, Fill in the Blanks, Spellings, Sentence Improvement, Active/Passive Voice.

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CHSLRE: Vocab & Comprehension

Synonyms, Antonyms, Idioms, One word substitution, Cloze/Comprehension Passage.

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Matriculation: General English

Vocabulary, grammar, sentence structure, synonyms, antonyms, and passage comprehension.

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General Intelligence & Reasoning

Logic & Coding Fundamentals

Alphabet Numerical Values (Crucial for Coding & Series)

Memorizing letter positions accelerates problem-solving. Use the EJOTY rule as anchors:

E
5
J
10
O
15
T
20
Y
25

Note: Reverse pairs (A-Z, B-Y, C-X) always sum up to 27. (e.g., C is 3. 27 - 3 = 24. X is 24).

CHSLRE: Analogies & Classification

Semantic/Number/Figural Analogy, Trends, Space Orientation, Classification, Venn Diagrams.

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CHSLRE: Patterns & Logic

Pattern-folding, Series, Embedded figures, Critical/Problem Solving, Coding, Numerical Operations.

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Matriculation: Logic & Series

Similarities/differences, space visualization, problem-solving, visual memory, arithmetical/non-verbal series.

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Numerical & Quantitative Aptitude

Core Mathematical Formulas

Algebraic Identities
$$ (a+b)^2 = a^2 + 2ab + b^2 $$
$$ (a-b)^2 = a^2 - 2ab + b^2 $$
$$ a^2 - b^2 = (a-b)(a+b) $$
$$ (a+b)^3 = a^3 + b^3 + 3ab(a+b) $$
Interest & Commercial
Simple Interest:
$$ SI = \frac{P \times R \times T}{100} $$
Compound Interest (Amount):
$$ A = P \left(1 + \frac{R}{100}\right)^n $$
Profit Percentage:
$$ \text{Profit \%} = \frac{\text{Profit}}{\text{Cost Price}} \times 100 $$
Mensuration (Volume)
Cylinder:
$$ V = \pi r^2 h $$
Cone:
$$ V = \frac{1}{3} \pi r^2 h $$
Sphere:
$$ V = \frac{4}{3} \pi r^3 $$

Arithmetic Foundations

Numbers, Decimals, Percentages, Ratios, Averages, Interest, Profit/Loss, Time/Distance.

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CHSLRE: Algebra & Geometry

Algebraic identities, surds, linear equations. Triangle centres, Circles (chords, tangents).

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Mensuration, Trig & Stats

2D/3D shapes, Trigonometric ratios/distances, Histograms, Frequency polygons, Bar/Pie charts.

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General Awareness

Everyday Science Fundamentals

Core Physics (Mechanics)
Speed:
$$ S = \frac{D}{T} $$
Force:
$$ F = m \times a $$
Kinetic Energy:
$$ KE = \frac{1}{2}mv^2 $$
Everyday Applications
  • Work: Work is only done when a force causes displacement. $$ W = F \times d $$
  • Surface Tension: The reason water droplets form spheres (it minimizes surface area).
  • Vitamins: Vitamin C deficiency causes Scurvy; Vitamin D causes Rickets.

General Awareness Core

Environment/society, current events. India and neighbors (History, Geography, Economy).

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