24 cardsCUET UG

CUET UG General Test and English Essentials

Essential quantitative problem-solving shortcuts, arithmetic reasoning principles, and high-frequency English vocabulary for the CUET UG Examination.

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Successive Percentage Changes Shortcut Formula

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Successive Percentage Changes Shortcut Formula

Net effective percentage change for two successive changes of a% and b% = [a + b + (a * b) / 100]%, where increases are positive and discounts/decreases are negative.

Direct Proportionality of Work, Men, and Days (MDH Formula)

(M1 D1 H1) / W1 = (M2 D2 H2) / W2, where M is workers, D is days, H is hours/day, and W is units of work accomplished.

Relative Speed Formula for Two Moving Bodies

Same direction: Relative speed = |v1 - v2|; Opposite directions (approaching): Relative speed = v1 + v2; to convert km/h to m/s, multiply by 5/18.

Difference Between Compound Interest and Simple Interest for 2 Years

CI - SI (for 2 years) = P * (R / 100)^2, where P is the principal and R is the annual interest rate.

Average Speed for Equal Distances at Speeds x and y

Average Speed = (2 x y) / (x + y), which is the harmonic mean of the two speeds, independent of the actual distance covered.

Clock Problems: Angle Between Hour and Minute Hands

Angle theta = |30 H - 5.5 M| degrees, where H is the hour (1-12) and M is the minute (0-59).

Calendar Concepts: Odd Days in a Normal Year vs Leap Year

A normal year has 365 days = 52 weeks + 1 odd day; A leap year has 366 days = 52 weeks + 2 odd days; 100 years has 5 odd days; 400 years has 0 odd days.

Formula for Alligation / Weighted Mixture

(Cheaper Quantity) / (Dearer Quantity) = (Price of Dearer - Mean Price) / (Mean Price - Price of Cheaper).

Arithmetic Mean vs Geometric Mean Inequality

AM >= GM for all positive real numbers: (a + b) / 2 >= sqrt(a * b), with equality holding if and only if a = b.

Number of Diagonals in an n-Sided Polygon

Number of diagonals = n(n - 3) / 2; for a triangle (n=3) = 0; quadrilateral (n=4) = 2; pentagon (n=5) = 5; hexagon (n=6) = 9.

Pythagorean Triples Quick Reference

Fundamental integer triples: (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41), (20, 21, 29), and any scalar multiples.

Divisibility Rules for 7, 11, and 13

For 11: Difference between sum of digits in odd places and sum in even places is 0 or divisible by 11; For 7 and 13: Partition number into 3-digit groups from right, and evaluate alternating sum.

Blood Relations: Mapping Standard Generations

Generation +2: Grandparents; Generation +1: Parents, Aunts, Uncles; Generation 0: Siblings, Cousins, Spouse; Generation -1: Children, Nephews, Nieces; Generation -2: Grandchildren.

Syllogism: Rules for Valid Conclusions

Two negative premises yield no valid conclusion; Two particular premises yield no valid conclusion; If one premise is negative, conclusion must be negative; If one is particular, conclusion must be particular.

English Vocabulary: 'Ubiquitous'

Present, appearing, or found everywhere at the same time; synonyms: omnipresent, pervasive, universal.

English Vocabulary: 'Ephemeral'

Lasting for a very short time; fleeting, transitory, transient, evanescent.

English Vocabulary: 'Pragmatic'

Dealing with things sensibly and realistically based on practical rather than theoretical considerations; matter-of-fact, utilitarian.

English Vocabulary: 'Anachronism'

A thing belonging or appropriate to a period other than that in which it exists, especially something conspicuously old-fashioned.

Idiom: 'Bite the Bullet'

To face an inevitable, difficult, or unpleasant situation with courage and fortitude rather than evading it.

Idiom: 'A Blessing in Disguise'

An apparent misfortune or negative event that eventually results in an unforeseen positive or beneficial outcome.

Grammar: Subject-Verb Agreement with 'None of'

'None of' can take either singular or plural verbs: with uncountable nouns it takes a singular verb ('None of the milk was spilled'); with plural countable nouns it standardly takes plural in modern usage ('None of the students were late').

Grammar: Dangling Modifiers Rule

An introductory participial phrase must be followed immediately by the noun or pronoun performing the action: 'Having finished the exam, the pen was dropped' is incorrect; 'Having finished the exam, the student dropped the pen' is correct.

Grammar: Lie vs Lay Distinction

'Lie' (intransitive: to recline): lie, lay, lain, lying ('He lies on the sofa'); 'Lay' (transitive: to place something down, requires an object): lay, laid, laid, laying ('She laid the keys on the table').

Grammar: Parallelism with Correlative Conjunctions

Elements connected by 'either... or', 'neither... nor', 'not only... but also' must belong to identical grammatical categories (both infinitives, both prepositional phrases, or both clauses).

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