CAT Free Online Test - Permutation Answers

Below are detailed answers for each of the questions asked in test, the explanations given below would further strengthen your understanding of Permutation & Combinations topic. 

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Q1. How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
Answer:
Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
Required number of numbers = (1 x 5 x 4) = 20.


Q2.In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
Answer:
Required number of ways           = (8C5 x 10C6)
= (8C3 x 10C4)
=           8 x 7 x 6           x           10 x 9 x 8 x 7   
3 x 2 x 1            4 x 3 x 2 x 1
= 11760.


Q3.In how many ways can 4 girls and 5 boys be arranged in a row so that all the four girls are together??
Answer:
Let 4 girls be one unit and now there are 6 units in all.
They can be arranged in 6! ways.
In each of these arrangements 4 girls can be arranged in 4! ways.
=> Total number of arrangements in which girls are always together
=6!*4!=720*24= 17280


Q4. 12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points?
For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is 12C4=495
. Therefore, we can draw 495 quadrilaterals.​


Q5. The Indian Cricket team consists of 16 players. It includes 2 wicket keepers and 5 bowlers. In how many ways can a cricket eleven be selected if we have to select 1 wicket keeper and at least 4 bowlers?
We are to choose 11 players including 1 wicket keeper and 4 bowlers
or, 1 wicket keeper and 5 bowlers.
Number of ways of selecting 1 wicket keeper, 4 bowlers and 6 other players
=2C1*5C4*9C6=840
Number of ways of selecting 1 wicket keeper, 5 bowlers and 5 other players
=2C1*5C5*9C5=252
=> Total number of ways of selecting the team:
=840+252= 1092


Q6. How many factors of (2^4)×(5^3)×(7^4) are odd numbers?
Any factor of this number should be of the form 2a×3b×5c.
For the factor to be an odd number, a should be 0.
b can take values 0,1, 2,3, and c can take values 0, 1, 2,3, 4.
Total number of odd factors =4×5= 20


Q7. How many factors of (2^5)×(3^6)×(5^2) are perfect squares?
Any factor of this number should be of the form 2a×3b×5c.
For the factor to be a perfect square a, b, c have to be even.
a can take values 0, 2, 4. b can take values 0,2, 4, 6 and c can take values 0,2.
Total number of perfect squares =3×4×2= 24

Q8. In how many ways can eight directors, the vice-chairman and chairman of a firm be seated at a round table, if the chairman has to sit between the vice-chairman and the director?
In a circular arrangement problem, we always fix one position and the look at ways of arranging the rest with respect to the fixed position.

Case 1 - seating of chairman - In this question, we fix the position of the Chairman. Thus the Chairman can be seated in 1 way only.

Case 2 - seating of vice-chairman - The vice-chairman can be to the left or right of the chariman. Thus the vice chairman can be seated in 2 ways.

Case 3 - seating of the 8 directors - The rest of the 8 directors can be seated in 8 positions in 8! ways. This is because the first director can be seated in andy of 8 positions in 8 ways. And then the second director can be seated in any of the remaning 7 positions in 7 ways and so on, thus giving the total number of ways of seating the 8 director as 8 * 7 * 6* 5 * 4 * 3 * 2 * 1, i.e. 8! ways.

Thus the desired answer is when case 1 and 2 and 3 happen together, which is 1 * 2 * 8! = 2 * 8! ways.


Q9. In how many ways can 15 people be seated around two round tables with seating capacities of 7 and 8 people?
‘n' objects can be arranged around a circle in (n - 1)!.

If arranging these 'n' objects clockwise or counter clockwise means one and the same, then the number arrangements will be half that number.
i.e., number of arrangements = (n-1)!/2.
You can choose the 7 people to sit in the first table in 15C7 ways.
After selecting 7 people for the table that can seat 7 people, they can be seated in (7-1)! = 6!.
The remaining 8 people can be made to sit around the second circular table in (8-1)! = 7! Ways.

Hence, total number of ways 15C8 * 6! * 7!


Q10. Suppose you can travel from a place A to a place B by 3 buses, from place B to place C by 4 buses, from place C to place D by 2 buses and from place D to place E by 3 buses. In how many ways can you travel from A to E?
The bus from A to B can be selected in 3 ways.
The bus from B to C can be selected in 4 ways.
The bus from C to D can be selected in 2 ways.
The bus from D to E can be selected in 3 ways.
So, by the General Counting Principle, one can travel from A to E in 3*4*2*3= 72 ways


Q11. How many words can be formed by using 4 letters at a time of word "SURPRISE" (words may be meaningful or meaningless according to dictionary)
(1) No. of words having all letters different = 6*5*4*3 = 360
(2) No. of words having any one letter repeated
=(2*1)*(5*4*3*2*1/3*2*1*2*1)*(4*3*2*1/2*1) = 240
(3) No. of words having two letter repeated = (1)*(4*3*2*1/2*1*2*1) = 6
Total words = 360+240+6 = 606



Permutation-Combinations Workshop for CAT

Factorial
Let n be a positive integer. Then, factorial n, denoted n! is defined as:
n! = n(n - 1)(n - 2) ... 3.2.1.
Solved Examples:
i. We define 0! = 1.
ii. 1! = 1.
iii. 4! = (4 x 3 x 2 x 1) = 24.
iv. 5! = (5 x 4 x 3 x 2 x 1) = 120.


Difference between Permutation & Combination
In English we use the word "combination" loosely, without thinking if the sequence/order of things is important or not. Examples:



"My mock-tail is a combination of  pineapple juice, grapes juice and lime juice" . 
In this case we don't care what order the juices are mixed in, they could also be "grapes juice, pineapple juice and lime juice" or "lime juice, grapes juice and pineapple juice", its the same mock-tail.





" 5178 is my ATM Pin combination ". 
Now in this case we do care for the order. 5187 will not work, nor will 5718, 5781, 1857, 1875 etc. The only sequence which will work is 5178.


In mathematics:
If the order doesn't matter, it is a Combination.
If the order does matter it is a Permutation.
=>     A Permutation is an ordered Combination.


Permutation - The order of arrangement matters
In mathematics permutation means act of rearranging (permuting) objects or values. In simple words: "the different arrangements of a given number of things by taking some or all at a time, are called permutations."
Consider following three fruits which needs to be arranged in a straight line on a thin bench:












What are the different ways one can arrange these 3 fruits on table?
Lets number these fruits as 1. Apple, 2. Mango and 3. Banana.













All possible arrangements of these 3 fruits are:







The number of different arrangements as you could see above is 6 or 3! = 3 • 2 • 1

-The number of permutations of n distinct objects is n×(n − 1)×(n − 2)×⋯×1, which is commonly denoted as "n factorial" and written "n!".
-All possible arrangements of letters of a word is a permutation of its letters. 
-For (a,b,c) or abc number of distinct objects are 3, hence permutation made with the letters a, b, c taking all at a time are 3! = 3*2 = 6 => (abc, acb, bac, bca, cab, cba)



Important Concepts on Permutation:

1. Taken r items at a time
Number of all permutations of n things, taken r at a time, is given by:
    
 nPr = n(n - 1)(n - 2) ... (n - r + 1) = n!/(n-r)! 


Solved Example: 
Question 1: How many different 3-digit numerals can be made from the digits  4, 5, 6, 7, 8 if a digit can appear just once in a numeral?
Answer:  We need to find permutation of 5 distinct numbers taken 3 at a time.
Applying formula for nPr => 5P3 = 5!/(5-3)! = (5*4*3*2*1)/(2*1) = 5*4*3 = 60

 
2 a. Identical Items in arrangement
If x out of n items are identical, then the number of different permutations of the n items is:  n!/x! 
Solved Example: 
Question 2: How many ways can you arrange the letters of the word 'twist'? 
Answer:  We need to find permutation of 5 letters(i,s,t,t,w) of which 2 are identical(t,t).
Applying n!/x! for identical items => 5!/2! = 60

 
2 b. Multiple Identical Items in arrangement
If a set of n items contains p identical items, q identical items, and r identical items etc.., then the total number of different permutations of n objects is:  n!/(p!.q!.r!...) 
Solved Example: 
Question 3: How many can you arrange the letters in the word 'MISSISSIPPI''? 
Answer:  We need to find permutation of 5 letters(I,I,I,I,M,P,P,S,S,S,S) of which 4Is, 2 Ps and 4Ss are identical.
Applying n!/(p!.q!.r!..) for multiple identical items => 11!/(4!.2!.4!) = 34,650

 
3. Conditional/Restrictive Permutation 
There are situations where we need to find out possible arrangements  by keeping some of conditions/restrictions in mind. 
Solved Example: 
Question 4:  Using the letters in the word  " square ", tell how many 6-letter arrangements, with no repetitions, are possible if the  first letter is a vowel? 
Answer:  When working with "arrangements", it is often helpful to put lines down to represent the locations of the items. 
       For this problem, six "locations" are needed for 6-letter arrangements.
       _____  •   _____  •  _____  •  _____  •  _____  •  _____

The first locations must be a vowel (u, a, e).  There are three ways to fill the first location.
       _3_ •  _____ •  _____ •  _____ •  _____ •  _____

After the vowel has been placed in the first location, there are 5 letters left to be arranged in the remaining five spaces.

      _3_ • _5_  • _4_  • _3_  •  _2__1_     or
                        
         3  5P5    =     3  120  =  360

 
4. Circular Arrangements
To understand circular arrangement better below illustration comparing it with linear arrangement would be useful:

1. Lets consider 4 people sitting around a round table and 4 people sitting on a linear bench

2.  Shifting each of the 4 people sitting around round table in clockwise direction we get following arrangements:
Looking at the above illustration we could say that if 4 persons are sitting at a round table, then they can be shifted four times, but these four arrangements will be the same, because the sequence of P1, P2, P3, P4 is same.

3. Now we will compare this with linear arrangement where 4 people P1, P2, P3 & P4 are sitting on a bench.  Shifting each of the 4 people sitting in a row on a bench all the 4 arrangement formed will be different:
 All the above 4 sequences are unique and are different arrangements: 
[P1, P2, P3, P4] , [P4, P1, P2, P3], [P3, P4, P1, P2], [P2, P3, P4, P1]

Thus you can see how results in a circular arrangement differs from linear one.



Number of circular-permutations of ‘n’ different things taken ‘n’ at a time
(a)  When clockwise & anti-clockwise order are considered different
If clockwise and anti clock-wise orders are considered different, then total number of circular-permutations is given by (n-1)!

(b)  When clockwise & anti-clockwise order are not considered different 
If clock-wise and anti-clock-wise orders are taken as not different, then total number of circular-permutations is given by  (n-1)!/2!

Solved Example: 
Question 5: If 6 people are going to sitting at a round table, how many different ways can the group of 6 sit
Answer:  Applying formula (n-1)! = (6-1)! = 120

Question 6:If 6 people are going to sitting at a round table, but Raj will not sit next to Simran, how many different ways can the group of 6 sit? 
Answer:
First Approach
a. Total circular permutations = (6-1)! = 5! = 120. 
b. Ways in which Raj and Simran sit together = 2! * 4! = 2*24 = 48 
Required ways = Total - Together = 120 - 48 = 72. 

Second Approach
a. We have total of 6 places. Fix Simran . Now Raj can't sit at either seat beside her. So number of places where Sam can sit = 5-2 = 3. 
For the other 4 people we can arrange them in 4! ways in 4 seats. 
So total ways = 3 * 4! = 72. 



Number of circular-permutations of ‘n’ different things taken ‘r’ at a time

(c) When clockwise & anti-clockwise order are considered different

If clock-wise and anti-clockwise orders are taken as different, then total number of circular-permutations  =   nPr /r


(d) When clockwise & anti-clockwise order are not considered different

If clock-wise and anti-clockwise orders are taken as not different, then total number of circular – permutation =  nPr/2r



Solved Example:
Question 7: How many necklace of 12 beads each can be made from 18 beads of different colors ? 
Answer:  Here clock-wise and anti-clockwise arrangement s are same.
Applying formula:  nPr/2r
Hence total number of circular–permutations = 18P12/2x12
=18!/(6! x 24)


 
Combinations: The order of arrangement doesn't matters
In mathematics a combination is a way of selecting several things out of a larger group, where  order does not matter.

Number of combinations 

The number of all combinations of n things, taken r at a time is:


nCr = n(n - 1)(n - 2) ... to r factors/r! = n!/(r!(n-r)!)


Important:

Solved Example: 
Question 8: In a class of 10 students, how many ways can a club of 4 students be formed? 
Answer: Applying nCr formula:
=> 10C4 = 10!/(4!*6!) = 21

Question 9: How many factors of 2^4 * 5^3 * 7^4 are odd numbers? ? 
AnswerAny factor of this number would be of the form 2^a * 3^b * 5^c. For the factor to be an odd number, a should be 0. b can take values 0,1, 2,3, and c can take values 0, 1, 2,3, 4. Total number of odd factors = 4 * 5 = 20 


Take Online Test on Permutation-Combinations to evaulate yourself 
Test Consists of 11 Questions
Time Allotted is 16 minutes
Total Mraks is 33
Average cut Off Score 25 out 33

Take Online Test

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Online Test - Permutation and Combinations

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Word List for Vocab Building

Below are 333 high frequency words which would be helpful in building your vocabulary. You can set a goal of 21 days to get familiar with all the 333 words in the list below:

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Vocab Word List

Abate – v – subside or moderate.
Aberrant – adj – abnormal or deviant
Abeyance – n – suspended action
Abscond – v – depart secretly and hide
Abstemious – adj – sparing in eating and drinking temperate
Admonish – v – warn; reprove.
Adulterate – v – make impure by adding inferior or tainted substances
Aesthetic – artistic dealing with or capable of appreciating the beautiful
Aggregate – v – gather; accumulate
Alacrity – n – cheerful promptness; eagerness
Alleviate – v – relieve
Amalgamate – v – combine; unite in one body
Ambiguous – adj – unclear or doubtful in meaning
Ambivalence – n – the state of having contradictory or conflicting emotional attitudes
Ameliorate – v – improve
Anachronism – n – something or someone misplaced in time
Analogous – adj – comparable
Anarchy – n – absence of governing body; state of disorder
Anomalous – adj – abnormal; irregular
Antipathy – n – aversion; dislike
Apathy – n - lack of caring; indifference
Appease – v – pacify or soothe; relieve
Apprise – v - inform
Approbation – n – approval
Appropriate – acquire; take possession of for one’s own use
Arduous – adj – hard; strenuous
Artless – adj – without guile; open and honest
Ascetic – adj – practicing self-denial; austere
Assiduous – adj- diligent
Assuage – v – ease or lessen (pain); satisfy (hunger); soothe (anger)
Attenuate – v – make thinner; weaken or lessen (in density, force, degree)
Audacious – adj – daring bold
Austere – forbiddingly stern; severely simple and unornamented
Autonomous – self-governing
Aver – assert confidently or declare; as used in law, state, formally as a fact
Banal – hackneyed; commonplace; trite; lacking originality
Belie – contradict; give a false impression
Beneficent – kindly; doing good
Bolster – support; reinforce
Bombastic – pompous; using inflated language
Boorish – rude; insensitive
Burgeon – grow forth
Burnish – make shiny by rubbing; polish
Buttress – support; prop up
Cacophonous – discordant; inharmonious
Capricious – unpredictable; fickle
Castigation-punishment; severe criticism
Catalyst – agent that influences the pace of a chemical reaction while it remains unaffected and unchanged; person or thing that causes action
Caustic – burning; sarcastically biting
Chicanery – trickery; deception
Coagulate – thicken; congeal; clot
Coda – concluding section of a musical or literary composition; something that rounds out, summarizes, or concludes
Cogent – convincing
Commensurate – corresponding in extent, degree, amount; proportionate
Compendium – brief; comprehensive summary
Complaisant – trying to please; overly polite; obliging
Compliant – yielding; conforming to requirements
Conciliatory – reconciling; soothing
Condone – overlook; forgive; give tacit approval; excuse
Confound – confuse; puzzled
Connoisseur – person competent to act as a judge of art
Contention – claim; thesis
Contentious – quarrelsome
Contrite – penitent; repentant
Conundrum – riddle; difficult problem
Converge – approach; tend to meet; come together
Convoluted – coiled around; involved; intricate
Craven – cowardly
Daunt – intimidate; frighten
Decorum – propriety; orderliness and good taste in manners
Default – failure to act
Deference – courteous regard for another’s wish
Delineate – portray; depict; sketch
Denigrate – blacken
Deride – ridicule; make fun of
Derivative; unoriginal; obtained from another source
Desiccate – dry up
Desultory – aimless; haphazard; digressing at random
Deterrent – something that discourage; hindrance
Diatribe – bitter scolding; invective
Dichotomy – split; branching into two parts (usually contradictory)
Diffidence – shyness
Diffuse – wordy; rambling; spread out
Digression – wandering away from the subject
Dirge – lament with music
Disabuse – correct a false impression; undeceive
Discerning – mentally quick and observant; having insight
Discordant – not harmonious; conflicting
Discredit – defame; destroy confidence in; disbelieve
Discrepancy – lack of consistency; difference
Discrete – separate; unconnected; consisting of distinct parts
Disingenuous – lacking genuine candor; insincere
Disinterested; unprejudiced
Disjointed – lacking coherence; separated at the joints
Dismiss – eliminate from consideration; reject
Disparage – belittle
Disparate – basically different; unrelated
Dissemble – disguise; pretend
Disseminate – distribute; spread; scatter
Dissolution – disintegration; looseness in morals
Dissonance – discord; opposite of harmony
Distend – expend; swell out
Distill – purify; refine; concentrate
Diverge – vary; go in different directions from the same point
Divest – strip; deprive
Document – provide written evidence
Dogmatic – opinionated; arbitrary; doctrinal
Dormant – sleeping; lethargic; latent
Dupe – someone easily fooled
Ebullient – showing excitement; overflowing with enthusiasm
Eclectic – selective; composed of elements drawn from disparate sources
Efficacy – power to produce desired effect
Effrontery – impudence; shameless boldness; sheer nerve; presumptuousness
Elegy – poem or song expressing lamentation
Elicit – draw out by discussion
Embellish – adorn; ornament; enhance, as a story
Empirical – based on experience
Emulate – imitate; rival
Endemic – prevailing among a specific group of people or in a specific area or country
Enervate – weaken
Engender – cause; produce
Enhance – increase; improve
Ephemeral – short-lived; fleeting
Equanimity – calmness of temperament; composure
Equivocate – lie; mislead; attempt to conceal the truth
Erudite – learned; scholarly
Esoteric – hard to understand; known only to the chosen few
Eulogy – expression of praise, often on the occasion of someone’s death
Euphemism – mild expression in place of an unpleasant one
Exacerbate – worsen; embitter
Exculpate – clear from blame
Exigency – urgent situation; pressing needs or demands; state of requiring immediate attention
Extrapolation – projection; conjecture
Facetious – joking (often inappropriately)
Facilitate – help bring about; make less difficult
Fallacious – false; misleading
Fatuous – brainless; inane; foolish, yet smug
Fawning – trying to please by behaving obsequiously, flattering, or cringing
Felicitous – apt; suitably expressed; well chosen
Fervor – glowing ardor; intensity of feeling
Flag – droop; grow feeble
Fledgling – inexperienced
Flout – reject; mock; show contempt for
Foment – stir up; instigate
Forestall – prevent by taking action in advance
Frugality – thrift, economy
Futile – useless; hopeless; ineffectual
Gainsay – deny
Garrulous – loquacious; wordy; talkative
Goad – urge on
Gouge – overcharge
Grandiloquent – pompous; bombastic; using high-sounding language
Gregarious – sociable
Guileless – without deceit
Gullible – easily deceived
Harangue – long, passionate, and vehement speech
Homogeneous – off the same kind
Hyperbole – exaggeration; overstatement
Iconoclastic – attacking cherished traditions
Idolatry – worship of idols
Immutable – unchangeable
Impair – injure; hurt
Impassive – without feeling; imperturbable; stoical
Impede – hinder; block
Impermeable – impervious; not permitting passage through its substance
Imperturbable – calm placid
Impervious – impenetrable; incapable of being damaged or distressed
Implacable – incapable of being pacified
Implicit – understood but not stated
Implode – burst inward
Inadvertently – unintentionally; by oversight; carelessly
Inchoate – recently begun; rudimentary; elementary
Incongruity – lack of harmony; absurdity
Inconsequential – insignificant; unimportant
Incorporate – introduce something into a larger whole; combine; unite
Indeterminate – uncertain; not clearly fixed; indefinite
Indigence – poverty
Indolent – lazy
Inert – inactive; lacking power to move
Ingenuous – na├»ve and trusting; young; unsophisticated
Inherent – firmly established by nature or habit
Innocuous – harmless
Insensible – unconscious; unresponsive
Insinuate – hint; imply; creep in
Insipid – lacking in flavor; dull
Insularity – narrow-mindedness; isolation
Intractable – unruly; stubborn; unyielding
Intransigence – refusal of any compromise; stubbornness
Inundate – overwhelm; flood; submerge
Inured – accustomed; hardened
Invective – abuse
Irascible – irritable; easily angered
Irresolute – uncertain how to act; weak
Itinerary – plan of a trip
Laconic – brief and to the point
Lassitude – languor; weariness
Latent – potential but undeveloped; dormant; hidden
Laud – praise
Lethargic – drowsy; dull
Levee – earthen or stone embankment to prevent flooding
Levity – lack of seriousness or steadiness; frivolity
Log – record of a voyage or flight; record of day-to-day activities
Loquacious – talkative
Lucid – easily understood
Luminous – shining; issuing light
Magnanimity – generosity
Malingerer – one who feigns illness to escape duty
Malleable – capable to being shaped by pounding; impressionable
Maverick – rebel; nonconformist
Mendacious – lying; habitually dishonest
Metamorphosis – change of form
Meticulous – excessively careful; painstaking; scrupulous
Misanthrope – one who hates mankind
Mitigate – appease; moderate
Mollify – soothe
Morose – ill-humored; sullen; melancholy
Mundane – worldly as opposed to spiritual; everyday
Negate – cancel out; nullify; deny
Neophyte – recent convert; beginner
Obdurate – stubborn
Obsequious – slavishly attentive; servile; sycophantic
Obviate – make unnecessary; get rid of
Occlude – shut; close
Officious – meddlesome; excessively pushy in offering one’s services
Onerous – burdensome
Opprobrium – infamy; vilification
Oscillate – vibrate pendulumlike; waver
Ostentatious – showy; pretentious; trying to attract attention
Paragon – model of perfection
Partisan – one-sided; prejudiced; committed to a party
Pathological – pertaining to disease
Paucity – scarcity
Pedantic – showing off learning; bookish
Penchant – strong inclination; liking
Penury – severe poverty; stinginess
Perennial – something long-lasting
Perfidious – treacherous; disloyal
Perfunctory – superficial; not thorough; lacking interest, care, enthusiasm
Permeable – penetrable; porous; allowing liquids or gas to pass through
Pervasive – spread throughout
Phlegmatic – clam; not easily disturbed
Piety – devoutness; reverence for God
Placate – pacify; conciliate
Plasticity – ability to be molded
Platitude – trite remark
Plethora – excess; overabundance
Plummet – fall sharply
Porous – full of pores; like a sieve
Pragmatic – practical (as opposed to idealistic); concerned with the practical worth or impact of something
Preamble – introductory statement
Precarious – uncertain; risky
Precipitate – rash; premature; hasty; sudden
Precursor – forerunner
Presumptuous – arrogant; taking liberties
Prevaricate – lie
Probity – uprightness; incorruptibility
Problematic – doubtful; unsettled; questionable
Prodigal – wasteful; reckless with money
Profound – deep; not superficial; complete
Prohibitive – tending to prevent the purchase or use of something
Proliferate – grow rapidly; spread; multiply
Propensity – natural inclination
Propitiate – appease
Propriety 0 fitness; correct conduct
Proscribe – ostracize; banish; outlaw
Pungent – stinging; sharp in taste or smell; caustic
Qualified – limited; restricted
Quibble - minor objection or complaint
Quiescent – at rest; dormant; temporarily inactive
Rarefied – made less dense (of a gas)
Recalcitrant – obstinately stubborn; determined to resist authority; unruly
Recant – disclaim of disavow; retract a precious statement
Recluse – hermit; loner
Recondite – abstruse; profound; secret
Refractory – stubborn, unmanageable
Refute – disprove
Relegate – banish to an inferior position; delegate; assign
Reproach – express disapproval or disappointment
Reprobate – person hardened in sin; devoid of a sense of decency
Repudiate - disown; disavow
Rescind – cancel
Resolution – determination
Resolve – determination; firmness of purpose
Reticent – reserved; uncommunicative; inclined to silence
Reverent – respectful; worshipful
Sage – person celebrated for wisdom
Salubrious – healthful
Sanction – approve; ratify
Satiate – satisfy fully
Saturate – soak thoroughly
Savor – enjoy; have a distinctive flavor, smell, or quality
Secrete – hide away or cache; produce and release a substance into an organism
Shard – fragment, generally of pottery
Skeptic – doubter; person who suspends judgment until having examined the evidence supporting a point of view
Solicitous – worried, concerned
Soporific – sleep-causing; marked by sleepiness
Specious – seemingly reasonable but incorrect; misleading (often intentionally)
Spectrum – color band produced when a beam of light passes through a prism
Sporadic – occurring irregularly
Stigma – token of disgrace; brand
Stint – be thrifty; set limits
Stipulate – make express conditions, specify
Stolid – dull; impassive
Striated – marked with parallel bands; grooved
Strut – pompous walk
Strut – supporting bar
Subpoena – writ summoning a witness to appear
Subside – settle down; descend; grow quiet
Substantiate – establish by evidence; verity; support
Supersede – cause to be set aside; replace; make obsolete
Supposition – hypothesis; surmise
Tacit – understood; not put into words
Tangential – peripheral; only slightly connected; digressing
Tenuous – thin; rare; slim
Tirade – extended scolding; denunciation; harangue
Torpor – lethargy; sluggishness; dormancy
Tortuous – winding; full of curves
Tractable – docile; easily managed
Transgression – violation of a law; sin
Truculence – aggressiveness; ferocity
Vacillate – waver; fluctuate
Venerate – revere
Veracious – truthful
Verbose – wordy
Viable – practical or workable; capable of maintaining life
Viscous – sticky, gluey
Vituperative – abusive; scolding
Volatile – changeable; explosive; evaporating rapidly
Warranted – justified; authorized
Wary – very cautious
Welter – turmoil; bewildering jumble
Whimsical – capricious; fanciful
Zealot – fanatic; person who shows excessive zeal (enthusiasm)


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