GRE: Permutation AND Combination

Permutation and Combination

In this chapter, we shall learn about some basic counting techniques which will be useful in determining the number of different ways of arranging and selecting objects without actually listing them.

Multiplication principle- Suppose student Mohan has 3 pants and 2 shirts. How many different pairs of a pant and shirt can he dress up with?

There are three ways in which a pant can be chosen.

For 1st pant————-any of the two shirts can be chosen———2 ways

For 2nd pant————-any of the two shirts can be chosen———2 ways

For 3rdpant————–any of the two shirts can be chosen———-2 ways

For every pant, there are two shirts, therefore, he can dress up with 3×2 = 6.

Let the three pants be P1, P2 and P3 and two shirts be S1, S2 and S3. Above can be easily understood by using this diagram:

 

 

 

 

 

 

 

 

 

For every pant, there are two shirts, therefore, he can dress up in 3×2 = 6 ways.

Number of pair of pants and shirts he can choose = (No. of pants he can choose) x (No. of shirts he can choose)

Problems of above type are solved by using multiplication principle or fundamental principle of multiplication which states that:

If an event can occur in p ways and another event can occur in n ways, number of ways in which both events p & q can be performed is equal to p x q.

Addition principle- If an event can occur in p different ways and another event can occur in q different ways, number of ways in which event p or q can be performed is equal to p + q.

Problem: In a debate competition, there are 5 candidates from science side, 4 from commerce side and 3 from humanities side. In how many ways a winner of competition can be selected?

Sol. A winner out of science students can be selected in 5 ways.

A winner out of commerce students can be selected in 4 ways.

A winner out of humanities students can be selected in 3 ways.

An overall winner of competition can be selected in 5 + 4 + 3 = 12 ways.

 

Problem 1) In a shop, there are 10 shirts and there are 10 pants

  • In how many ways can a pair of pant and a pair of shirt can be selected.
  • In how many ways can a pair of cloth (pant or shirt) can be selected.

Sol.  Number of ways in which a pair of pant and a pair of shirt can be selected = 10 x 10 = 100

Number of ways in which a pair of cloth (pant or shirt) can be selected = 10 + 10 = 20

 

Factorial notation- The notation n! (factorial n) represents the product of first n natural numbers. Factorial of only natural numbers is defined.

For example, 5! = 1 x 2 x 3 x 4 x 5

0! = 1

n! = n (n – 1)! = n (n-1) (n-2)! = n (n-1) (n-2) (n-3)! (provided n ≥ 3)

n! tool for arrangement- Number of ways in which, we can palace N things in N places = N!

or No. of ways in which we can arrange n things = N!

 

Problem 2) How many 4-digits numbers can be formed from digits 1, 2, 3 and 4? (Repetition is not allowed)

Sol. Number of 4-digits numbers that can be formed from digits 1, 2, 3 and 4 = 4! = 24

 

Problem: How many 7 letter words with or without meaning can be formed from letters M, N, O, P, Q, R and S?

Sol.  Number of 7 letter words with or without meaning formed from letters M,N,O,P,Q, R and S = 7!

 

Problem 3) Of the different words that can be formed from the letters of the word BEGINS how many words begins with B and end with S?

Sol.  Number of words beginning with B and ending with S formed from letters of word BEGINS = 4! (Number of arrangements of letters E, G, I, N)

 

Question based on combination of fundamental principle of multiplication and n! principle

Problem 4) In how many ways can the 7 letters M, N, O, P, Q, R and S be arranged so that P and Q occupy continuous position?

Sol.  We should assume PQ as a single word. No. of arrangements of words M, N, O, PQ, R and S = 6!

PQ may act as a single word and QP may also act as a single word.

No. of ways in which letters M, N, O, P, Q, R and S can be arranged so that P and Q occupy continuous position = 6! X 2! = 1440

 

Combination (nCr) tool for arrangement- This tool is used for specific situation of counting, the number of ways of selecting r things out of n distinct things = [ nCr].

The number of ways of selecting r things out of n identical things = 1.

nCr = n! /r! x (n-r)!

important points regarding nCr

  • nCr + nCr – 1 = n + 1Cr
  • nCx = nCy

It implies that (x = y) or (x + y = n)

  • When n is constant and r is variable, for nCr to be greatest
  1. If n is even, r = n/2
  2. If n is odd, r = (n + 1)/2 or (n-1)/2

 

Problem 5) A committee of 5 members is to be formed from group of 8 members. In how many ways can this be done?

Sol.  5 members out of 8 members can be selected in 8C5ways. Number of ways in which 5 members out of 8 members can be selected = 8C5 = 56

 

Problem 6) How many chords can be drawn through 21 points on a circle?

Sol.  Drawing a chord is equivalent to selecting two specific points. Number of chords that can be drawn through 21 points = 21C2

 

Problem 7) In how many ways can a student choose a program of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

Sol.  2 specific courses are compulsory. Therefore, student has to choose 3 courses out of 7 courses. Number of ways in which a student can choose a program of 5 courses if 9 courses are available and 2 specific courses are compulsory = 7C3

 

Question based on combination of fundamental principle of multiplication and Combination

 

Problem 8) A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?

Sol.  We have to select 1 man out of 3 men and 2 women out of 3 women. No. of ways in which this can be done = 2C1 X 3C2

 

Problem 9) In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

Sol.  We have to select 4 bowlers out of 5 bowlers and we have to select 7 players out of remaining 12 players. This can be done in 5C4 X 12C7

 

Problem 10) A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected?

  • If balls of same color are distinct.
  • If balls of same color are identical.

Sol.  If balls of same color are distinct. No. of ways in which 2 black ball out of 5 black ball can be selected = 5C2 X 6C3

If balls of same color are same. No. of ways in which 2 black ball out of 5 black ball can be selected = 1

 

Permutation (arrangement) nPr

Number of ways in which r things out of N distinct things can be selected and can be arranged at r different places = NCr x r! = NPr

 

Problem 11) In how many ways 5 fruits out of group of 8 fruits can be selected and arranged at 5 different places?

Sol.  Number of ways in which 5 fruits out of 8 fruits can be selected and arranged at 5 different places =  8C5 x 5 = 56

Arrangement of objects not all distinct

Number of arrangements of N things out of which P1 are of one type, P2 are of second type, P3 are of third type and the rest are all different = (N! / (P1! P2! P3!))

 

Problem 12) How many words with or without meaning can be formed with the letters of following words: –

1) ALLAHABAD

2) MISSISSIPPI

3) APPLE

Sol.  Number of words that can be formed with the letters of word ALLAHABAD = (9!)/ (4!2!) = 7560

Number of words that can be formed with the letters of word MISSISSIPPI = (11!)/ (4!4!2!) = 34650

Number of words that can be formed with the letters of word APPLE = (5!)/ (2!) = 60.

 

Circular permutations

There are three objects A, B and C. We can linearly arrange these three objects in 3! = 6 possible ways. There are following linear arrangements of these three objects: – ABC, ACB, CAB, CBA, BAC, BCA.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

If we talk about circular arrangements, we can observe from figure 1 that three arrangements ACB, CBA and BAC are same. We can observe from figure 2 that three arrangements ABC, BCA and CAB are same.

We conclude that there are two ways of circular arrangements of these three objects. This happens because there is no point of a starting point on a circular arrangement. Three objects can be arranged in ((3!)/3) ways = 2! Ways.

Generalizing the whole concept, on circular table, N objects can be arranged in (N – 1)! Ways or (N!)/N.

 

Problem 13) In how many ways five guests can sit on a round table?

Sol.  If we talk about necklace or garland, where we can turn necklace or garland and clockwise and anti-clockwise arrangements are not different.

No. of circular arrangements of N different beads of necklace = (N – 1)! /2.

 

Problem 14) How many different garlands can be formed from eight different beads?

Sol.  Number of garlands formed from eight different beads = 7!/2 = 2520.

 

Selection of any number of things out of N distinct things

If there are N distinct things, 1 thing out of N distinct thing can be chosen in NC1.

m things out of N distinct things can be chosen in NCm ways.

Any number (0 or 1 or 2) of things out of N can be chosen in

  (NC0 + NC1 + NC2 + NC3 + NC4 + NC5 . . . . . . . . . . . .. NCN) ways. (By using combination and fundamental principle of addition)

NC0 + NC1 + NC2 + NC3 + NC4 + NC5 . . . . . . . . . . . .. NCN = 2N

The number of selections of 1 or more things out of N different things =

NC1 + NC2 + NC3 + NC4 + NC5 . . . . . . . . . . . .. NCN = 2N– 1

 

Problem 15) A boy has gone to a library and there are 200 different books in library. In how many ways he can pick one or more books from library?

Sol.  Number of ways in which he can pick one or more book =

\({ 2 }^{ 200 }-1\)

 

Number of diagonals of N sided polygon

Number of diagonals of N sided polygon = (Number of straight lines formed by joining N points) – (Number of sides) = NC2 – N

Number of straight lines formed by N points of which l are collinear

NC2 straight lines are formed by joining N points which are not collinear and only 1 straight line is formed by joining R collinear points. Therefore, number of straight lines formed by joining N points of which l are collinear =

NC2 –  lC2 + 1

Number of Triangles formed by N points of which l are collinear

NC3 triangles are formed by joining N points which are not collinear and no triangle is formed by joining R collinear points. Therefore, number of triangles formed by joining N points of which l are collinear =

NC3 –  lC3

Number of parallelograms formed by intersection of m parallel lines with n parallel lines

Two lines out of m parallel lines can be selected in mC2 ways and two lines out of n parallel lines can be selected in nC2 ways. Therefore, parallelogram is formed by selecting two lines out of m parallel lines and two lines out of n parallel lines. Number of parallelograms formed by intersection of m parallel lines with n parallel lines =

mC2 x nC2

 

 

Problem 16)   Find the number of diagonals & triangles formed in a decagon?

a) 35, 130

b) 25, 120

c) 35, 120

d) 45, 120

Sol.  No. of diagonals formed by decagon =

\({ _{ }^{ 10 }{ C } }_{ 2 }-10\\ =\frac { 9\times 10 }{ 2 } -10\\ ={ (35) }^{ Ans }\)

No. of triangles formed in a decagon =

\(=_{ }^{ 10 }{ { C }_{ 3 } }\\ =\frac { 8\times 9\times 10 }{ 2\times 3 } \\ ={ (120) }^{ Ans }\)

 

Problem 17) Out of 18 points in a plane, no three are in a straight line except 5 which are collinear. How many straight lines can be formed.

a) \(_{ }^{ 18 }{ { C }_{ 2 } }\)

b) \(_{ }^{ 18 }{ { C }_{ 2 } }-_{ }^{ 5 }{ { C }_{ 2 } }\)

c) \(_{ }^{ 18 }{ { C }_{ 2 }-_{ }^{ 5 }{ { C }_{ 2 }+1 } }\)

d) \(_{ }^{ 18 }{ { C }_{ 2 }-_{ }^{ 5 }{ { C }_{ 2 }-1 } }\)

e) \(_{ }^{ 18 }{ { C }_{ 2 }-_{ }^{ 5 }{ { C }_{ 2 }+2 } }\)

Sol.  No. of straight lines that can be formed =

\(=_{ }^{ 18 }{ { C }_{ 2 }-_{ }^{ 5 }{ { C }_{ 2 }+1 } }\)

 

Problem 18) How many numbers of 3-digits can be formed with the digits 1, 2, 3, 4, 5 (repetition of digits not allowed)

a) 125

b) 120

c) 60

d) 180

Sol.  The number of numbers formed would be given by

\(=5\times 4\times 3=60\)

(First digit can be filled in 5 ways, second can be filled in 4 ways & third can be formed in 3 ways.)

 

Problem 19)   How many nos. between 2000 & 3000 can be formed with the digits 0, 1, 2, 3, 4, 5, 6, 7 (repetition of digits not allowed)?

a) 42

b) 210

c) 336

d) 440

Sol.  The first digit can only be 2 (1 way), 2nd digit can filled only in 7 ways, 3rd digit can be filled only in 6 ways & 4th digit can be filled only in 5 ways.

No. of object =

\(=7\times 6\times 5=210\quad ways\)

 

Problem 20) In how many ways can a person send invitation cards to 6 of his friends if he has four servants to distribute the cards?

a) 42

b) 210

c) 24

d) 120

Sol.  Each invitation can be sent in 4 ways.ways.

Thus

\(4\times 4\times 4\times 4\times 4\times 4={ (4) }^{ 6 }\)

 

Problem 21) In how many ways can 7 Indians, 5 Pakistanis & 6 Dutch be seated in a row so that all persons of the same nationality sit together?

a) 3!

b) 7!5!6!

c) 3!7!5!6!

d) 182

Sol.  We should assume 7 Indians as one person, 5 Pakistanis as one person, 6 Dutch as one person. 5 Pakistanis can be arranged in 5! Ways. 7 Indians can be arranged in 7! Ways & 6 Dutch can be arranged in 6! Ways Pakistanis, Dutch & Indians can be arranged in 5! Ways.

Therefore, 7 Indians, 5 Pakistanis and 6 Dutch can sit in (7!×5!×6!×3!) ways.

 

Problem 22) In how many ways five chocolates can be chosen from an unlimited number of dairy milk, five-star & perk chocolates?

a) 81

b) 243

c) 21

d) 31

Sol. We have to choose five chocolates. We can choose first chocolate in three ways (either dairy milk or five-star or perk). Similarly, we can choose another chocolate in three way.

Therefore, five chocolates can be choosen in \(3\times 3\times 3\times 3\times 3={ (3) }^{ 5 }\) ways.

 

Problem 23) There are 6 pups & 4 cats. In how many ways can they be seated in a row so that no cats sit together?

Sol.  1st arrange 6 pups in 6 places in 6! ways. This will leave us with 7 places for 4 cats.

Assume = \( _{ }^{ 7 }{ { P }_{ 4 }(6!) }\) ways

 

Problem 24) A state issues automobile license plates that begin with two letters selected from a 26-letter alphabet, followed by four numerals selected from the digits 0 through 9 inclusive. Repeats are permitted. For example, one possible license plate combination is GF3352.

Quantity A:       The number of possible unique license plate combinations.

Quantity B:       60,00,000

a) Quantity A is greater

b) Quantity B is greater

c) The two quantities are equal

d) The relationship cannot be determined from the information given.

Sol.  The license plate have 2 letters followed by 4 numbers.

No. of possible license plate = \(26\times 26\times { 10 }^{ 4 }={ (6760000) }^{ Ans }\)

 There are 26 letters in the alphabet and 10 digits to pick from.

 

Problem 25) A 10-student class is to choose a president, vice president & security from the group. If no person can occupy more than one post, in how many ways can this be accomplished?

Sol.  There are 10 students from whom president can be chosen & after that there are 9 students from which vice president can be chosen, 8 students from which secretary can be chosen.

Whole process can be accomplished in = (8×9×10) = 720 ways.

 

Problem 26) A history exam features five questions. There of the questions are multiple-choice with four options each. The other two questions are true or false. If Caroline selects one answer for every question, how many ways can she/he answer the exam?

Sol.  No. of ways in ways she/he answer the question

\(=4\times 4\times 4\times 2\times 2=64\times 4={ (256) }^{ Ans }\)

 

Problem 27) In a school of 150 students, 75 study Latin, 110 study Spanish & 11 study neither.

Quantity   A:     The no. of students who study only Latin

Quantity   B:     46

a) Quantity A is greater

b) Quantity B is greater

c) The two quantities are equal

d) The relationship cannot be determined from the information given.

Sol.

Let A be the no. of students who study only Latin. Let B the no. of students who study both Latin & Spanish. Let C be the no. of students who study only Spanish. Let D be the no. of students who studies neither.

\(A+B+C+D=150\\ A+B=75\\ B+C=110\\ D=11\\ A=29,\quad B=46,\quad C=64\)

No. of students who study only Latin = 29

Quantity B is greater.

 

Problem 28) Mario’s pizza has two choices of crust. The restaurant also has 5 choices of toppings. Finally Mario’s offers every pizza in extra-cheese as well as regular. If Linda’s volleyball team decides to order a pizza with four different toppings, how many different choices do the teammates have at Mario’s pizza?

Sol. Consider the topics first, four the toppings are on the pizza & one isn’t. Four out of five can be chosen in \(_{ }^{ 5 }{ { C }_{ 4 } }\) ways.

If each of these pizzas can be offered in 2 choices of crust, 2 choices of cheese & 5 choices of toppings. Total no. of choices do the teammates have at Mario’s pizza = 5×2×2 = 20 ways

 

Problem 29) Country X has a four-digit postal code assigned to each town & none of the digits is repeated.

Quantity A:       The numbers of possible portal codes in country X

Quantity B:       4536

a) Quantity A is greater

b) Quantity B is greater

c) The two quantities are equal

d) The relationship cannot be determined from the information given.

Sol.  No. of possible postal code in country X = 10×9×8×7 = 5040

Quantity A is bigger.

 

Problem 30) 8 athletes compete in a race in which gold, silver & a bronze medal will be awarded to the top three finishers, in that order.

Quantity A: The number of ways in which the medals can be awarded.

Quantity B:       8×3!

a) Quantity A is greater

b) Quantity B is greater

c) The two quantities are equal

d) The relationship cannot be determined from the information given.

Sol.  No. of ways in which the medals can be awarded

[/latex]=8\times 7\times 6=336\quad ways\(\)

Quantity A is bigger.

(Gold medal winner can be selected in 8 ways, silver medal winner can be selected in 7 ways & bronze medal winner can be selected in 6 ways.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHAPTER 30 on Vocabulary

DISQUIET (Verb)

Meaning- to make (someone) worried or nervous.

Synonym- DISCOMPOSE, PERTURB

Uses-

  • In the exam, I was disquieted by the strange noises we herd outside our school.

DISQUIET (Noun)

Meaning- A feeling of worry (or Nervousness) or lack of peace (or tranquility).

Synonym- ANXIETY

Uses-

  • There is increasing public disquiet about the number of crimes against women in the city.
  • A period of disquiet before the results of the elections was confirmed.

                                

DISSEMBLE (Verb)

Meaning- 1) to hide your true feeling, opinion, nature etc.

2) to make a false show of.

Mnemonic trick- The word dissemble contains word ‘ssemble’. ‘ssemble’ sounds similar to assemble. Director dissembled after ‘de-assembling’ the company. Therefore, dissemble means to hide your true feeling, opinion, nature etc. or to make a false show of.

Synonym- COUNTERFEIT, FEIGN, PRETEND, SHAM

Uses-

  • He accused the government of dissembling the facts about our economy.
  • Children learn to dissemble at a surprisingly early age.
  • Hayden’ s friend dissembled his real feeling regarding his wife’ s leaving him for another man.
  • He dissembled his feelings at the news that his old girlfriend was getting married to someone else.

 

DISSONANCE (Adj.)

Meaning- 1) lack of agreement; especially: inconsistency between the beliefs.

2) mingling of discordant or inharmonious sounds.

Mnemonic trick- The word dissonance is opposite in meaning to word resonance. The word resonance means the quality of sound that stays loud, clear and pleasant for a long time or quality that makes something personally meaningful or important to see. Therefore, dissonance means mingling of inharmonious sounds or conflict of opinion.

Synonym- DISHARMONY, DISACCORD, DISCORDANCE

Uses-

  • Western composers often use dissonance -clashing or unresolved chords for special effects in their musical work.
  • Ending as an unsolved dissonance is a peculiar quality of his stories.

                             

DISTRAIT (Adj.)

Meaning- Inattentive or distracted especially because of anxiety.

Synonym- DELIRIOUS, DISTRACTED, DISTRAUGHT

Uses-

  • He grew more and more distrait as hours passed without confirmation that there were survivors of the plane crash.
  • When Rahul did not show up for the meeting, her employer was uneasy and distrait.
  • I appeared to be distrait before the exam because I lost admit card before the exam.

                       

DOCILE (OR PLIABLE) (Verb)

Meaning- 1) Easily, taught, led or controlled.

2) Easily managed or obedient.

Synonym- AMENABLE, TRACTABLE, OBEDIENT

Uses-

  • I had a docile, well-behaved pet.
  • Docile people sometimes wonder why they are not more popular; after all, they never make any trouble for anyone.
  • When a child becomes unusually pliant, obedient and manageable, he or she may, in short, become docile.
  • Other people usually find nothing admirable or necessarily likable about a docile person who is willing to be pushed around, or who does what he or she is told out of fear of offending others.

 

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CHAPTER 29 on Vocabulary

DISABUSE (Verb)

Meaning- Free someone from a mistake in thinking.

Uses-

  • Do you really believe that toilets flush one way in the Northern hemisphere and another way in the Southern hemisphere? Any physicist would be happy to disabuse you of that silly notion.

 

DISCERN (Verb)

Meaning-  1) to see, recognize or understand something that is not clear.

2) to see or understand the difference.

Mnemonic trick- The word discern contains word ‘ern’. ‘ern’ sounds similar to earn. We normally try to discern how much our competitors earn. Therefore, discern means to see, recognize or understand something that is not clear.

Synonym- PERCEIVE, DISTINGUISH, OBSERVE

Uses-

  • The reason behind this sudden change is difficult to discern.
  • I was barely able to discern anything in the darkness.

         

EMANCIPATE (OR DISENTHRALL) (Verb)

Meaning- to free somebody especially from legal, political or social restrictions.

Synonym- FREE, LIBERATE, MANUMIT

Uses-

  • Slaves were not emancipated until 1863 in the United States.
  • The women’ s liberation movement would like to emancipate women from being restricted to their homes.
  • Mildred was quite smart and received her high school diploma while she was just 15, enabling her to start her university education in another city and being independent; therefore, being emancipated from control by her mother and father.

 

DISJOINT (Verb)

Meaning- 1) to separate something at the joints.

2) to force or to move something out of its usual position, or be moved out of the usual position.

3) to destroy the unity or coherence of something.

Synonym- DECOUPLE, DISJOINT, DISUNITE, SEPARATE

Uses-

  • He is disjointing himself from the organization because he realizes his organization id advocating illegal practices.
  • The author deliberately disjoints his narrative in favor of a more impressionistic account of the war.

                              

DISPARATE (Adj.)

Meaning- Different from each other.

Mnemonic trick- The word disparate contains word ‘sparate’. ‘Sparate’ sounds similar to separate. If we combine separated things, then we get a disparate combination of things. Therefore, disparate means different from each other.

Synonym- HETEROGENEOUS, DISSIMILAR, INCONGRUENT, CONTRASTING, DISTINCT

Uses-

  • This wine has more disparate flavor than that one.
  • When I discussed the cashless economy with my relatives, I got disparate ideas from adults and children.
  • The school was composed of students from disparate cultures.
  • Even though the boys were twins, their personalities were disparate.

 

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CHAPTER 28 on Vocabulary

DIATRIBE (Adj.)

Meaning- bitter scolding or piece of writing that strongly criticizes someone or something.

Mnemonic trick- The word diatribe contains word ‘tribe’. If you speak something against any tribe or quota for schedule tribe. Definitely, tribe will launch a diatribe against you. Therefore, diatribe means bitter scolding or piece of writing that strongly criticizes someone or something.

Synonym- TIRADE, HARANGUE, JEREMIAD, PHILIPPIC, DENUNCIATION

Uses-

  • His novel was a strong and more outspoken diatribe against society and marriage laws.
  • The article is a diatribe against mainstream media.
  • During the lengthy diatribe delivered by his opponent, he remained calm and self-controlled.
  • Channel launched an open diatribe against government policies.

 

DIFFIDENT (Adj.)

Meaning- 1) lack of confidence or not feeling comfortable around certain people.

2) very careful about acting or speaking.

Mnemonic trick- The word diffident is opposite in meaning to word confident. The word diffident is used for a person having lack of self-confidence and who does not feel comfortable around certain people.

Synonym- UNASSERTIVE, SHY, INTROVERTED, HESISTANT, RESERVED, MODEST

Uses-

  • When John is called on to answer a question that his teacher is asking, he usually has a diffident way of expressing himself even when he is certain that he is correct.
  • When the reporter asked the politician, if he would be running for a third term, she made a diffident response because she wanted to avoid questions on his governance.

 

DIGRESS (Verb) & DIGRESSION (Noun)

DIGRESS (Verb)

Meaning- to speak or write about something that is different from the main subject being discussed.

Synonym- SWERVE, DEVIATE

Uses-

  • Mayor did not take a stand on corruption, he digressed from the topic.
  • If I can digress for a moment, I want to briefly mention her earlier films.

DIGRESSION (Noun)

Meaning- A spoken topic or written document about something which is different from the main subject being discussed.

Uses-

  • The speaker at the conference presented many humorous digressions even though it was supposed to be a serious financial report.
  • On TV, the political commentator was revealing the social and political digressions that the senator had committed while he was a member of the U.S Congress.

                  

DILETTANTE (OR DABBLER) (Noun)

Meaning- person whose interest in an art or in an area of knowledge is not very deep or serious

Mnemonic trick- dilettante contains two words ‘dil’ and ‘let’. We are not letting our dil or heart or heart to completely open for something. It means that we are not deeply engaged in or concerned with something. Therefore, dilettante means a person whose interest in an art or in an area of knowledge is not very deep or serious.

Synonym- SUPERFICIAL, AMATEUR

Uses-

  • Michael flit like a butterfly from interest to interest, never concentrating for any length of time on one. He is a true dilettante.
  • AS a Salesman, Erwin was still a dilettante because he was really not interested in that type of work.
  • He is not a struggling artist. Just like a dilettante, he follows the art as a pastime.
  • You can tell the difference between a true expert and a scientist who is just a dilettante.

                                    

DIRGE (Noun)

Meaning- A slow song or piece of music that expresses sadness or sorrow.

Mnemonic trick- The word dirge sounds similar to Hindi word ‘dird’. Dirge expresses ‘dird’. Therefore, dirge means a slow song or piece of music that expresses sadness or sorrow.

Synonym- ELEGY, THRENODY, LAMENT, REQUIEM

Uses-

  • The choir will sing dirge from Bollywood movie.
  • The funeral dirge stirred us to tears.

 

 

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CHAPTER 27 on Vocabulary

DERIDE (Adj.)

Meaning- 1) to write or to talk about another person, or something in a very critical or insulting way.

2) to say that someone or something is of no value or is ridiculous.

Mnemonic trick- The word deride can be memorized by thinking that it is made up of two words ‘de’ and ‘ride’. When I ask him for ride by saying ‘de de ride’, he derided me. When a person fell off a ride in an amusement park. He was derided by his friends. Therefore, deride means to write or to talk about another person, or something in a very critical or insulting way.

Synonym- RIDICULE, SCOFF, MOCK, SCORN, TAUNT

Uses-

  • My friends derided my efforts, but were forced to eat their words when we won first place.
  • Deriding other politicians is a contemporary fashion in Indian politics.
  • A newspaper critic derided David’ s book as dull and worthless.
  • His boss derided his ideas as ludicrous.

  

SACRILEGE (OR BLASPHEMY OR DESECRATION OR IRREVERENCE) (Noun)

Meaning- The act of treating a holy thing or place without respect.

Synonym- IMPIETY, DEFILEMENT

Uses-

  • Hindu consider it sacrilege to wear shoes inside a temple.
  • They accused him of committing a sacrilege.
  • In 2010, Advertisement agency, produced images of Prophet Mohammad in an episode that featured the Prophet as a bear mascot. Angered by the blasphemy, one Islamic website threatened the producer for what they deemed as a high level of disrespect for the Prophet.

                          

DESICCATE (Verb)

Meaning- 1) to dry up.

2) to preserve (something such as food) by removing the moisture.

3) to drain the power or ability of something to continue to live, be successful etc.

Mnemonic trick- The word desiccate can be memorized by thinking that it is made up of two words ‘des’ and ‘cat’. ‘DESERT KI CAT’ died because of scarcity of water or because of desiccation. Therefore, desiccate means to dry up.

Synonym- PARCH, SHRIVEL, DEHYDRATE, WITHER, EXSICCATE

Uses-

  • The surgeon thoroughly desiccated the tissue with a needle electrode.
  • While making sweets for the party, Elizabeth used a cup of desiccated coconuts.
  • This movie revolves around the married life and desiccated romance after marriage.
  • Historian’ s prose desiccates what is actually an exciting period in European history.
  • Desiccated land or drought is a result of environmental degradation.

 

DESPONDENT (OR DEJECTED OR DISCONSOLATE) (Adj.)

Meaning- very sad and without hope because of loss, failure etc.

Synonym- DEPRESSED, MELANCHOLIC, GLOOMY

Uses-

  • Karan was very despondent about losing his job after fifteen years of work in the company; however, the business was having economic problems and laying off many of its employees.
  • He became despondent after working very hard and failing to achieve desired results.
  • She looked despondent when she was told that she had n’ t got the job.

 

DESPOT (OR TYRANT) (Noun)

Meaning- a person especially a ruler who has unlimited power over other people and often uses it unfairly and cruelly.

Synonym- DICTATOR

Uses-

  • The king was regarded as having been an enlightened despot.
  • Persians installed despots to rule their Greek subjects, but such rulers were unpopular.
  • There are some despots, even in these modern times, who are ruling their people in cruel and inhumane ways.
  • My uncle was a good football coach; however, a lot of people considered him to be a despot because he was always dictating what the players had to do during the games.

 

DESTITUTE (OR IMPECUNIOUS OR PENURIOUS OR INDIGENT OR PENNILESS) (Adj.)

Meaning- very poor or having little or no money.

Synonym- PAUPERIZED

Antonym- AFFLUENT, PLUSH, PROSPEROUS, OPULENT

Explanation- Destitute, impecunious, penurious, indigent and penniless means poor. Impoverish has two meanings. It means to make someone poor or to deplete the quality or richness of something. For example –

  • poor farming practices impoverished the soil.
  • Dictators enriched themselves but impoverished the public.

Uses of Destitute-

  • He got fired from the job and now he is destitute.
  • Many families were left destitute by the second world war.

 

DESULTORY (Adj.)

Meaning- not having a plan or purpose or done without making a serious effort.

Mnemonic trick- The word desultory contains word desult. Desult sounds similar to result. Something done without aiming to produce a good result is desultory. Therefore, desultory means something done just perfunctorily without making a serious effort or without aiming to produce a good result.

Synonym- AIMLESS, UNFOCUSSED, HAPHAZARD

Uses-

  • We usually make a desultory search on the internet for entertainment.
  • Michael was searching for something of interest on television desultorily.
  • Your essay seems desultory and unclear. You should write to the point.
  • She made a desultory attempt at conversation.

 

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CHAPTER 26 on Vocabulary

DELINEATE (Verb)

Meaning- to describe, show or explain something in detail.

Mnemonic trick- The word delineate contains word deli and eat. Deli sounds similar to Delhi. My parents clearly delineated what to eat and what not to eat in the crowded market of Delhi. Therefore, delineate means to explain or describe something in detail.

Synonym- SPECIFY, OUTLINE, DELIMIT, DEFINE

Uses-

  • Our objectives need to be properly delineated.
  • The ship’ s route is clearly delineated on the map.
  • The politician was delineating his development plan in his election rally.
  • In his novel, the story was carefully delineated.

                 

DEMAGOGUE (Adj.) AND PEDAGOGUE (Adj.)

DEMAGOGUE (Adj.)

Meaning- A political leader who wins support by exciting people’ s emotions rather than by having good ideas. Demagogue tries to get support by making false claims and promises.

Explanation- “dem” is a root word for people. For example- Democracy means the government of the people. Greek word “agogos” means “leading”. Therefore, demagogue means leader of the mob who appeals to the passions and prejudices of the mob in order to get political advantage.

Synonym- RABBLE-ROUSER

Uses-

  • His opponent called him a bigoted demagogue.
  • Here’s what demagogues like Trump do to their countries when they take power.
  • He was an enthusiastic, but a fickle and ambitious demagogue, and he achieved a better reputation as a writer.

PEDAGOGUE (Adj.)

Meaning- School teacher especially who gives attention to formal rules or traditional method of teaching.

Explanation- ped- is a word-forming element. It means “child or boy”. Greek word “agogos” means “leading”. Therefore, pedagogue means teacher or schoolmaster.

Synonym- PEDANTIC TEACHER, EDUCATIONIST

Uses-

  • The teaching of a pedagogue consisted entirely of reading directly from the textbook in the same tone.
  • Teaching and giving direction to children is what a pedagogue does.

 

 

DENIZEN (OR INHABITANT) (Noun)

Meaning- a person or animal that lives in a particular place.

Mnemonic trick- The word denizen sounds similar to citizen. Therefore, citizen or denizen means a person who lives in particular place.

Synonym- DWELLER, NATIVE

Uses-

  • The denizens of this island don’ t like the tourist.
  • Lion-tailed macaque, koala bears are among the denizens of the forest.
  • The polar bear is an iconic denizen of the snowy Arctic.

        

DEPRECIATE (Verb) and DEPRECATE (Verb)

DEPRECIATE(Verb)

Meaning- to decrease in value or to describe something as having little value

Synonym- REDUCE, ATTENUATE

Uses-

  • The value of the property has depreciated greatly.
  • There was a slight period during which the stocks seemed to depreciate but they rallied after a short time.
  • He made unworthy attempt to depreciate the learning of great historians.
  • Michael felt that he had to depreciate Seema’ s effort to help her.

DEPRECATE (Verb)

Meaning- to criticize or express disapproval of something

Synonym- BELITTLE, DISPARAGE

Uses-

  • He looks down on the acts of others or He deprecates.
  • He showed contempt and disapproval of younger generation. He deprecated the younger generation.

 

 

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CHAPTER 25 on Vocabulary

DECISIVE (Adj.)

Meaning- 1) able to make decisions quickly and confidently.

2) having the power to determine an outcome.

Mnemonic trick- The word decisive sounds similar to a decision. A decisive person has the ability to make decisions quickly and confidently. Therefore, decisive means ability to make decisions quickly and confidently or having the power to determine an outcome.

Synonym- DETERMINED, SINGLE-MINDED, UNMISTAKABLE

Uses-

  • Carol’ s argument was the decisive one in determining when her family would go on their vacation.
  • RBI governor was known for his decisive manners.
  • Caste factor will have a decisive influence in upcoming assembly elections.
  • Toppers will cast decisive votes in student union elections.

 

EMBEZZLE (OR PECULATE OR DEFALCATE) (Verb)

Meaning- to secretly take money that is in your care or that belongs to an organization or company you work for.

Synonym- MALVERSATION

Uses-

  • He was convicted of embezzling.
  • He was caught embezzling money from his clients.
  • She embezzled thousands of dollars from the charity.
  • She got deferred sentence for embezzlement.
  • I don’ t think he was in a position to embezzle anything from the coffee shop.
  • The president of the country was embezzling several million dollars from the country’s treasury so he could have a very fancy house to live in and even to have his own private zoo.

                                

DEFERENCE (Noun)

Meaning- A way of behaving that shows respect for someone or something.

Mnemonic trick- The word deference sounds similar to defense. We show deference or respect to defense personnel. Because they sacrifice their lives for us. Therefore, deference means a way of behaving that shows respect for someone or something.

Synonym- ACQUIESCENCE, COMPLIANCY, OBEDIENCE, SUBMISSIVENESS, REVERENCE, OBSEQUIOUSNESS, ESTEEM

Uses-

  • I was taught to show deference to people who were as old as my grandparents.
  • The junior lawyer showed deference to his senior partner by agreeing with his request to adjourn.
  • He treats her with such deference.

 

DELEGATE (Verb & Noun)

DELEGATE (Verb)

Meaning- 1) to give (Control, responsibility, authority etc.) to someone.

2) to choose (someone) to do something.

Uses-

  • The manager will delegate authority to the best employees of this company so the project can succeed.

DELEGATE (Noun)

Meaning- A person who is acting for another’s as a representative to a convention or conference.

Uses-

  • The president will delegate the union leader as a delegate to the convention.

 

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CHAPTER 24 on Vocabulary

DEBACLE (Noun)

Meaning- 1) A great disaster.

2) complete failure.

Mnemonic trick- The word debacle contains word bac. Bac sounds similar to back. If we get back or reappear or supplementary in our semester exam. It is a complete debacle of our semester’ s result.

Synonym- FIASCO, CALAMITY, CATASTROPHE

Uses-

  • The result of 2015 Delhi assembly elections was a total debacle for the ruling Bhartiya Janta party who lost completely.
  • The opposition is viewing demonetization as a debacle for the Indian economy.
  • After the debacle of the author’ s first novel, he had difficulty getting another publisher to consider printing his next fictional story.
  • It makes me wonder that she has not learned anything from his debacle.

                                     

DEBAUCH(Verb)

Meaning- 1) to participate or to behave in corrupt and unacceptable activities.

2) to cause a change in value or quality of something.

Mnemonic trick- The word debauch contains word bauch. Bauch sounds similar to watch. If we do not watch or take care of our children, he will debauch or he will start behaving in corrupt and unacceptable activity. Therefore, debauch means to participate in corrupt and unacceptable activities.

Synonym- DEBASE, PERVERT, DEPRAVE

Explanation- Debase implies a loss of position, worth, value or dignity. Deprave is used when something has made evil or morally bad or corrupting influence on someone. Pervert means to cause to turn away from what is good or morally right. Debauched (Adj.) means weakened or destroyed by bad sexual behavior.

Uses-

  • The scandal sheets are full of stories of efforts to debauch young people by some adults.
  • The nefarious old man attempted to debauch his nephew by encouraging him to commit illegal activities.
  • He debauched the delicate painting by splashing green paint all over it.

 

DEBILITATE (OR ENFEEBLE) (Verb)

Meaning- to make (someone or something) weak.

Synonym- WEAKEN, DEVITALIZE, ENERVATE, ENFEEBLE, ETIOLATE

Uses-

  • Sharon was debilitated by the excessively hot weather and so she felt abnormally tired and incapacitated mentally and physically.
  • One financial set back after another one can debilitate a company’s prospects for continuing to stay in business.
  • The long period of being confined to a hospital bed will enfeeble anyone.
  • He was debilitated by infection.
  • Hectic schedule in office and his poor health completely debilitated him.

 

 

DEBONAIR (Adj.)

Meaning- 1) dressing and acting in an appealing and sophisticated way.

2) fashionable, attractive and confident.

Mnemonic trick- 1) After reading DEBONAIR magazine and after watching debonair ladies in Debonair magazine. You will start wearing fashionable clothes and be a debonair to impress debonair ladies.

2) The word debonair contains word DEBO. Debojit (Deboo Da) is debonair of west Bengal. Therefore, debonair means Dashing.

Synonym- JAUNTY, SUAVE, ELEGANT, REFINED, URBANE, CULTURED, REFINED

Uses-

  • A debonair man in black suit and top hat.
  • His success in reality show made him debonair of London.
  • This man could be described as debonair.

 

DECIMATE (OR EXTERMINATE) (Verb)

Meaning- to kill a large number of plants, animals, people etc. or to severely damage a large part of something.

Mnemonic trick- The word decimate sounds similar to Hindi word desi maid. Desi maid decimated his all the family members for money. Therefore, decimate means to kill a large number of plants, animals, people etc. or to severely damage large part of something.

Synonym- ANNIHILATE, DEMOLISH, DESTROY

Meaning explanation- Annihilate implies complete destruction of something and decimate means to kill a large number of plants, animals, people or to severely damage a large part of something. Demolish means to destroy (a building, bridge etc.) so that it cannot be repaired.

Uses-

  • If we do not get rain soon, it will decimate the farm crops in this area.
  • Demonetization has decimated the small business in rural areas.
  • The government’s budget cuts will decimate public services in many small towns.
  • The invaders in the eighteenth century decimated thousands of native people of our country.

 

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CHAPTER 23 on Vocabulary

CUPIDITY (Noun)

Meaning- A strong desire for money or possessions.

Synonym- ACQUISITIVENESS, AVIDITY, GREED, GRASPINGNESS, AVARICE, COVETOUSNESS, MERCENARINESS, RAPACITY, RAPACIOUSNESS

Uses-

  • The investigation revealed the cupidity of politician.
  • Jake had a cupidity for wealth and powerful influences over other people.

 

CYNICAL (Adj.)

Meaning- 1) Gives reference to those people who are distrustful of human nature and motives or those who believe that people are generally selfish and dishonest.

2) Selfish and dishonest in a way that shows no concern about treating other people fairly.

Mnemonic trick- The word cynical contains word ‘cynic’. ‘cynic’ sounds similar to Hindi word ‘SAINIK’. ‘SAINIK’ or army personnel are always cynical about nature and motives of personnel of opposition army. Therefore, cynical gives reference to those people who are distrustful of human nature and motives or those who believe that people are generally selfish and dishonest.

Synonym- PESSIMISTIC, MISANTHROPIC

Uses-

  • Cynical people say there is no such thing as true love.
  • He started laughing and mocked the old man with cynical derision.
  • For all his talk about the power of positivity, I confess I am cynical about whether things will get better in our lifetime.
  • His limited opportunities add to his bitter, cynical attitude towards

 

CYNOSURE (Noun)

Meaning- 1) A person or thing having a quality of excellence or great beauty which attracts a lot of attention.

2) Someone or something acting as a guide or used for direction.

Mnemonic trick-

Synonym- COMPASS, DIRECTION, POLESTAR

Uses-

  • The famed pianist was the cynosure of the critics for the newspapers.
  • The iceberg was the cynosure for the tourist boat in the Arctic.
  • The cynosure at the intersection of the two roads helped to reassure Mark that he was going in the right direction to the museum.

                  

DILETTANTE (OR DABBLER) (Noun)

Meaning- person whose interest in an art or in an area of knowledge is not very deep or serious

Mnemonic trick- dilettante contains two words ‘dil’ and ‘let’. We are not letting our dil or heart or heart to completely open for something. It means that we are not deeply engaged in or concerned with something. Therefore, dilettante means a person whose interest in an art or in an area of knowledge is not very deep or serious.

Synonym- SUPERFICIAL, AMATEUR

Uses-

  • Michael flit like a butterfly from interest to interest, never concentrating for any length of time on one. He is a true dilettante.
  • AS a Salesman, Erwin was still a dilettante because he was really not interested in that type of work.
  • He is not a struggling artist. Just like a dilettante, he follows the art as a pastime.
  • You can tell the difference between a true expert and a scientist who is just a dilettante.

                  

DAUNT (OR DISMAY OR FAZE) (Verb)

Meaning- to make someone afraid or less confident

Mnemonic trick- Daunt sounds similar to Hindi word ‘Daant’. ‘DAANT KHAANE KE BAAD WE GET FRIGHTENED OR INTIMIDATED’. Therefore, Daunt means to make someone afraid or less confident.

Synonym- FRIGHTEN, INTIMIDATE, DISCOURAGE, DISHEARTEN, APPALL

Uses-

  • She was a brave woman but she felt daunted by the task ahead.
  • Don’ t let the new phase of educational reform daunt you, Tina. We, teachers, have watched this happen before.
  • Next generation of star kids will seldom succeed as actors if they let criticism daunt them.
  • This man’ s behavior is rather daunting.

 

 

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CHAPTER 22 on Vocabulary

CORROBORATE (Verb)

Meaning- to add proof or certainty to an account, statement, idea etc. or to support something.

Mnemonic trick- The word corroborate sounds similar to collaborate. If we Collaborate with someone, we definitely corroborate or support him. Therefore, corroborate means to support someone or something.

Synonym- SUPPORT, AUTHENTICATE, ATTEST

Uses-

  • Recent research seems to corroborate this theory.
  • I had access to a wide range of documents which corroborated the story.
  • The committee continued to collaborate on their research; in fact, their most recent findings seemed to corroborate their earlier conclusion.

 

COUNTENANCE (Noun)

FIRST Meaning- the appearance or expression of someone’s face.

Mnemonic trick- COUNT is in the word countenance. The countenance of people is different while counting money. Therefore, countenance means facial expression.

Uses-

  • He was of noble countenance.

SECOND Meaning- To support something or to agree to something happening.

Antonym- DISCOUNTENANCE

Uses-

  • The committee refused to countenance his proposals.

                                    

CRASS (Noun)

Meaning- stupid in a grossly inconsiderate way or stupid without carrying for other people

Mnemonic trick- crass is similar to word class. In school kids make crass complaints of fellow students to the teacher. They pass crass comments in class. Therefore, crass means coarse and stupid or stupid in a grossly inconsiderate way.

Synonym- GROSS, INSENSIBLE

Uses-

  • Don’ t use sadness as an excuse for crass behavior.
  • He is free from crass superstition.
  • His crassness makes it impossible for him to be accepted by refined people.
  • Crass misrepresentation of the facts was done by him.
  • Such crass materialism will never lead to real happiness.

                     

CREDULOUS (OR GULLIBLE) (Adj.)

Meaning- easily fooled or quick to believe something that is not true

Synonym- TRUSTING, UNWARY

Antonym- INCREDULOUS

Uses-

  • Children are not gullible these days.
  • I am not gullible enough to believe something that is outrageous.
  • There is a gullible side to Indian people. They can be easily misled. Religion is the best device used to mislead them.

                             

CRESCENDO (Noun)

Meaning- 1) A gradual increase in loudness of a sound or gradual increase in volume or intensity of something.

2) The highest or loudest point of something that increases gradually.

Mnemonic trick- The word crescendo contains word ‘cres’ and ‘scend’. ‘cres’ sounds similar to crest and ‘scend’ sounds similar to sound. The crest of the sound wave contains point at which intensity of sound is highest. Therefore, crescendo means highest or loudest point of something that increases gradually.

Synonym- ACME, APEX, APOGEE, CLIMAX, ZENITH, PINNACLE, SUMMIT

Uses-

  • The musicians were following the directions of leader to begin the crescendo of the musical performance.
  • Their divorce was merely the formal crescendo of a long period of marital stress and quarreling.
  • The excitement of the audience reached its crescendo when the singer came on stage.
  • Complaints about the corruption and other economic conditions have reached such a crescendo that it is very difficult for the current political party to be re-elected.

 

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