Know Yourself

Superfluous Thesaurus: Adjective : extra                   excess, excessive, extreme, inessential, lavish, left over, unnecessary, overflowing, spare, surplus, useless, unrequired ... Antonyms : necessary, important... Example sentences: ·          His brother knows everything and the guide is superfluous.      ·           They're superfluous.

Problems on Permutations and Combinations: 1. In how many ways can 18 books on Mathematics and 15 books on English be placed in a row on a shelf so that two books on English may not be together? Solution:                The arrangement will be                                E M E M E M ..... E M _ M _ M _ M_               So 15 places out of 19 can be chosen =    19 C15                                                                           =    19 C4                                                                           = 19*18*17*16/ 1*2*3*4                                                                           = 3876. 2. Out of 5 consonants and 3 vowels, how many words of 2 consonants and 1 vowel can be formed? Solution:                2 Consonants out of 5 and 1 vowel out of 3 =  (   5 C2 *   3 C1) = 5*4/1*2 *3               The Number of groups, each having  2 consonants and 1 vowel = 30.               Each group contains 3 letters.               T

Recoup Thesaurus: Verb : recover           compensate, get well, redeem, refund, regain, repay, retrieve... Antonyms : lose... Example sentences: ·          They've recouped everything which they lost last year.   ·           He must recoup his losses. 

Problems on Permutations and Combinations: 1. A box contains 4 white balls, 2 black balls and 5 red balls. In how many ways can 2 balls be drawn from the box if at least one white ball is to be included in the draw? Solution:              = One white ball and one black or red ball + Two white balls              =  (   4 C1 *   7 C1) + (   4 C2)              = 4*7 + (4*3/1*2)              =  28 + 6              = 34. 2. How many 4-digit numbers can be formed from the digits 1, 3, 5, 7 and 9, which are divisible by 5 and none of the digits is repeated? Solution:               The unit place must be 5 since the numbers should be divisible by 5.               Here the possibility is 1.               The tens place should be any of the remaining 4 numbers.               Here the possibility is 4.              The hundreds place should be any of the remaining 3 numbers.              Here the possibility is 3.              The thousands place should be any of the rem

Mandate Thesaurus: Noun : authority, order            behest, charge, command, dictate, directive, instruction, warrant... Antonyms : denial, turndown, veto... Example sentences: ·          The officer mandates to fire the gun.   ·           He has the mandate to start an election. 

Problems on Permutations and Combinations: 1. From a group of 4 men and 2 women, 3 persons are to be selected to form a committee so that at least 2 men are there on the committee. In how many ways can it be done? Solution:                =    4 C2 *    2 C1 +   4 C3                =    4 C2 *    2 C1 +   4 C1                =  (4*3)/(1*2) * 2 +                = 12 +4                = 16. 2.  From a group of 6 boys and 3 girls, 5 children are to be selected. In how many different ways can they be selected such that at least 3 boys should be there? Solution:                = (   6 C3 *   3 C2) + (   6 C4 *    3 C1 ) +(   6 C5 )                = [(6*5*4)/(1*2*3) *  3 C1] +[  6 C2 * 3 ] +   6 C1                = [20*3] +[(6*5/1*2)*3] +6                = 60+45+6                = 111.

Gnaw Thesaurus: Verb: chew, worried about            bite, gnash,, eat, crunch, gum, chaw, champ...            annoy, be bothered, distress, irritate, trouble...                                            Example sentences: ·        He used to gnaw his nails.  ·        She was gnawed  her problems.  

Problems on Permutations and Combinations: 1. In how many ways can a group of 4 men and 3 women be made out of a total 6 men and 5 women? Solution:                =    6 C4 *    5 C3                =     6 C2 *    5 C2                =  (6*5)/(1*2) * (5*4)/(1*2)                = 150. 2.  In how many ways a committee, consisting of 2 men and 4 women can be made from 5 men and 5 women? Solution:                =    5 C2 *    5 C4                =    5 C2 *    5 C1                =  (5*4)/(1*2) * 5                =   50.

Confiscate Thesaurus: Verb: steal            seize, grab, hijack, swipe, take, take over, accroach...                                          Antonyms: offer. ..                                        Example sentences: ·        The police department confiscated all his research papers.   ·        They're ready to confiscate his goods. 

Problems on Permutations and Combinations: 1.In how many different ways can the letters of the word 'EAT' be arranged in such a way that the vowels occupy only the odd positions? Solution:                There are 3 letters in the given word.                The positions are                                              1     2     3                              Now, the 2 vowels E and A can be placed at 2 odd positions 1 and 3.                The consonant T will occupy the even position 2.                The number of ways of arranging the vowels =   2 P2 = 2! = 2.                The number of ways of arranging the consonant =    1 P1 = 1! = 1.                Total number of ways = 2*1 = 2. 2.  In how many different ways can the letters of the word 'TABLE' be arranged in such a way that the vowels occupy only the odd positions? Solution:              There are 5 letters in the given word.                The positions are                  

Mitigate Thesaurus: Verb: lighten           appease, blunt, calm, dull, ease, lessen, diminish, pacify, reduce, soothe, weaken, soften...                                        Antonyms: increase, aggravate, worsen. ..                                        Example sentences: ·        He mitigated the crowd in no time.  ·        They couldn't mitigate the fire. 

Problems on Permutations and Combinations: 1.In how many different ways can the letters of the word 'SUCCEED' be arranged so that the vowels always come together? Solution:                The arrangement will be SCCD (UEE)                The 5 letters can be arranged in 5!/2! = 120/2 = 60.                The vowels can be arranged among themselves in 3!/2! = 6/2= 3.                The required number of ways = 60*3 = 180. 2.  In how many different ways can the letters of the word 'MOMENT' be arranged so that the vowels always come together? Solution:                The arrangement will be MMNT (OE)                The 5 letters can be arranged in 5!/2! = 120/2 = 60.                The vowels can be arranged among themselves in 2! = 2.                The required number of ways = 60*3 =  180.

Authentic Thesaurus: Adjective: real                    actual, certain, accurate, genuine, factful, faithful, original, true, trustworthy...                                          Antonyms: fake, false, unreal, ungenuine. ..                                        Example sentences: ·        The illusions made me feel authentic .  ·        Those fake flowers look authentic. 

Problems on Permutations and Combinations: 1.  In how many different ways can the letters of the word 'POWER' be arranged so that the vowels always come together? Solution:                The arrangement will be PWR (OE)                The 4 letters can be arranged in 4! = 24.                The vowels can be arranged among themselves in 2! = 2.                The required number of ways = 24*2 = 48. 2.  In how many different ways can the letters of the word 'SIGNAL' be arranged so that the vowels always come together?  Solution:                The arrangement will be SGNL (IA)                The 5 letters can be arranged in 5! = 120.                The vowels can be arranged among themselves in 2! = 2.                The required number of ways = 120*2 = 240.

Nostalgia Thesaurus: Noun: fond memories             homesickness, longing, reminiscence, remorse, pleasant remembrances, yearning...                                      Example sentences: ·        She's feeling nostalgia by seeing her childhood albums.  ·       The cookies from that shop makes me nostalgia. 

Problems on Permutations and Combinations: 1. In how many different ways can the letters of the word 'FINE' be arranged so that the vowels always come together? Solution:                The arrangement will be FN (IE)                The 3 letters can be arranged in 3! = 6.                The vowels can be arranged among themselves in 2! = 2.                The required number of ways = 6*2 = 12. 2.  In how many different ways can the letters of the word 'DISPUTE' be arranged so that the vowels always come together? Solution:                The arrangement will be DSPT (IUE)                The 5 letters can be arranged in 5! = 120.                The vowels can be arranged among themselves in 3! = 6.                The required number of ways = 120*6 = 720.

Slugger Thesaurus: Noun: aggresor             antagonist, boxer, brawler, bully, opponent, rival, soldier, warrior, scrapper...                                               Antonyms: appeaser, pacifier, peacemaker. ..                                        Example sentences: ·        He used to be a slugger in his school life.  ·       Harry is misunderstood as a slugger . 

Problems on Permutations and Combinations: 1. How many arrangements can be made out of the word 'ENTREPRENEUR'? Solution:                The given word has 12 letters and E is repeated 4 times, N is repeated twice and R is repeated thrice. Hence,                 12! / 4! 2! 3! = 1663200. 2. How many words can be formed from the letters of the word 'VOLUME' so that the vowels always come together? Solution:                The arrangement will be VLM (OUE)                The 4 letters can be arranged in 4! = 24.                The vowels can be arranged among themselves in 3! = 6.                The required number of ways = 24*6 = 144.

Appetizer Thesaurus: Noun: snack before meal             cocktail, finger food, munchies, antipasto, sample, taste...                                               Antonyms:  meal, lunch. ..                                        Example sentences: ·        They served some carrots as an appetizer .   ·       What kind of appetizer do you prefer?  

Problems on Permutations and Combinations: 1. In how many different ways can the letters of the word 'REPRESS' be arranged?  Solution:                The given word has 7 letters and the letters R, E and S are repeated twice. Hence,                7!/ 2! 2! 2! = 7*6*5*4*3*2! / 2! (4)                                  = 7*6*5*3                                  =  630.  2. How many words can be formed by using all the letters of the word,'SQUEEZE'? Solution:                The given word has 7 letters and E is repeated thrice. Hence,                7! / 3! = 7*6*5*4*3!/3!                           = 840.        

Lethal Thesaurus: Adjective: deadly                    dangerous, harmful, destructive, hurtful, noxious, mortal, poisonous...                                               Antonyms: harmless, helpful. ..                                        Example sentences: ·        Don't go in his way, he's a lethal one.   ·       These fertilizers are lethal to the plants.

Problems on Permutations and Combinations: 1. In how many ways can the letters of the word 'TELL'be arranged?  Solution:                There are 4 letters in the given word and L is repeated twice. Hence,                4!/2! = 4*3*2!/2!                        = 12. 2. In how many ways can the letters of the word 'TEMPLE' be arranged? Solution:               There are 6 letters in the given word and E is repeated twice. Hence,               6!/2! = 6*5*4*3*2!/2!                        = 360. 

Mugger Thesaurus: Noun: attacker             assaulter, assailant, thug, thief, criminal, crocodile...                                         Example sentences: ·        The mugger robbed everything from his house.  ·        He is the mugger who is the reason for all the crime which happened yesterday.

Problems On Permutations and Combinations: 1. How many 3-letter words with or without meaning, can be formed out of the word, 'MOTHER' if repetition is not allowed? Solution:                  The word MOTHER has 6 letters and we should form 3-letter words. Hence,                   6 P3 = 6!/ (6-3)!                         = 6*5*4*3!/3!                         = 120.  2. How many words with or without meaning, can be formed by using all the letters of the word, 'MOTHER' using each letter exactly once? Solution:                 The word MOTHER has 6 letters. Hence,                   6 P6 = 6! = 720.

Intimidate Thesaurus: Verb: threaten             bluster, bully, alarm, frighten, nag, bully, dismay, daunt, scare, terrify...                                               Antonyms: encourage, delight. ..                                        Example sentences:   ·        They're intimidating .   ·       That task doesn't intimidate  him. 

Problems on Permutations and Combinations: 1. In how many ways can a team 5 be chosen from 7 players? Solution:                The Required number of ways =  7 C5                                                                 =  7 C7-5 =  7 C2                                                                 =  7*6/1*2                                                                 = 21. 2. In how many ways, a group of 6 members can be selected from 8 men and 6 ladies, consisting of 4 men and 2 ladies? Solution:                The Required number of ways =  8 C4 *  6 C2                                                                  = (8*7*6*5/ 1*2*3*4) * (6*5/1*2)                                                                  = 1050.        

Concede Thesaurus: Verb: accept             admit, acknowledge, award, confess, surrender, grant...                                               Antonyms:  disacknowledge, fight, refuse, reject. ..                                   Example sentences: ·        She finally conceded the idea which was given by her colleague.  ·       They forced me to concede the plans.