Practice Test


Q1) If 12 school teams are participating in a quiz contest, then the number of ways the first, second and third positions may be won is Show Answer


Q2) Letter of the word COMPUTER can be arranged in Show Answer


Q3) If vowels must be together, then number of arrangements of letters in the word FAILURE is Show Answer


Q4) Number of ways in which letters of the word TRIANGLE can be arranged so that the word ANGLE will always be present is Show Answer


Q5) If the letter of the word DAUGHTER are so arranged that vowels occupy odd places, then number of different words are Show Answer


Q6) If no digit is repeated, then the number of 4-digit numbers formed from the digits 0, 1, 2, 3, 4 is Show Answer


Q7) If no digit is repeated, then the number of 4-digit numbers greater then 5000, formed from the digits 3, 4, 5, 6, 7 is Show Answer


Q8) Number of numbers lying between 100 and 1000 which are formed with the digits 1, 2, 3, 4, 5, 6, 7 without repetition is Show Answer


Q9) Number of numbers lying between 10 and 1000 formed with the digits 2, 3, 4, 0, 8, 9 without repetition is Show Answer


Q10) Sum of all 4-digit numbers containing the digits 0, 1, 2, 3 taken all at a time, is Show Answer


Q11) There are 6 books on Eco, 3 on Maths and 2 on stats. In how many ways can they be arranged on a shelf so that books on the same subject are together ? Show Answer


Q12) Number of arrangements of 10 different objects, taken 4 at a time, in which one particular object always occurs is Show Answer


Q13) Number of arrangements of 10 different objects, taken 4 at a time, in which a particular object never occurs is Show Answer


Q14) 5 persons are sitting along a round table in such a way that the tallest person is always on the right-side of the shortest person. Number of such arrangements is Show Answer


Q15) Number of ways in which 7 boys sit around a round table so that two particular boys are always together is Show Answer


Q16) 3 boys and 3 girls are to be seated around a table in a circle. Among them, the boy X does not want any girl neighbour and the girl Y does not want any boy neighbour. The number of such arrangements is Show Answer


Q17) Letters of the words CALCUTTA and AMERICA are arranged in all possible ways. Ratio of the numbers of these arrangements is Show Answer


Q18) In how many ways can a cricket eleven choose a captain and a vice-captain from amongst themselves ? Show Answer


Q19) Three prizes are to be distributed in a class of 10 students. If a student can get only one prizes, then this can be done in Show Answer


Q20) Three prizes are to be distributed in a class of 10 students. If a student can get any number of prizes, then the number of ways is Show Answer


Q21) How many 2-digit numbers can be formed from the digits 1, 3, 5, 7, 9 if repetition is not allowed ? Show Answer


Q22) How many 2-digit numbers can be formed from the digits 1, 3, 5, 7, 9 if repetition is allowed ? Show Answer


Q23) How many 3-digit numbers can be formed from the digits 3, 4, 6, 0, 7, 8 if repetition is not allowed ? Show Answer


Q24) How many 3-digit numbers can be formed from the digits 3, 4, 6, 0, 7, 8 if repetition is allowed ? Show Answer


Q25) How many numbers between 10 and 100 can be formed from the digits 3, 0, 4, 5, 6 if repetition is allowed ? Show Answer


Q26) How many 4-digit numbers greater than 7000 can be formed from the digits 1, 2, 3, 5, 7, 8, 9 if repetition is not allowed ? Show Answer


Q27) How many numbers, greater than 23000, can be formed from the digits 1, 2, 3, 4, 5 if repetition is not allowed ? Show Answer


Q28) How many 4-digit numbers greater than 3400, can be formed from the digits 1, 2, 3, 4, 5, 6, 7 if repetition is not allowed ? Show Answer


Q29) How many 5-digit numbers, divisible by 5, can be formed from the digits 3, 1, 7, 0, 9, 5 if repetition is not allowed ? Show Answer


Q30) How many 5-digit numbers, not divisible by 5, can be formed from the digits 3, 1, 7, 0, 9, 5 if repetition is not allowed ? Show Answer


Q31) How many numbers between 3000 and 4000, divisible by 5, can be formed from the digits 3, 4, 5, 6, 7, 8 if repetition is not allowed ? Show Answer


Q32) 5 persons can sit on 8 chairs in a row in Show Answer


Q33) 7 books can be arranged on a shelf in Show Answer


Q34) Number of arrangements of letter of the word FATHER which begin with A and end with R is Show Answer


Q35) Number of arrangements of letter of the word EQUATION which begin with and end with consonant is Show Answer


Q36) Number of arrangements of letter of the word FAILURE in which consonants occupy even places is Show Answer


Q37) Number of arrangements of letter of the word VOWEL in which vowels occupy even places is Show Answer


Q38) Number of arrangements of letter of the word MOBILE in which consonants occupy odd places is Show Answer


Q39) Number of arrangements of 3 boys and 5 girls in a row so that all the boys are together is Show Answer


Q40) X and Y are amongst five persons who are to be seated on chairs in a row. If X and Y always sit together, then number of arrangements is Show Answer


Q41) X and Y are amongst five persons who are to be seated on chairs in a row. If X and Y are never together, then number of arrangements is Show Answer


Q42) A, B, C are amongst seven persons who are to be seated in a row. Number of arrangements in which A, B, C sit together in any order is Show Answer


Q43) A, B, C are amongst seven persons who are to be seated in a row. Number of arrangements in which A,B,C sit together in particular order is Show Answer


Q44) Number of arrangements of letters of the word STRANGE in which the vowels are never separated from each other is Show Answer


Q45) There are 6 men and 4 women. Number of ways in which they can be seated in a row so that no two women are together is Show Answer


Q46) There are 7 English, 5 Marathi and 4 Hindi Books. Number of ways in which they can be arranged on a shelf so that books of the same language are together is Show Answer


Q47) A family consisting of an old man, 6 adults and 4 children is to be seated in a row for dinner. The children wish to occupy the two seats at each end and the old man refuses to have a child on wither side to him. Number of such arrangements is Show Answer


Q48) Number of distinct (distinguishable) permutations of letter of the word MISSISSIPPI is Show Answer


Q49) How many different numbers can be formed using all of the digits 3, 3, 4, 5, 5, 8 ? Show Answer


Q50) Number of distinct arrangements of letters of the word RANGOON in which the two N's are together but not the two O's is Show Answer


Q51) Number of distinct arrangements of letters of the word RANGOON in which neither the N's nor the O's are together is Show Answer


Q52) Number of distinct arrangements of letters of the word RANGOON in which the two N's are never together is Show Answer


Q53) In how many ways can 4 boys and 3 girls be arranged in a row so that boys and girls are placed alternatively ? Show Answer


Q54) In how many ways can 7 persons seat along a round table so that two particular persons are never together ? Show Answer


Q55) Number of arrangements of the letter a, b, c, d in which b does not follow a,c does not follow b and d does not follow c, is
Show Answer


Q56) Number of numbers formed from the digits 1, 2, 3, 4, 3, 2, 1 by placing the odd digits in odd places is Show Answer


Q57) Number of integers from 1 to 1000 which are divisible by neither 10 nor 15 nor 25 is Show Answer


Q58) Number of 7-digit numbers which do not change even when the order of digits is reversed is Show Answer


Q59) Number of n-digit numbers in which no two consecutive digits are same is Show Answer


Q60) A committee of 5 is to be formed from 8 men and 4 ladies. Number of committees which include at least 2 ladies is Show Answer


Q61) Every person shakes hands with the other guests in a party. If the total number of hand-shakes is 66, then the number of guests in the party is Show Answer


Q62) If, in the combinations of 20 objects taken 5 at a time, m = number a combinations which include a particular object and n = number of combinations which do not include it, then Show Answer


Q63) 8 points are marked on a circumference of a circle. Number of chords obtained by joining these points is Show Answer


Q64) Number of parallelograms formed from a set of 4 parallel lines intersecting another set of 3 parallel lines is Show Answer


Q65) There are 12 points in a plane of which 5 are collinear. Number of triangles formed by joining them is Show Answer


Q66) Number of diagonals in a decagon is Show Answer


Q67) A person has 8 friends. Number of ways in which he can invite one or more of them to a dinner is Show Answer


Q68) Number of ways of selecting a cricket eleven from 14 players is Show Answer


Q69) From a group of 16 boys and 10 girls, a committee of 4 boys and 2 girls is to be formed. Number of ways of forming such a committee is Show Answer


Q70) A person has 12 friends of whom 8 are relatives. In how many ways can be invite 7 guests of whom 5 are relatives ? Show Answer


Q71) Staff of a bank consists of the manager, the deputy manager and 10 other officers. A committee of 4 is to be formed amongst them. Number of ways in which this can be done so as to include the manager is Show Answer


Q72) Staff of a bank consists of the manager, the deputy manager and 10 other officers. A committee of 4 is to be formed amongst them. Number of ways in which this can be done so as to include the manager but not the deputy manager. Show Answer


Q73) Staff of a bank consists of the manager, the deputy manager and 10 other officers. A committee of 4 is to be formed amongst them. Number of ways in which this can be done so as to include neither the manager nor the deputy manager. Show Answer


Q74) There are 4 teachers and 16 students, and a committee of 5 persons is to be formed. Number of ways in which this can be done so as to include exactly 3 teachers is Show Answer


Q75) There are 4 teachers and 16 students, and a committee of 5 persons is to be formed. Number of ways in which this can be done so as to include at least 3 teachers is Show Answer


Q76) There are 4 teachers and 16 students, and a committee of 5 persons is to be formed. Number of ways in which this can be done so as to include at most 3 teachers is Show Answer


Q77) A team of 11 cricketers is to be chosen, from 9 batsmen and 6 bowlers, to give a majority to batsmen. Then, the number of possible teams which also include at least 3 bowlers is Show Answer


Q78) A committee of 4 men and 3 ladies is to be formed from amongst the members of a club consisting of 10 men and 6 ladies. Number of ways in which a particular lady is included but two particular men are excluded is Show Answer


Q79) For an examination a candidate has to select 7 subjects from three different groups A, B and C. There are 4 subjects in group A, 5 in B and 6 in C. He has to select at least 2 subjects from each group. Then, the total number of ways in which the candidate can select his subjects is Show Answer


Q80) From 4 accountants, 3 lawyers and 5 salesmen, a committee of 7 persons is to be formed. Number of different committee which include at least 1 lawyer and at least one salesman is Show Answer


Q81) In an examination, there are 3 multiple choice questions and each question has 4 choices. Number of ways in which a student can fail to get all correct answers is Show Answer


Q82) There are 10 lamps in a room. Each of them can be switched on independently. Number of ways the room can be illuminated is Show Answer


Q83) Number of diagonals of an octagon is Show Answer


Q84) If a polygon has 44 diagonals, then the number of its sides is Show Answer


Q85) If the number of diagonals of a polygon equals its number of sides, then the polygon is a Show Answer


Q86) Number of ways in which a term of 11 players can be selected from 22 players, including 2 of them and excluding 4 of them, is Show Answer


Q87) Number of words which can be formed from the letters a,b,c,d,e,f taken 3 at a time, each word containing at least 1 vowel, is Show Answer


Q88) There are 10 true-or-false questions. Number of ways in which they can be answered is Show Answer


Q89) Number of other ways in which the letters of the word SIMPLETON can be arranged is Show Answer


Q90) P(n,r) is equal to Show Answer


Q91) Compute the value of 8! Show Answer


Q92) If (n +1)! = 20 (n -1)!, then value of n is - Show Answer


Q93) Find the value of n if (n+1)! = 42
(n—1)!
Show Answer


Q94) If six times the number permutations of n things taken 3 at a time are equal to seven times the number of permutations of (n—1) things chosen 3 at a time, find 'n'. Show Answer


Q95) There are 4 routes for going from Dumdum to Sealdah and 5 routes for going from Sealdah to Chandni. In how many different ways can you go from Dumdum to Chandni Via Sealdah? Show Answer


Q96) A computer has 5 terminals and each terminal is capable of four distinct positions including the positions of rest what is the total number of signals that can be made? Show Answer


Q97) In order to pass PCC examination minimum marks have to be secured in each of 7 subjects. In how many ways can a pupil fail? Show Answer


Q98) There are 10 trains plying between Calcutta and Delhi. The number of ways in which a person can go from Calcutta to Delhi and return by a different train is - Show Answer


Q99) A dealer provides you Maruti Car & Van in 2 body patterns and 5 different colours. How many choices are open to you? Show Answer


Q100) There are 6 routes for journey from station A to station B. In how many ways you may go from A to B and return if for returning you make a choice of any of the routes? Show Answer


Q101) There are 6 routes for journey from station A to station B.if you decided to take the same route you may do it in — number of ways. Show Answer


Q102) There are 6 routes for journey from station A to station B. if you decided not take the same route you may do it in — number of ways. Show Answer


Q103) In how many ways can 9 letters be posted in 4 letter boxes? Show Answer


Q104) How many arrangements can be made out of the word DRAUGHT, the vowels never being separated? Show Answer


Q105) The number of different arrangements of the letters of the word 'CALCUTTA' is – Show Answer


Q106) The number of ways the letters of the word COMPUTER can be rearranged as - Show Answer


Q107) The number of arrangements of the letters in the work FAILURE, so that vowels are always coming together is - Show Answer


Q108) The number of words, with or without meaning that can be formed by using all the letters of the word "DELHI", using each letter exactly once is - Show Answer


Q109) The number of ways in which the letters of the word MOBILE be arranged so that consonants always occupy the odd places is - Show Answer


Q110) In how many ways the word 'Article' can be arranged in a row so that the vowels occupy even places? Show Answer


Q111) The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do not end with N is - Show Answer


Q112) In how many ways the words 'failure' can be arranged so that the consonants occupy only the odd positions? Show Answer


Q113) In how many ways can the word 'strange' be arranged so that the vowels are never separated? Show Answer


Q114) How many different permutations are possible from the letters of the word CALCULUS? Show Answer


Q115) The number of words which can be formed with 2 different consonants and 1 vowel out of 7 different consonants and 3 different vowels the vowel to lie between 2 consonants is - Show Answer


Q116) If the letter of the word ATTEMPT are written down at random, the chance that all Ts are consecutive is - Show Answer


Q117) The letters of the words CALCUTTA and AMERICA are arranged in all possible ways. The ratio of the number of these arrangements is - Show Answer


Q118) Find the number of ways in which arrangements of 4 letters can be made from the word "MATHEMATICS". Show Answer


Q119) How many arrangements of the word 'PUBLIC' will begin with 'B' - Show Answer


Q120) How many arrangements of the letters of the word 'BHARAT will not have 'B' and 'H' together"- Show Answer


Q121) How many different arrangements are possible from the letters of the word CALCULATOR? Show Answer


Q122) In how many different ways 7 letter words can be formed using the letters of the words SPECIAL? Show Answer


Q123) How many arrangements can be made by using all the letters of word Monday? Show Answer


Q124) In how many ways can the letters of the word PENCIL be arranged so that N is always next to E - Show Answer


Q125) The no. of permutation can be made out the letters of word "COMMERCE” is - Show Answer


Q126) How many words of 3 consonants and 2 vowels can be formed from 6 consonants and 4 vowels? Show Answer


Q127) The number of words that can be formed using the letter A thrice, the letter B twice and the letter C once is - Show Answer


Q128) If all the permutations of the letters of the word "CHALK" are written in a dictionary the rank of this word will be - Show Answer


Q129) In how many ways the letters of the word 'FAILURE' can be arranged with the condition that the four vowels are always together? Show Answer


Q130) In how many ways can be letters of the word 'VIOLENT be arranged so that the vowels occupy even places only? Show Answer


Q131) The number of ways the letters of the word 'SIGNAL' can be arranged such that the vowels occupy only odd position is - Show Answer


Q132) How many different words can be formed beginning with 'E' of the word 'TRIANGLE'? Show Answer


Q133) With 'E' of the word 'TRIANGLE' how many of them will begin with 'T and end with 'E? Show Answer


Q134) the word 'TRIANGLE' how many of them have T and 'E' in the end places? Show Answer


Q135) the word 'TRIANGLE' how many of them have consonants never together? Show Answer


Q136) the word 'TRIANGLE' how many of them have arrangements that no two vowels are together? Show Answer


Q137) the word 'TRIANGLE' how many of them have arrangements that consonants and vowels are always together? Show Answer


Q138) the word 'TRIANGLE' how many of them have arrangements that vowels occupy odd places? Show Answer


Q139) Find how many five letter words can be formed out of the word "LOGARITHMS"
(the words may not convey any meaning). Show Answer


Q140) The number of ways the letters of the word "TRIANGLE" to be arranged so that the word "ANGLE" will be always present is - Show Answer


Q141) In how many ways can the word 'STRANGE' be arranged so that the vowels never come together? Show Answer


Q142) In how many ways can the word 'STRANGE' be arranged so that the vowels occupy only the odd places? Show Answer


Q143) In how many ways it is possible to write the word 'ZENITH' in a dictionary? Show Answer


Q144) The number of arrangements that can be made with the word 'assassination' is Show Answer


Q145) The number of permutation of the word "ALLAHABAD" is - Show Answer


Q146) The number of subsets formed from the letters of the word "ALLAHABAD". Show Answer


Q147) In how many ways the vowels of the word "ALLAHABAD" will occupy the even places? Show Answer


Q148) In how many ways can the letters of the word 'ARRANGE' be arranged? Show Answer


Q149) In how many ways the word 'ARRANGE' be arranged such that the 2 ‘r's come together? Show Answer


Q150) In how many ways the word 'ARRANGE' be arranged such that the 2 ‘r’s do not come together? Show Answer


Q151) In how many ways the word 'ARRANGE' be arranged such that the 2 ‘r’s and 2 'a's come together? Show Answer


Q152) The total number of 9 digit numbers of different digits is - Show Answer


Q153) How many three digit numbers are there, with distinct digits, with each digits odd? Show Answer


Q154) The number of numbers lying between 100 and 1,000 can be formed with the digits 1,2,3,4,5,6,7 is - Show Answer


Q155) How many six digits numbers can be formed with the permutation of digits 9,5,3,1,7,0? Show Answer


Q156) with the permutation of digits 9,5,3,1,7,0, how many numbers will have 0's in ten's palace? Show Answer


Q157) How many numbers between 3,000 and 4,000 can be formed with 1 2……. 6? Show Answer


Q158) How may numbers between 1,000 and 10,000 can be formed with the digits 1,2,3,4,5,6 Show Answer


Q159) How many 3 digit numbers are there if repetition of digits is not allowed? Show Answer


Q160) The number of four digit numbers that can be formed using the digits 1, 7, 6 and 9 without repetition is - Show Answer


Q161) Find the number of 4 digit numbers greater than 5,000 that can be formed out of the digits 3,4,5,6 and 7 (no. digit is repeated). Show Answer


Q162) The number of 4 digit numbers that can be formed from seven digits 1,2,3,5,7,8,9 such that no digit being repeated in any number, which are greater than 3000 are: Show Answer


Q163) No. of 4 digit numbers that can be formed out of the figures 0,1,2,3,4 (no digit is repeated) is - Show Answer


Q164) The number of numbers lying between 10 and 1,000 can be formed with the digits 2,3,4,0,8,9 is - Show Answer


Q165) How many six digit numbers can be formed out of 4 5 …… 9 no digits being repeated? Show Answer


Q166) out of 4 5 …… 9 how many of them are not divisible by 5? Show Answer


Q167) How many numbers between 1000 and 10000 can be formed with 1, 2,...9? Show Answer


Q168) How many numbers higher than a million can be formed with the digits 0,4,4,5,5,5,3 ? Show Answer


Q169) The total number of numbers less than 1,000 and divisible by 5 formed with 0, 1, 2, ..... 9 such that each digit does not occur more than once in each number is Show Answer


Q170) How many four digits number can be formed by using 1, 2 ….. 7? (without repetition of digits) Show Answer


Q171) How many four digits numbers can be formed by using 1, 2, ....7 which are greater than 3,400? Show Answer


Q172) How many telephones connections may be allotted with 8 digits from the numbers 0,1,2,....9? Show Answer


Q173) A letter lock has three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock? Show Answer


Q174) In how many different ways 3 rings of a lock can not combine when each ring has digits 0, 1, 2 .....9 leading to unsuccessful events? Show Answer


Q175) The number of even numbers greater than 300 that can be formed with the digits 1,2,3,4,5 without repetition is Show Answer


Q176) How many 4 digit numbers greater than 7,000 can be formed out of the digits 3, 5, 7, 8, 9? Show Answer


Q177) The number of different ways in which 5 girls may be arranged in a row is - Show Answer


Q178) Three persons enter a railway carriage, where there are 5 vacant seats. The number of ways they can seat themselves is - Show Answer


Q179) 3 persons go into a railway carriage having 8 seats. In how many ways they may occupy the seats? Show Answer


Q180) In a group of boys the number of arrangements of 4 boys is 12 times the number of arrangements of 2 boys. The number of boys in the group is - Show Answer


Q181) In how many different ways can seven persons stand in a line for a group photograph? Show Answer


Q182) A family of 4 brothers and three sisters is to be arranged for a photograph in one row. In how many ways can they be seated if all the sisters sit together? Show Answer


Q183) A family of 4 brothers and three sisters is to be arranged for a photograph in one row. In how many ways can they be seated if no two sisters sit together? Show Answer


Q184) There are 6 students of whom 2 are Indians, 2 Germans and the remaining 2 are British. They have to stand in a row for a photograph so that the two Indians are together, the two Germans are together and so also the two British. The number of ways such an arrangement can be made is - Show Answer


Q185) Eight guests have to be seated 4 on each side of a long rectangular table. 2 particular guests desire to sit on one particular side of the table and 3 on the other side. The number of ways in which the sitting arrangements can be made is - Show Answer


Q186) The total number of sitting arrangements of 7 persons in a row if 3 persons sit together in any order is - Show Answer


Q187) The total number of sitting arrangements of 7 persons in a row if 2 persons occupy the end seats is - Show Answer


Q188) The total number of sitting arrangements of 7 persons in a row if one person occupies the middle seat is - Show Answer


Q189) In how many number of ways can 'n' books be arranged on a shelf so that two particular books are not together? Show Answer


Q190) In how many ways 5 Sanskrit, 3 English and 3 Hindi books be arranged keeping the books of the same language together? Show Answer


Q191) If there are 50 stations on a railway line how many different kinds of single first class tickets may be printed to enable a passenger to travel from one station to other? Show Answer


Q192) Eleven students are participating in a race. In how many ways the first 5 prizes can be won? Show Answer


Q193) Number of 2 digit numbers which are divisible by 6 is — Show Answer


Q194) Mr. X and Mr. Y enter into a railway compartment having six vacant seats. The number of ways in which they can occupy the seats is - Show Answer


Q195) 10 examination papers are arranged in such a way that the best and worst papers never come together. The number of arrangements is – Show Answer


Q196) The number of arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is - Show Answer


Q197) The number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs is - Show Answer


Q198) How many different signals are possible if we wish to make signals by arranging 3 red, 2 yellow and 2 green flags in one post. Show Answer


Q199) Let S be the collection of eight points in the plane with no three points on the straight line. Find the number of triangles that have points of S as vertices. Show Answer


Q200) There are 5 speakers A, B, C, D & E. the number of ways in which A will speak always immediately before B is – Show Answer


Q201) The number of ways in which 8 sweets of different sizes can be given among 8 persons of different ages so that the largest sweet always goes to be younger assuming that each one of them gets a sweet is - Show Answer


Q202) The total number of ways in which six '+' and four ‘–’ signs can be arranged in a line such that no two ‘–’ signs occur together is - Show Answer


Q203) If you have 5 copies of one book, 4 copies of each of two books, 6 copies each of three books and single copy of 8 books you may arrange it how many number of ways? Show Answer


Q204) In how many ways 21 red balls and 19 blue balls can be arranged in a row so that no two blue balls are together? Show Answer


Q205) The number of circular permutations of n different things chosen at a time is - Show Answer


Q206) In how many ways can 4 persons sit at a round table for a group discussion? Show Answer


Q207) The number of ways in which 7 girls form a ring is - Show Answer


Q208) The number of ways in which 8 different beads be strung on a necklace is - Show Answer


Q209) If 50 different jewels can be set to form a necklace then the number of ways is - Show Answer


Q210) In how many ways can 8 persons be seated at a round table, such that 2 particular persons sit together? Show Answer


Q211) The Chief Ministers of 17 States meet to discuss the hike in oil price at a round table. In how many ways they seat themselves if the Kerala and Bengal chief ministers choose to sit together? Show Answer


Q212) In how many ways 4 men and 3 women are arranged at a round table if the women always sit together? Show Answer


Q213) In how many ways 4 men and 3 women are arranged at a round table if the women never sit together? Show Answer


Q214) In how many ways can 4 Americans and 4 English men be seated at a round table so that no 2 Americans may be together? Show Answer


Q215) In how many ways can 6 boys and 6 girls be seated a round table so that no 2 boys are adjacent? Show Answer


Q216) In how many ways 6 men can sit at a round table so that all shall not have the same neighbours in any two occasions? Show Answer


Q217) 5 persons are sitting in a round table in such way that Tallest Person is always on the right-side of the shortest person. The number of such arrangements is Show Answer


Q218) Six Persons A, B, C, D, E and F to be seated at a circular table. In how many ways can this be done, if A must always have either B or C on his right and B must always have either C or D on his right? Show Answer


Q219) If 5 books of English, 4 books of Tamil and 3 books of Hindi are to be arranged in a single row so that books of same language come together Show Answer


Q220) 5 Boys and 4 girls are to be seated in row. If the girls occupy even places then the no. of such arrangements Show Answer


Q221) 2, 5, 8, 11, 14, 17... is an A.P in which the common difference is? Show Answer


Q222) Determine the common difference of progression 16, 13, 10... 25 terms Show Answer


Q223) Two A.Ps have the same common difference. If the difference between their 100th terms is 111222333 then the difference between their millionth terms is Show Answer


Q224) If a, b, c are in A.P., then 2b = ____ Show Answer


Q225) Find the 7th term of the A.P 8, 5, 2, -1, -4,.…….. Show Answer


Q226) The 20th term of the progression 1, 4, 7, 10 ……… is Show Answer


Q227) For the A.P 2, 5, 8, 11, 14, ...., 12th term is- Show Answer


Q228) The 13th term of series 93, 90, 87 .... is Show Answer


Q229) The nth element of the sequence 1,3,5,7,.... is Show Answer


Q230) The nth term of the sequence 2, 4, 6, 8 ………. is Show Answer


Q231) If the first term of an A.P. is 5 and its 100th term is -292, then its 51st term is - Show Answer


Q232) The mth term of an A.P is n and nth term is m, the rth term of it is Show Answer


Q233) If the 5th and 12th terms of the A.P are 14 and 35 respectively, find the A.P. Show Answer


Q234) Which term of the A. P 11, 8, 5,2 ,... is -10? Show Answer


Q235) Which term of the progression -1, -3, -5,.... is -39? Show Answer


Q236) Which one is true - Show Answer


Q237) If c(n, 8) = c (n, 6), find c(n, 2) Show Answer


Q238) A team of 12 men is to be formed out of n persons. Then the number of times 2 men "A" and "B" are together is - Show Answer


Q239) A committee is to be formed of 3 persons out of 12. Find the number of ways of forming such Committee. Show Answer


Q240) There are 7 men and 3 ladies. Find the number of ways in which a committee of 6 can be formed of them if the committee is to include at least 2 ladies? Show Answer


Q241) Out of 7 gents and 4 ladies a committee of 5 is to be formed. The number of committee such that each committee includes at least one lady is - Show Answer


Q242) 5 letters are written and there are five letter-boxes. The number of ways the letters can be dropped into the boxes, one in each. Show Answer


Q243) In forming a committee of 5 out of 5 males and 6 females how many choices you have to make so that there are 3 males and 2 females? Show Answer


Q244) In forming a committee of 5 out of 5 males and 6 females how many choices you have to make if there are 2 males? Show Answer


Q245) In forming a committee of 5 out of 5 males and 6 females how many choices you have to make if there is no female? Show Answer


Q246) In forming a committee of 5 out of 5 males and 6 females how many choices you have to make if there is at least one female? Show Answer


Q247) In forming a committee of 5 out of 5 males and 6 females how many choices you have to make if there are not more than 3 males? Show Answer


Q248) A committee of 7 members is to be chosen from 6 Chartered Accountants, 4 Economist and 6 Cost Accountants. In how many ways can this be done if in the committee, there must be at least one member from each group and at least 3 Chartered Accountants Show Answer


Q249) A committee of 3 ladies and 4 gents is to be formed out of 8 ladies and 7 gents. Mrs.X refuses to serve in a committee in which Mr.Y is a member. The number of such committees is - Show Answer


Q250) Out of 6 members belonging to party "A" and 4 to party "B" in how many ways a committee of 5 can be selected so that members of party "A" are in a majority? Show Answer


Q251) A person has 8 friends. The number of ways in which he may invite one or more of them to a dinner is - Show Answer


Q252) A person has 10 friends of which 6 of them are relatives. He wishes to invite 5 persons so that 3 of them are relatives. In how many ways he can invites? Show Answer


Q253) In how many ways 4 members can occupy 9 vacant seats in a row Show Answer


Q254) The number of ways in which a person can chose one or more of the four electrical appliances: T.V, Refrigerator, Washing Machine and a cooler is - Show Answer


Q255) You are selecting a cricket team of first 11 players out of 16 including 4 bowlers and 2 wicket-keepers. In how many ways you can do it so that the team contains exactly 3 bowlers and 1 wicket-keeper? Show Answer


Q256) You are selecting a cricket team of first 11 players out of 16 including 4 bowlers and 2 wicket-keepers. would your answer be different if the team contains at least 3 bowlers and at least 1 wicket-keeper? Show Answer


Q257) A building contractor needs three helpers and ten men apply. In how many ways can these selections take place? Show Answer


Q258) A Company having 6 departments wishes to simultaneously promote two of its Department's Heads to Asst. Managers. In how many ways these promotions can take place? Show Answer


Q259) Every person shakes hands with each other in a party and the total number of hand shakes is 66. The number of guests in the party is Show Answer


Q260) The total number of Hand shakes in a group of 10 persons to each other are Show Answer


Q261) 6 seats of articled clerks are vacant in a ’Chartered Accountant firm’. How many different batches of candidates can be chosen out of 10 candidates if one candidate is always selected? Show Answer


Q262) In your office 4 posts have fallen vacant. In how many ways a selection out of 31 candidates can be made if one candidate is always included? Show Answer


Q263) In your office 4 posts have fallen vacant. would your answer be different if one candidate is always excluded? Show Answer


Q264) In your college Union Election you have to choose candidates. Out of 5 candidates 3 are to be elected and you are entitled to vote for any number of candidates but not exceeding the number to be elected. In how ways it can be done? Show Answer


Q265) A party of 6 is to be formed from 10 men and 7 women as so as to include 3 men and 3 women. In how many ways the partly can be formed if two particular women refuses to join it? Show Answer


Q266) In how many ways can a consonant and a vowel be chosen out of the letters of the word 'LOGARITHM? Show Answer


Q267) Find the number of ways of selecting 4 letters from the word EXAMINATION. Show Answer


Q268) Find the number of ways in which a selection of 4 letters can be made from the word "Mathematics" Show Answer


Q269) In how many ways can a consonant and a vowel be chosen out of the letters of the word 'EQUATION? Show Answer


Q270) Out of 10 different consonants and 4 different vowels how many words can be formed each containing 6 consonant and 3 vowels? Show Answer


Q271) The number of different words that can be formed with 12 consonants and 5 vowels by taking 4 consonants and 3 vowels in each word is - Show Answer


Q272) How many different numbers can be formed by using any three out of five digits 1, 2, 3, 4, 5, no digit being repeated in any number? Show Answer


Q273) How many different numbers can be formed by using any three out of five digits 1, 2, 3, 4, 5, no digit being repeated in any number? How many of these will begin with a specified digit? Show Answer


Q274) How many different numbers can be formed by using any three out of five digits 1, 2, 3, 4, 5, no digit being repeated in any number? How many of these will begin with a specified digit and end with another specified digit? Show Answer


Q275) How many four digit numbers can be formed out of the digits 1, 2, 3, 5, 7, 8, 9, if no digit is repeated in any number? How many of these will be greater than 3,000? Show Answer


Q276) First, second and third prizes are to be awarded at an engineering fair in which 13 exhibits have been entered. In how many ways can the prizes be awarded? Show Answer


Q277) In how many ways 3 scholarships can be awarded to 5 students when each student is eligible for any of the scholarships? Show Answer


Q278) A question paper contains 6 questions, each having an alternative. The number of ways an examinee can answer one or more questions is - Show Answer


Q279) If you have to make a choice of 7 questions out of 10 questions set you can do it in - Show Answer


Q280) A candidate is required to answer 6 out of 12 questions which are divided into two groups containing 6 questions in each group. He is not permitted to attempt not more than four from any group. The number of choices are - Show Answer


Q281) A box contains 7 red, 6 white and 4 blue balls. How many selections of three balls can be made so that (a) all are red (b) none is red, (c) one is of each colour? Show Answer


Q282) You have to make a choice of 4 balls out of one red one blue and ten while balls. The number of ways this can be done to always the red ball is — Show Answer


Q283) You have to make a choice of 4 balls out of one red one blue and ten while balls.the number of ways in which this can be done to include the red ball but exclude the blue ball always is - Show Answer


Q284) You have to make a choice of 4 balls out of one red one blue and ten while balls. the number of ways in which this can be done to exclude both the red and blues ball is - Show Answer


Q285) Out of 8 different balls taken three at a time without taking the same three together more than once for how many number of times you can select a particular ball? Show Answer


Q286) Out of 8 different balls taken three at a time without taking the same three together more than once for how many number of times you can select any ball? Show Answer


Q287) The number of diagonals in a decagon is - Show Answer


Q288) A regular Polygon has 45 diagonals then the no. of sides are - Show Answer


Q289) There are 12 points in a plane of which 5 are collinear. The number of triangles is - Show Answer


Q290) The number of straight lines obtained by joining 16 points on a plane, no twice of them being on the same line is - Show Answer


Q291) There are 12 points in a plane no.3 of which are collinear except that 6 points which are collinear. The number of different straight lines is - Show Answer


Q292) The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is - Show Answer


Q293) 8 points are marked on the circumference of a circle. The number of chords obtained by joining these in pairs is - Show Answer


Q294) A committee is to be formed of 2 teachers and 3 students out of 10 teachers and 20 students. The number of ways in which this can be done is - Show Answer


Q295) A committee is to be formed of 2 teachers and 3 students out of 10 teachers and 20 students. if a particular teacher is included the number of ways in which this can be done is - Show Answer


Q296) A committee is to be formed of 2 teachers and 3 students out of 10 teachers and 20 students. if a particular student is excluded the number of ways in which this can be done is - Show Answer


Q297) Five bulbs of which three are defective are to be tried in two bulb points in a dark room. Number of trials the room shall be lighted - Show Answer


Q298) A boat's crew consists of 8 men 3 of whom can row only on one particular side and 2 only on the other. The number of ways in which the crew can be arranged is Show Answer


Q299) The number of ways in which 15 mangoes can be equally divided among 3 students is – Show Answer


Q300) If 7 distinct things are to be divided in 3 groups, consisting of 2, 2, and 3 things respectively, find the number of ways this can be done. Show Answer


Q301) In a school number of students in each section is 36. If 12 new students are added, then the number of sections are increased by 4, and the number of students in each section becomes 30. The original number of sections at first is: Show Answer


Q302) A student has 3 books on computer, 3 books on Economics, 5 on Commerce. If these books are to be arranged subject wise then these can be placed on a shelf in the _____ number of ways: Show Answer


Q303) Find the number of divisors of 21,600 excluding 1 and the number itself - Show Answer


Q304) The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the straight line, is: Show Answer


Q305) A code word is to consist of two English Alphabets followed by two distinct numbers between 1 and 9 . How many such a code words are there? Show Answer


Q306) A boy has 3 library tickets and 8 books of his interest in the library of these 8, he does not want to borrow Mathematics part II unless mathematics part I is also borrowed? In how many ways can he choose the three books to be borrowed? Show Answer


Q307) An examination paper consists of 12 question divided into two parts A and B Part A contains 7 questions and Part B contain 5 questions. A candidate is required to attempted 8 questions selecting at least 3 from each part. In how many maximum ways can be candidate select the question? Show Answer


Q308) A supreme Court Bench Consist of 5 judges. In how many ways, the bench can give a majority division? Show Answer


Q309) Given: P (7, k) = 60; P (7, k - 3). Then: Show Answer


Q310) The number of ways in which n books can be arranged on a shelf so that two particular books are not together is: Show Answer


Q311) In how many ways can a party of 4 men and 4 women be seated at a circular table, so that no two women are adjacent? Show Answer


Q312) Find the number of Combinations of the letters of the word COLLEGE taken four together: Show Answer


Q313) How many words can be formed with the letters of the word 'ORIENTAL' so that A and E always occupies odd places: Show Answer


Q314) How many numbers greater than a million can be formed with the digits 4, 5, 5, 0, 4, 5, 3? Show Answer


Q315) There are three blue balls, four red balls and five green balls. in how many ways can they be arranged in a row? Show Answer


Q316) How many six digit telephone numbers can be formed by using 10 distinct digits? Show Answer


Q317) In how many ways a committee of 6 members can be formed from a group of 7 boys and 4 girls having at least 2 girls in the committee. Show Answer


Q318) Number of ways of painting a face of a cube by 6 colours is . . . . . . Show Answer


Q319) 7 books are to be arranged in such a way so that two particular books are always at first and last place. Final the number of arrangements. Show Answer


Q320) In how many ways can 17 billiard balls be arranged if 7 of them are black, 6 red and 4 white? Show Answer


Q321) Six points are on circle. The number of quadrilateral that can be formed are: Show Answer


Q322) The number of ways of arranging 6 boys and 4 girls in a row so that all 4 girls are together is: Show Answer


Q323) A garden having 6 tall trees in a row. In how many ways 5 children stand, one in a gap between the trees in order to pose for a photograph? Show Answer


Q324) How many ways a team of 11 players can be made out of 15 players if one particular player is not to be selected in the team. Show Answer


Q325) Find the number of arrangements of 5 things taken out of 12 things, in which one particular thing must always be included. Show Answer


Q326) In how many ways 3 prizes out of 5 can be distributed amongst 3 brothers equally? Show Answer


Q327) There are 12 questions to be Answered to be Yes or No. How many ways van these be Answered? Show Answer


Q328) A man has 3 sons and 6 schools within his reach. In how many ways he can send them to school, if two of his sons are to read in the same school? Show Answer


Q329) How many different words can be formed with the letters of the word "LIBERTY": Show Answer


Q330) In how many way can a family consist of three 3 children here different birthdays in a leap year: Show Answer


Q331) A person has ten friends of whom six are relatives. if he invite five guests such that three of them are his relatives, then the total number of ways in which he can invite them are: Show Answer


Q332) A student has three books on computer, three books on Electronics and five books on Commerce. If these books are to be arranged subject wise, then these can be placed on a shelf in the number of ways: Show Answer


Q333) An examination paper with 10 question consists, of 6 questions in mathematics and 4 questions in statistics part. At least one question from each part is to be attempted in how many ways can this be done? Show Answer


Q334) There are 6 men and 4 women in a group, then the number of ways in which a committee of 5 persons can be formed of them, if the committee is to include at least 2 women are: Show Answer


Q335) In how many ways can a selection of 6 out of 4 teachers and 8 students be done so as to include at least two teachers? Show Answer


Q336) There are 10 students in a class including 3 girls. The number of ways to arrange them in a row when any two girls out of three never comes together: Show Answer


Q337) The maximum number of points of intersection of 10 circles will be: Show Answer


Q338) The number of parallelograms, formed from a set of six parallel line intersecting another set of four parallel line is: Show Answer


Q339) The number of words which can be formed by letters of the word ALLAHABAD is: Show Answer


Q340) If 3 books on computer, 3 books on computer, and 5 books on economics are arranged in such a way that the books of same subject are kept together, then the number of ways in which this can be done are: Show Answer


Q341) A bag contain 4 red, 3 black, and 2 white balls, in how many ways 3 balls can be drawn from his bag so that they include at least one black balls? Show Answer


Q342) The value of N in?1/(7!)?+?1 / (8!)?=?N / (9!)?is : Show Answer


Q343) Which of the following is a correct statement: Show Answer


Q344) If these are 40 guests in a party. If each guest takes a shake hand with all the remaining guests. Then the total number of hands shake is________: Show Answer


Q345) In how many ways can the crew of an 8 oared boat be arranged so that 3 of crew can row only on a stroke side and 2 row on the other side? Show Answer


Q346) Three girls and five boys are to be seated in a row so that no two girls sit together. Total no. of ways of this arrangement are: Show Answer


Q347) How many numbers can be formed with the help of 2,3,4,5.6,1 which are not divisible by 5, given that it is five digit no. and digits are not repeating? Show Answer


Q348) How many different groups of 3 people can be formed from a group of 5 people? Show Answer


Q349) In how many ways can 4 people be selected at random from 6 boys and 4 girls if there are to be exactly 2 girls? Show Answer


Q350) A fruity basket contains 7 apples, 6 bananas, and 4 mangoes. How many selections of 3 fruits can be made so that all 3 are apples? Show Answer


Q351) Out of 7 boys and 4 girls, a team of a debate club of 5 is to be chosen. The number of team such that each team includes at least one girl is: Show Answer


Q352) From a group of 8 men and 4 women, 4 persons are to be selected to from a committee so that at least 2 women are there on the committee. In how many ways can it be done? Show Answer


Q353) 8 chairs are numbered from 1 to 8. 2 women and 3 men are to be selected by allowing 1 chair for each. 1st, the women choose the chairs from the chairs numbered 1 to 4 and then men select the chairs from the remaining. The number of possible arrangement is: Show Answer


Q354) 'n' locks and 'n' corresponding keys are available but the actual combination is not known. The maximum number of trials that are needed to assign the key to the corresponding locks is: Show Answer


Q355) There are 10 flights operating between city A and city B. The number of ways in which a person can travel from city A to city B and return by different flight is: Show Answer


Q356) How many four-digit odd numbers can be formed with digits 0,1,2,3,4,7 and 8? Show Answer


Q357) In how many different ways can the letters of the word 'DETAIL' be arranged so that the vowels occupy only the odd positions? Show Answer


Q358) A business houses wishes to simultaneously elevate two of its 6 branch heads. In how many ways can these elevations take place? Show Answer


Q359) A person can go from place 'A' to 'B' by 11 different modes of transport but is allowed to return to "A" by any mode other than the one earlier. The number of different ways in which the entire journey can be completed is: Show Answer


Q360) How many numbers of 7 digit numbers which can be formed from the digits 3,4,5,6,7,8,9 no digits being repeated are not divisible by 5? Show Answer


Q361) The number of ways 5 boys and 5 girls can be seated at a round table, so no two boys are adjacent is: Show Answer


Q362) The number of 4 letter words can be formed using the letters of the word DECTIONARY is Show Answer


Q363) The number of words that can be formed using the letters of the "PETROL" such that the words do not have "P" in the 1st position, is Show Answer


Q364) The number of different ways the letters of the word "DETAIL" can be arranged in such a way that the vowels can occupy only the odd position is Show Answer


Q365) 6 boys and 5 girls are to be seated for a photograph in a row such that no 2 girls sit together and no 2 boys sit together. Find the number of ways in which this can be done. Show Answer


Q366) If a man travels from place A to B in 10 ways then by how many ways can he come back by another train? Show Answer


Q367) If four words are taken with or without meaning from the word 'Logaritham' without repetition. How many words will be formed?
Show Answer


Q368) 7 boys and 4 girls from which a team of 5 is to be selected, each team should have at least one girl is: Show Answer


Q369) 8 people are seated in a row in a meeting among them the president and vice president are to be seated always in the center. What is the arrangement? Show Answer


Q370) There are 5 questions each have four options. Then in how many different ways can we answer the questions?
Show Answer


Q371) If there are 6 points in a line and 4 points in another line. Find the number of parallelogram formed? Show Answer


Q372) There are 20 points in a plane area. How many triangles can be formed by these points if 5 points are collinear?
Show Answer


Q373) The number of ways 4 boys and 3 girls can be seated in a row so that they are alternate is:
Show Answer


Q374) How many 3 digit odd numbers can be formed using the digits 5,6,7,8,9 if the digits can be repeated?
Show Answer


Q375) In the next world cup these will be 12 teams,divided equally into two equal groups.Team each group will play a match against other.From each group 3 top teams will qualify for next round.In this round each team will play against each other.Four top teams of his round will qualify for the semi-final round, when each team will play against the others once.Two top teams of this round will go to final round, where they will play the best of three matches.The minimum number of matches in the next world cup will be:
Show Answer


Q376) A committee of 3 women and 4 men is to be formed out of 8 women and 7 men.Mrs. Kajal refuses to serve in a committee in which Mr.Yash ia a member .The number of such committee can be.
Show Answer


Q377) Find the number of ways in which the letters of the word SOFTWARE be arranged such that all the vowels are always together?
Show Answer


Q378) In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together? Show Answer