Practice Test

Q1) In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included? Show Answer

Q2) 17 students are present in a class. In how many ways can they be made to stand in 2 circles of 8 and 9 students? Show Answer

Q3) Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? Show Answer

Q4) How many arrangements can be made out of the letters of the word ‘ENGINEERING’? Show Answer

Q5) If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chess board? Show Answer

Q6) There are 6 periods in each working day of a college. In how many ways can one organize 5 subjects such that each subject is allowed at least one period? Show Answer

Q7) How many 8 digit mobile numbers can be formed if any digit can be repeated and ‘0’ can also start the mobile number? Show Answer

Q8) Using all the letters of the word ‘NOKIA’, how many words can be formed, which begin with N and end with A? Show Answer

Q9) How many even numbers of 3 different digits can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 (repetition is not allowed)? Show Answer

Q10) There are 4 parcels and 5 post-offices. In how many different ways the registration of parcel can be made ______. Show Answer

Q11) In a train five seats are vacant, then how many ways can three passengers sit ______. Show Answer

Q12) Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is ________. Show Answer

Q13) In how many ways can 10 balls be divided between two boys, one receiving two and the other eight balls ______. Show Answer

Q14) The number of words which can be formed from the letters of the word MAXIMUM, if two consonants cannot occur together, is ______. Show Answer

Q15) How many words can be formed from the letters of the word COURTESY, whose first letter is C and the last letter is Y ______. Show Answer

Q16) The letters of the word MODESTY are written in all possible orders and these words are written out as in a dictionary, then the rank of the word MODESTY is ______. Show Answer

Q17) How many numbers greater than hundred and divisible by 5 can be made from the digits 3, 4, 5, 6, if no digit is repeated ______. Show Answer

Q18) The number of ways in which 9 persons can be divided into three equal groups is ______. Show Answer

Q19) If eleven members of a committee sit at a round table so that the President and Secretary always sit together, then the number of arrangement is ______. Show Answer

Q20) In how many ways can 12 gentlemen sit around a round table so that three specified gentlemen are always together ______. Show Answer

Q21) There are 12 volleyball players in all in a college, out of which a team of 9 players is to be formed. If the captain always remains the same, then in how many ways can the team be formed ______. Show Answer

Q22) In how many ways can a girl and a boy be selected from a group of 15 boys and 8 girls ______. Show Answer

Q23) How many words can be formed by taking 3 consonants and 2 vowels out of 5 consonants and 4 vowels ______. Show Answer

Q24) In how many ways can 6 persons be selected from 4 officers and 8 constables, if at least one officer is to be included ______. Show Answer

Q25) 4 buses run between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by another bus, then the total possible ways are ______. Show Answer

Q26) How many words comprising of any three letters of the word UNIVERSAL can be formed? Show Answer

Q27) There are 4 male and 3 female. In how many ways a person is selected if either a male or a female is selected? Show Answer

Q28) 5 chocolates can be given to 3 children. If each child can get any number of chocolates, then the number of ways of giving chocolate is _______. Show Answer

Q29) Sunil has 2 foot rules, 4 pencils and 5 erasers. For an examination he has to select one of each. The number of ways in which he can do the selection is ________. Show Answer

Q30) 28 games were played in a tournament where each player played once against the rest. The number of players was ________. Show Answer

Q31) The number of all four-digit numbers with distinct digits is _______. Show Answer

Q32) There are 7 distinct points on a circle. The number of straight lines obtained by joining them is ________. Show Answer

Q33) If 12 different flowers can be arranged in a garland such that 4 particular flowers are never separated, the number of garlands prepared is ________. Show Answer

Q34) The letters of the word PENCIL are arranged in all possible ways. The number of ways in which N always occur next to E is ________. Show Answer

Q35) Everybody in a room shakes hands with everybody else. If the total number of hand shakes is 153, the number of persons in the room is ________. Show Answer

Q36) The number of ways of selecting at least one thing from n different things is given by _______. Show Answer

Q37) The number of ways in which n things of which p are alike, can be arranged in a circular order is _______. Show Answer

Q38) If clockwise and anti-clockwise are different, the number of circular permutations of n different things taken r at a time is ______. Show Answer

Q39) The number of different ways in which a man can invite one or more of his 6 friends to dinner is ________. Show Answer