Practice Test

Q1) There are 6 multiple choice question in an examination. How many sequence of answers are possible, if the first three questions have 4 choices each and the next three have 5 each? Show Answer

Q2) How many numbers are there between 100 and 1000 in which all the digits are different? Show Answer

Q3) For a set of five true-false question, no student has written all correct answers and no two students have given the same sequence of answers. What is the maximum number of students in the class, for this to be possible? Show Answer

Q4) Sunita has 5 friends to invite on her birthday party. She has three servants to carry the invitation cards. In how many ways can she send invitation cards to them? Show Answer

Q5) In how many ways four different rings can be fixed in four fingers with at most one in each finger? Show Answer

Q6) How many different signals can be given using nay number of flags from 5 flags of different colours? Show Answer

Q7) In how many ways can a cricket eleven be chosen out of a batch of 15 players in which two particular players are always there? Show Answer

Q8) In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies? Show Answer

Q9) Ramesh has 6 friends. In how many ways can be invite one or more of them at a Dinner party? Show Answer

Q10) There are 10 points in a plane, out of these 6 are col-linear. The number of triangles formed by joining these points are Show Answer

Q11) In an examination there are three multiple choice questions and each question has 4 choices. Number of ways in which a student can fail to get all answers correct is Show Answer

Q12) The number of diagonals that can be drawn by joining the vertices of an octagon is Show Answer

Q13) The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of 3 parallel lines is Show Answer

Q14) How many 10 digits numbers can be written by using the digits 1 and 2? Show Answer

Q15) There are 10 lamps in a hall. Each one of them can be switched on independently. The number of ways in which the hall can be illuminated is Show Answer

Q16) The number of ways in which a team of eleven players can be selected from 22 players including 2 of them and excluding 4 of them is Show Answer

Q17) Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? Show Answer

Q18) How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? Show Answer

Q19) A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw? Show Answer

Q20) In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there? Show Answer

Q21) In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women? Show Answer

Q22) What is the sum of the digits in the unit place of all numbers formed using 1, 2, 3, 4, 5, 6 taken all at a time without repeating any of them? Show Answer

Q23) A five-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. What is the total number of different ways in which this can be done? Show Answer

Q24) In how many ways can a bowler take four wickets in a single 6-ball over? Show Answer

Q25) The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line, is Show Answer

Q26) If S = {2, 3, 4, 5, 7, 9} then the number of different three-digit numbers (with all distinct digits) less than 400 that can be formed from S is Show Answer

Q27) The number of ways in which 5 boys and 5 girls can sit in a ring are Show Answer

Q28) The number of ways in which 8 people can be seated at a round table when 3 of them would like to sit together? Show Answer

Q29) Number of straight lines by joining 12 points in a plane, 5 of these points are collinear, is Show Answer

Q30) How many words can be formed by using all letters of the word 'BIHAR'? Show Answer

Q31) How many words can be formed by using all the letters of the words 'DAUGHTER' so that the vowels always come together? Show Answer

Q32) How many words can be formed from the letters of the word 'EXTRA', so that the vowels are never together? Show Answer

Q33) How many words can be formed from the letters of the word 'DIRECTOR' so that the vowels are always together? Show Answer

Q34) How many words with or without meaning, can be formed by using all letters of the word 'DELHI' using each letter only once? Show Answer

Q35) In how many ways can the letters of the word 'LEADER' be arranged? Show Answer

Q36) In how many ways can the letters of the word 'MACHINE' be arranged so that the vowels may occupy only odd positions? Show Answer

Q37) In how many different ways can be the letters of the word 'DETAIL' be arranged so that the vowels may occupy only odd positions? Show Answer

Q38) In how many different ways can be the letters of the word 'BANKING' be arranged so that the vowels always come together? Show Answer

Q39) In how many different ways can be the letters of the word 'AUCTION' be arranged so that the vowels always come together? Show Answer

Q40) How many words can be formed by using all the letters of the word 'ALLAHABAD'? Show Answer

Q41) How many words can be formed from the letters of the word 'SIGNATURE' so that the vowels always come together? Show Answer

Q42) In how many ways 7 children can be seated around a circular table so that two of them always want to sit together? Show Answer

Q43) There are 14 beads of different colours. How many rings with these beads can be formed? Show Answer

Q44) A man invites 9 friends to a dinner and placed 4 at one round table and 5 on another round table. The number of ways of arranging the guests is Show Answer

Q45) The number of positive integral solutions of a b c = 30 is Show Answer

Q46) Everybody in a room shakes hands with every body else. The total number of hand shakes is 66. The total number of persons in the room is Show Answer

Q47) A polygon has 170 diagonals. How many sides will it have? Show Answer

Q48) All the letters of the word 'EAMECT' are arranged in possible ways. The number of such arrangements in which no two vowels are adjacent to each other is Show Answer

Q49) The number of words that can be formed from the letters of the word "INDRAPRASTHA' when the vowels are never separated, is Show Answer

Q50) The number of ways, in which a student can choose 3 course out of 9 courses, when 2 courses are compulsory, is Show Answer

Q51) The number of arrangements which can be made by using all the letters of the words 'LAUGH', if the vowels are adjacent is Show Answer

Q52) The number of two digit even numbers that can be formed from the digits 1, 2, 3 and 5 repetition being not allowed is Show Answer

Q53) The number of different four digit numbers that can be formed with the digits 2, 3, 4, 5, 6, 7 using each digit only once is Show Answer

Q54) How many 10 digits numbers can be written by using the digits 1and 2? Show Answer

Q55) There are 10 lamp in a hall. Each one of them can be switched on independently. The number of ways in which the hall can be illuminated is Show Answer

Q56) If A be a set containing 10 distinct elements, then the total number of distinct functions from A to A is Show Answer

Q57) The product of r consecutive positive integers, divided by r! is Show Answer

Q58) The number of permutations of n distinct things taken r together, in which 3 particular things must occur is Show Answer

Q59) In how many ways 5 boys and 3 girls can sit in a row so that no two girls are together? Show Answer

Q60) There are 3 candidates for a part and one is to be selected by the votes of 7 men. The number of ways in which votes can be given is Show Answer

Q61) Every body in a room shake hands with every body else. The total number of hand shakes is 66. The total number of persons in the room is Show Answer

Q62) Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select from the remaining. The number of possible arrangements is Show Answer

Q63) 20 persons are invited for a party. The number of ways in which they and the host can be seated at a circular table if two particular persons be seated on either side of the host is equal to Show Answer

Q64) In an examination, there are three multiple choice questions and each question has 4 choices. Then, the number of ways in which a student can fail to get all answer correct is Show Answer

Q65) The number of committees of 5, consisting at least one female member, that can be formed from 6 males and 5 females is Show Answer

Q66) Given 5 line segments of lengths 2, 3, 4, 5, 6 units. Then the number of triangles that can be formed by joining these lines are Show Answer

Q67) Seven women and seven men are to sit round a circular table such that there is a man on either side of every women, then the number of seating arrangements is Show Answer

Q68) The number of ways in which 6 prizes can be distributed among 4 boys, while each boy is capable of having any number of prizes is Show Answer

Q69) In how many ways can 10 balls be divided between two boys, one receiving two and the other eight balls? Show Answer

Q70) There are 5 books of mathematics, 4 of physics, 3 of chemistry and 3 books of literature on different subjects. There are 15 books placed on a book-self.
The number of ways so that the book of same subject are placed together is given by Show Answer

Q71) The number of 5 digit telephone number having at least one of their digits repeated is Show Answer

Q72) Four dice (six faced) are rolled. The number of possible outcomes in which at least one die shows 2 is Show Answer

Q73) How many words can be made from the letters of the word 'DELHI', if L comes in the middle in very word? Show Answer

Q74) There are 60 greeting cards and 60 envelopes both marked 1 to 60. The number of ways in which the greeting cards can be put in the envelope so that exactly one of them is put in a wrong envelope is Show Answer

Q75) Gentlemen are in majority. Show Answer

Q76) Ladies are in majority. Show Answer

Q77) Exactly 3 ladies are chosen. Show Answer

Q78) If repetition is not allowed Show Answer

Q79) If repetition is allowed Show Answer

Q80) If C (28, 2 r) = C (28, 2r - 4), then what is r equal to? Show Answer

Q81) In how many ways can the letters of the word 'GLOOMY' be arranged so that the two O's should not be together? Show Answer

Q82) If P (77, 31) = x and C (77, 31) = y, then which one of the following is correct? Show Answer

Q83) What is the number of diagonals which can be drawn by joining the angular points of a polygon of 100 sides? Show Answer

Q84) The number of permutations that can be formed from all the letters of the word 'BASEBALL' is Show Answer

Q85) What is the number of ways that 4 boys and 3 girls can be seated so that boys and girls alternate? Show Answer

Q86) How many diagonals will be there in an n-sided regular polygon? Show Answer

Q87) There are 4 candidates for the post of a lecturer in Mathematics and one is to be selected by votes of 5 men. What is the number of ways in which the votes can be given? Show Answer

Q88) Using the digits 1, 2, 3, 4 and 5 only once, how many numbers greater than 41000 can be formed? Show Answer

Q89) A, B, C, D and E are coplanar points and three of the lie in a straight line. What is the maximum number of triangles that can be drawn with these points as their vertices? Show Answer

Q90) What is the value of n, if
P (15, n - 1) : P (16, n - 2) = 3 : 4? Show Answer

Q91) In how many ways can 6 girls be seated in 2 empty chairs? Show Answer

Q92) What is the total number of combinations of n different things taken 1, 2, 3, ..., n at a time? Show Answer

Q93) 5 books are to be chosen from a lot of 10 books. If m is the number of ways of choice when one specified book is always included and n is the number of ways of choice when a specified book is always excluded, then which one of the following is correct? Show Answer

Q94) What is the number of words that can be formed from the letters of the word 'UNIVERSAL', the vowels remaining always together? Show Answer

Q95) What is the number of signals that can be sent by 6 flags of different colours taking one or more at a time? Show Answer

Q96) What is the maximum number of straight lines that can be drawn with any four points in a plane such that each line contains at least two of these points? Show Answer

Q97) In how many ways can a committee consisting of 3 men and 2 women be formed from 7 men and 5 women? Show Answer

Q98) What is the number of ways of arranging the letters of the word 'BANANA', so that no two N's appear together? Show Answer

Q99) What is the number of three digit odd numbers formed by using the digits 1, 2, 3, 4, 5, 6 if repetition of digits is allowed? Show Answer

Q100) How many times does the digit 3 appear while writing the integers from 1 to 1000? Show Answer

Q101) If C (n, 12) = C (n, 8), then what is the value of C (22, n)? Show Answer

Q102) What is the number of words formed from the letters of the word 'JOKE', so that the vowels and consonants alternate? Show Answer

Q103) What is the value of r, if P (5, r) = P (6, r - 1)? Show Answer

Q104) If P (32, 6) = kC (32, 6), then what is the value of k? Show Answer

Q105) What is the smallest natural number n such that n! is divisible by 990? Show Answer

Q106) How many words, with or without meaning can be formed by using all the letters of the word 'MACHINE', so that the vowels occurs only the odd positions? Show Answer

Q107) In how many ways can 3 books on Hindi and 3 books on English be arranged in a row on a shelf, so that not all the Hindi books are together? Show Answer

Q108) If a polygon has 20 diagonals, then what is the number of sides? Show Answer