Practice Test

Q1) How many numbers of 3-digits can be formed with the digits 1, 2, 3, 4, 5 (repetition of digits not allowed)? Show Answer

Q2) How many numbers between 2000 and 3000 can be formed with the digits 0, 1, 2, 3, 4, 5, 6, 7 (repetition of digits not allowed)? Show Answer

Q3) In how many ways can a person send invitation cards to 6 of his friends if he has four servants to distribute the cards? Show Answer

Q4) In how many ways can 5 prizes be distributed to 8 students if each student can get any number of prizes? Show Answer

Q5) In how many ways can 7 Indians, 5 Pakistanis and 6 Dutch be seated in a row so that all persons of the same nationality sit together? Show Answer

Q6) There are 5 routes to go from Allahabad to Patna and 4 ways to go from Patna to Kolkata, then how many ways are possible for going from Allahabad to Kolkata via Patna? Show Answer

Q7) There are 4 qualifying examinations to enter into Oxford University : RAT, BAT, SAT, and PAT. An Engineer cannot go to Oxford University through BAT or SAT. A CA on the other hand can go to the Oxford University through the RAT, BAT and PAT but not through SAT. Further there are 3 ways to become a CA (viz., Foundation, Inter and Final). Find the ratio of number of ways in which an Engineer can make it to Oxford University to the number of ways a CA can make it to Oxford University. Show Answer

Q8) How many straight lines can be formed from 8 non-collinear points on the X-Y plane?
Show Answer

Q9) In how many ways can the letters of the DELHI be arranged? Show Answer

Q10) In how many ways can the letters of the PATNA be rearranged? Show Answer

Q11) How many words will start with P and end with T? Show Answer

Q12) For the arrangements of the letters of the word PATNA, how many words would start with the letter P? Show Answer

Q13) How many numbers of four digits can be formed with the digits 0, 1, 2, 3 (repetition of digits is not allowed)? Show Answer

Q14) How many numbers of four digits can be formed with the digits 0, 1, 2, 3 (repetition of digits being allowed)? Show Answer

Q15) How many numbers between 200 and 1200 can be formed with the digits 0, 1, 2, 3 (repetition of digits is not allowed)? Show Answer

Q16) How many numbers between 200 and 1200 can be formed with the digits 0, 1, 2, 3 (repetition of digits being allowed)? Show Answer

Q17) Arjit being a party animal wants to hold as many parties as possible amongst his 20 friends. However, his father has warned him that he will be financing his parties under the following conditions only :
(a) The invitees have to be amongst his 20 best friends.
(b) He cannot all the same set of friends to a party more than once.
(c) The number of invitees to every party have to be the same.
Given these constraints Arjit wants to hold the maximum number of parties. How many friends should he invite to each party? Show Answer

Q18) In how many ways can 10 identical presents be distributed among 6 children so that each child gets at least one present? Show Answer

Q19) How many four digit numbers are possible, criteria being that all the four digits are odd? Show Answer

Q20) A captain and a vice-captain are to be chosen out of a team having eleven players. How many ways are there to achieve this? Show Answer

Q21) There are five types of envelopes and four types of stamps in a post office. How many ways are there to buy an envelope and a stamp? Show Answer

Q22) In how many ways can Ram choose a vowel and a consonant from the letters of the word ALLAHABAD? Show Answer

Q23) There are three rooms in a motel : one single, one double and one for four persons. How many ways are there to house seven persons in these rooms? Show Answer

Q24) How many ways are there to choose four cards of different suits and different values from a deck of 52 cards? Show Answer

Q25) How many new words are possible from the letters of the word PERMUTATION? Show Answer

Q26) A set of 15 different words are given. In how many ways is it possible to choose a subset of not more than 5 words? Show Answer

Q27) In how many ways can 12 papers be arranged if the best and the worst paper never come together? Show Answer

Q28) In how many ways can the letters of the word 'EQUATION' be arranged so that all the vowels come together? Show Answer

Q29) A man has 3 shirts, 4 trousers and 6 ties. What are the number of ways in which he can dress himself with a combination of all the three? Show Answer

Q30) How many motor vehicle registration number of 4 digits can be formed with the digits 0, 1, 2, 3, 4, 5? (No digit being repeated.) Show Answer

Q31) How many motor vehicle registration number plates can be formed with the digits 1, 2, 3, 4, 5 (No digit being repeated) if it is given that registration number can have 1 to 5 digits? Show Answer

Q32) How many straight lines can be formed? Show Answer

Q33) How many triangles can be formed from these points? Show Answer

Q34) How many quadrilateral can be formed from these points? Show Answer

Q35) There are ten subjects in the school day at St. Vincent's High School but the sixth standard students have only 5 periods in a day. In how many ways can we form a time table for the day for the sixth standard students if no subject is repeated? Show Answer

Q36) There are 8 consonants and 5 vowels in a word jumble. In how many ways can we form 5 - letter words having three consonants and 2 vowels? Show Answer

Q37) How many batting orders are possible for the Indian cricket team if there is a squad of 15 to choose from such that Sachin Tendulkar is always chosen? Show Answer

Q38) There are 5 blue socks, 4 red socks and 3 green socks in Debu's wardrobe. He has to select 4 socks from this set. In how many ways can he do so? Show Answer

Q39) In how many weeks will he be able to go to the principal without repeating the group of same three which accompanies him? Show Answer

Q40) If on the very first visit the principal appoints one of the boys accompanying him as the head boy of the school and lays down the condition that the class prefect has to be accompanied by the head boy every time he comes then for a maximum of how many weeks (including the first week) can the class prefect ensure that the principal sees a fresh group of three accompanying him? Show Answer

Q41) How many distinct words can be formed out of the word PROWLING which start with R and end with W? Show Answer

Q42) How many 7 - digit numbers are there having the digit 3 three times and the digit 5 four times? Show Answer

Q43) How many 7 - digit numbers are there having the digit 3 three times and the digit 0 four times? Show Answer

Q44) From a set of three capital consonants, five small consonants and 4 small vowels how many words can be made each starting with a capital consonant and containing 3 small consonants and two small vowels. Show Answer

Q45) Several teams take part in a competition, each of which must play one game with all the other teams. How many teams took part in the competition if they played 45 games in all? Show Answer

Q46) In how many ways a selection can be made of at least one fruit out of 5 bananas, 4 mangoes and 4 almonds? Show Answer

Q47) Find the number of ways in which at least one book can be given away. Show Answer

Q48) Find the number of ways in which at least one book of each author can be given. Show Answer

Q49) There is a question paper consisting of 15 questions. Each question has an internal choice of 2 options. In how many ways can a student attempt one or more questions of the given fifteen questions in the paper? Show Answer

Q50) How many numbers can be formed with the digits 1, 6, 7, 8, 6, 1 so that the odd digits always occupy the odd places? Show Answer

Q51) There are five boys of McGraw-Hill Mindworkzz and three girls of I.I.M Lucknow who are sitting together to discuss a management problem at a round table. In how many ways can they sit around the table so that no two girls are together? Show Answer

Q52) Amita has three library cards and seven books of her interest in the library of Mindworkzz. Of these books she would not like to borrow the D. I. book, unless the Quants book is also borrowed. In how many ways can she take the three books to be borrowed? Show Answer

Q53) From a group of 12 dancers, five have to be taken for a stage show. Among them Radha and Mohan decide either both of them would join or none of them would join. In how many wasy can the 5 dancers be chosen? Show Answer

Q54) Find the number of 6 - digit numbers that can be found using the digits 1, 2, 3, 4, 5, 6 once such that the 6 - digit number is divisible by its unit digit. (The unit digit is not 1.) Show Answer

Q55) An urn contains 5 boxes. Each box contains 5 balls of different colours red, yellow, white, blue and black. Rangeela wants to pick up 5 balls of different colours, a different coloured ball from each box. If from the first box in the first draw, he has drawn a red ball and from the second box he has drawn a black ball, find the maximum number of trials that are needed to be made by Rangeels to accomplish his task if a ball picked is not replaced. Show Answer

Q56) How many rounds of matches does a knock-out tennis tournament have if it starts with 64 players and every player needs to win 1 match to move at the next round? Show Answer

Q57) There are N men sitting around a circular table at N distinct points. Every possible pair of men except the ones sitting adjacent to each other sings a 2 minute song one pair after other. If the total time taken is 88 minutes, then what is the value of N? Show Answer

Q58) In a class with boys and girls a chess competition was played wherein every student had to play 1 game with every other student. It was observed that in 36 matches both the players were boys and in 66 matches both were girls. What is the number of matches in which 1 boy and 1 girl play against each other? Show Answer

Q59) Zada has to distribute 15 chocolates among 5 of her children Sana, Ada, Jiya, Amir and Farhan. She has to make sure that Sana gets at least 3 and at most 6 chocolates. In how many ways can this be done? Show Answer

Q60) Mr. Shah has to divide his assets worth Rs. 30 crores in 3 parts to be given to three of his songs Ajay, Vijay and Arun ensuring that every son gets assets at least worth Rs. 5 crores. In how many ways can this be done if it is given that the three sons should get their shares in multiples in multiples of Rs. 1 crore? Show Answer

Q61) Three variables x, y, z have a sum of 30. All three of them are non-negative integers. If any two variables don't have the same value and exactly one variable has a value less than or equal to three, then find the number of possible solutions for the variables. Show Answer

Q62) The letters of the word ALLAHABAD are rearranged to form new words and put in a dictionary. If the dictionary has only these words and one word on every page in alphabetical order then what is the page number on which the word LABADALAH comes? Show Answer

Q63) If x, y and z can only take the values 1, 2, 3, 4, 5, 6, 7 then find the number of solutions of the equation x + y + z = 12. Show Answer

Q64) There are nine points in a plane such that no three are collinear. Find the number of triangles that can be formed using these points as vertices. Show Answer

Q65) There are nine points in a plane such that exactly three points out of them are collinear. Find the number of triangles that can be formed using these points as vertices. Show Answer

Q66) Ten points are marked on a straight line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points? Show Answer

Q67) For a scholarship, at the most n candidates out of 2n + 1 can be selected. If the number of different ways of selection of at least one candidate is 63, the maximum number of candidates that can be selected for the scholarship is Show Answer

Q68) One red flag, three white flags and two blue flags are arranged in a line such that,
(a) no two adjacent flags are of the same colour
(b) the flags at the two ends of the line are of different colours
In how many different ways can the flags be arragned? Show Answer

Q69) Sam has forgotten his friend's seven-digit telephone number. He remembers the following : the first three digits are either 635 or 674, the number is odd, and the number nine appears once. If Sam were to use a trial and error process to reach his friend, what is the minimum number of trials he has to make before be can be certain to succeed? Show Answer

Q70) There are three cities A, B and C. Each of these cities is connected with the other two cities by at least one direct road. If a traveler wants to go from one city (origin) to another city (destination), she can do so either by traversing a road connecting the two cities directly, or by traversing two roads, the first connecting the origin to the third city and the second connecting the third city to the destination. In all there are 33 routes from A to B (including those via C). Similarly there are 23 routes from B to C (including those via A). How many roads are there from A to C directly? Show Answer

Q71) Let n be the number of different 5 - digit numbers, divisible by 4 that can be formed with the digits 1, 2, 3, 4, 5 and 6, with no digit being repeated. What is the value of n? Show Answer

Q72) How many number greater than 0 and less than a million can be formed with the digits 0, 7 and 8? Show Answer

Q73) In how many ways is it possible to choose a white square and a black square on a chess board so that the squares must not lie in the same row or column? Show Answer

Q74) How many four-letter computer passwords can be formed using only the symmetric letters (no repetition allowed)? Show Answer

Q75) How many three-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter? Show Answer

Q76) Twenty seven persons attend a party. Which one of the following statements can never be true? Show Answer

Q77) There are 6 boxes numbered 1, 2, ...6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is Show Answer

Q78) How many numbers can be formed with odd digits 1, 3, 5, 7, 9 without repetition? Show Answer

Q79) In how many ways five chocolates can be chosen from an unlimited number of Cadbury, Five-star, and Perk chocolates? Show Answer

Q80) How many even numbers of four digits can be formed with the digits 1, 2, 3, 4, 5, 6 (repetitions of digits are allowed)? Show Answer

Q81) The number of participants in the tournament were? Show Answer

Q82) The total number of games played in the tournament were? Show Answer

Q83) How many 4 digit numbers divisible by 5 can be formed with the digits 0, 1, 2, 3, 4, 5, 6 and 7? Show Answer

Q84) There are 6 pups and 4 cats. In how many ways can they be seated in a row so that no cats sit together? Show Answer

Q85) How many new words can be formed with the word MANAGEMENT all ending in G? Show Answer

Q86) Find the total number of 9 - digit numbers that can be formed all having different digits. Show Answer

Q87) There are V lines parallel to the x-axis and 'W' lines parallel to y-axis. How many rectangles can be formed with the intersection of these lines? Show Answer

Q88) Find the number of ways of doing so if the committee consists of a president, a vice-president and three secretaries? Show Answer

Q89) What will be the number of ways of selecting the committee with at least 3 women such that at least one woman holds the post of either a president or a vice-president? Show Answer

Q90) Find the number of ways of selecting the committee with a maximum of 2 women and having at the maximum one woman holding one of the two posts on the committee. Show Answer

Q91) The crew of an 8 member rowing team is to be chosen from 12 men, of which 3 must row on one side only and 2 must row on the other side only. Find the number of ways of arranging the crew with 4 members on each side. Show Answer

Q92) In how many ways 5 MBA students and 6 Law students can be arranged together so that no two MBA students are side by side? Show Answer

Q93) The latest registration number issued by the Delhi Motor Vehicle Registration Authority is DL-5S 2234. If all the numbers and alphabets before this have been used up, then find how many vehicles have a registration number starting with DL-5? Show Answer

Q94) Find the sum of the number of sides and number of diagonals of a hexagon. Show Answer

Q95) In how many ways can a selection be made of 5 letters out of 5As, 4Bs, 3Cs, 2Ds and 1E? Show Answer

Q96) The number of positive numbers of not more than 10 digits formed by using 0, 1, 2, 3 is Show Answer

Q97) There is a number lock with four rings. How many attempts at the maximum would have to be made before getting the right number? Show Answer

Q98) Find the number of numbers that can be formed using all the digits 1, 2, 3, 4, 3, 2, 1 only once so that the odd digits occupy odd places only. Show Answer

Q99) There is a 7 - digit telephone number with all different digits. If the digit at extreme right and extreme left are 5 and 6 respectively, find how many such telephone numbers are possible. Show Answer

Q100) How many ways can the selections be made to include at least one male? Show Answer

Q101) How many ways can the selections be made to if it has to contain at the maximum three women? Show Answer

Q102) How many figures are required to number a book containing 150 pages? Show Answer

Q103) There are 8 orators A, B, C, D, E, F, G and H. In how many ways can the arrangements be made so that A always comes before B and B always comes before C. Show Answer

Q104) How many ways can wrong choices be made? Show Answer

Q105) Find the number of ways in which only one letter goes in the wrong envelope? Show Answer

Q106) Find the number of ways in which only two letters go in the wrong envelopes? Show Answer

Q107) A train is running between Patna to Howrah. Seven people enter the train somewhere between Patna and Howrah. It is given that nine stops are there in between Patna to Howrah. In how many ways can the tickets be purchased if no restriction is there with respect to the number of tickets at any station? 2 people do not buy the same ticket. Show Answer

Q108) What is the number of shoes required to be drawn out? Show Answer

Q109) What is the minimum number of shoes required to be drawn out to get at least 1 pair of correct shoes (either white or black)? Show Answer

Q110) In how many ways one white and one black rook can be placed on a chessboard so that they are never in an attacking position? Show Answer

Q111) How many 6 - digit numbers have all their digits either all odd or all even? Show Answer

Q112) How many 6 - digit numbers have at least 1 even digit? Show Answer

Q113) How many 10 - digit numbers have at least 2 equal digits? Show Answer

Q114) On a triangle ABC, on the side AB, 5 points are marked, 6 points are marked on the side BC and 3 points are marked on the side AC (none of the points being the vertex of the triangle). How many triangles can be made by using these points? Show Answer

Q115) If we have to make 7 boys sit with 7 girls around a round table, then the number of different relative arrangements of boys and girls that we can make so that there are no two boys nor any two girls sitting next to each other is Show Answer

Q116) If we have to make 7 boys sit alternately with 7 girls around a round table which is numbered, then the number of ways in which this can be done is Show Answer

Q117) In the Suniti Building in Mumbai there are 12 floors plus the ground floor. 9 people get into the lift of the building on the ground floor. The lift does not stop on the first floor. If 2, 3 and 4 people alight from the lift on its upward journey, then in how many ways can they do so? (Assume they alight on different floors.) Show Answer

Q118) 1 surgeon and an assistant Show Answer

Q119) 1 surgeon and 4 assistants Show Answer

Q120) In how many ways can 10 identical marbles be distributed among 6 children so that each child gets at least 1 marble? Show Answer

Q121) Seven different objects must be divided among three people. In how many ways can this be done if one or two of them can get no objects? Show Answer

Q122) How many 6 - digit even numbers can be formed form the digits 1, 2, 3, 4, 5, 6 and 7 so that the digits should not repeat? Show Answer

Q123) How many 6 - digit even numbers can be formed form the digits 1, 2, 3, 4, 5, 6 and 7 so that the digits should not repeat and the second last digit is even? Show Answer

Q124) How many 5 - digit numbers that do not contain identical digits can be written by means of the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9? Show Answer

Q125) How many different 4 - digit numbers are there which have the digits 1, 2, 3, 4, 5, 6, 7 and 8 such that the digit 1 appears exactly once. Show Answer

Q126) How many different 7 - digit numbers can be written using only three digits 1, 2 and 3 such that the digit 3 occurs twice in each number? Show Answer

Q127) How many different 4 - digit numbers can be written using the digits 1, 2, 3, 4, 5, 6, 7 and 8 only once such that the number 2 is contained once. Show Answer

Q128) The number of ways in which four particular persons A, B, C, D and six more persons can stand in a queue so that A always stands before B, B always before C and C always before D is
Show Answer

Q129) The number of circles that can be drawn out of 10 points of which 7 are collinear is Show Answer

Q130) How many different 9 - digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even position?









Show Answer

Q131) How many diagonals are there in an n-sided polygon (n > 3)? Show Answer

Q132) A polygon has 54 diagonals. Find the number of sides. Show Answer

Q133) The number of natural numbers of two or more than two digits in which digit from left to right are in increasing order is Show Answer

Q134) In how many ways a cricketer can score 200 runs with fours and sixes only? Show Answer

Q135) A dices is rolled six times. One, two, three, four, five and six appears on consecutive throws of dices. How many ways are possible of having 1 before 6? Show Answer

Q136) The number of permutations of the letters a, b, c, d, e, f, g such that neither the pattern 'beg' nor 'acd' occurs is Show Answer

Q137) In how many ways can the letters of the English alphabet be arranged so that there are seven letters between the letters A and B? Show Answer

Q138) There are 20 people among whom two are sisters. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two sisters? Show Answer

Q139) There are 10 points on a straight line AB and 8 on another straight line, AC none of them being A. How many triangles can be formed with these points as vertices? Show Answer

Q140) In an examination, the maximum marks for each of the three papers is 50 each. The maximum marks for the fourth paper is 100. Find the number of ways with which a student can score 60% marks in aggregate. Show Answer

Q141) How many rectangles can be formed out of a chess-board? Show Answer

Q142) Find the number of squares. Show Answer

Q143) Find the number of rectangles. Show Answer

Q144) How many handshakes are there if there are 10 participants in all, 3 finalists and 60 spectators? Show Answer

Q145) What is the ratio of the number of handshakes involving the host to the number of handshakes not involving the host? Show Answer

Q146) What is the percentage increase in the total number of handshakes if all the guests are required to shake hands with each other once? Show Answer

Q147) In how many ways can the students be placed in two rows of six each so that there should be no identical variants side by side and that the students sitting one behind the other should have the same variant? Show Answer

Q148) If there are now three variants of the test to be given to the twelve students (so that each variant is used for four students) and there should be no identical variants side by side and that the students sitting one behind the other should have the same variant. Find the number of ways this can be done. Show Answer

Q149) Five boys and three girls are sitting in a row of eight seats. In how many ways can they be seated so that not all girls sit side by side? Show Answer

Q150) Seven different objects must be divided among three people. In how many ways can this be done if one or two of them must get no objects? Show Answer

Q151) Seven different objects must be divided among three people. In how many ways can this be done if at least one of them gets exactly 1 object? Show Answer

Q152) How many 4 - digit numbers that are divisible by 4 can be formed from the digits 1, 2, 3, 4, and 5? Show Answer

Q153) How many natural numbers smaller than 10,000 are there in the decimal notation of which all the digits are different? Show Answer

Q154) How many 4 - digit numbers are there whose decimal notation contains not more than two distinct digits? Show Answer

Q155) How many different 7 - digit numbers are there the sum of whose digits are odd? Show Answer

Q156) How many 6 - digit numbers contain exactly 4 different digits? Show Answer

Q157) Six white and six black balls of the same size are distributed among ten urns so that there is at least one ball in each urn. What is the number of different distributions of the balls? Show Answer

Q158) A bouquet has to be formed from 18 different flowers so that it should contain not less than three flowers. How many ways are there of doing this in? Show Answer

Q159) How many distinct 6 - digits numbers are there having 3 odd and 3 even digits? Show Answer

Q160) How many 8 - digits numbers are there the sum of whose digits is even? Show Answer

Q161) The number of participants in the tournament were : Show Answer

Q162) The total number of games played in the tournament were : Show Answer

Q163) There are 5 bottles of sherry and each have their respective caps. If you are asked to put the correct cap to the correct bottle then how many ways are there so that not a single cap is on the correct bottle? Show Answer

Q164) How many possible numbers does Amartya have to try to be sure that he gets the correct number? Show Answer

Q165) If Amartya is reminded by his friend Sharma that apart from what he remembered there was the additional fact that the last digit of the number was not repeated under any circumstance then how many possible numbers does Amartya have to try to be sure that he gets the correct number? Show Answer

Q166) How many natural numbers not more than 4300 can be formed with the digits 0, 1, 2, 3, 4 (if repetitions are allowed)? Show Answer

Q167) How many natural numbers less than 4300 can be formed with the digits 0, 1, 2, 3, 4 (if repetitions are not allowed)? Show Answer

Q168) How many even natural numbers divisible by 5 can be formed with the digits 0, 1, 2, 3, 4, 5, 6 (if repetitions of digits not allowed)? Show Answer

Q169) The letters of the word PASTE are written in all possible orders and these words are written out as in a dictionary. Then the rank of the word SPATE is. Show Answer

Q170) The side AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The total number of triangles that can be constructed by using these points as vertices are Show Answer

Q171) A library has 20 copies of CAGE; 12 copies each of RAGE Part 1 and Part 2; 5 copies of PAGE Part 1, Part 2 and Part 3 and single copy of SAGE, DAGE and MAGE. In how many ways can these books be distributed? Show Answer

Q172) The AMS MOCK CAT test CATALYST 19 consists of four sections. Each section has a maximum of 45 marks. Find the number of ways in which a student can qualify in the AMS MOCK CAT if the qualifying marks is 90. Show Answer

Q173) 18 guests have to be seated, half on each side of a long table. 4 particular guests desire to sit on one particular side and 3 others on the other side. Determine the number of ways in which the sitting arrangements can be made Show Answer

Q174) If m parallel lines in a plane are intersected by a family of n parallel lines, find the number of parallelograms that can be formed. Show Answer

Q175) A father with eight children takes three at a time to the zoological garden, as often as he can without taking the same three children together more than once. How often will he go and how often will each child go? Show Answer

Q176) A candidate is required to answer 7 questions out of 2 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. In how many different ways can he choose the 7 questions? Show Answer

Q177) Find the sum of all 5 digit numbers formed by the digits 1, 3, 5, 7, 9 when no digit is being repeated. Show Answer

Q178) Consider a polygon of n sides. Find the number of triangles, none of whose sides is the side of the polygon. Show Answer

Q179) The number of 4 digit numbers that can be formed using the digits 0, 2, 3, 5 without repetition is Show Answer

Q180) Find the total number of words that can be made by using all the letters from the word MACHINE, using them only once. Show Answer

Q181) What is the total number of words that can be made by using all the letters of the word REKHA, using each letter only once? Show Answer

Q182) How many different 5 - digit numbers can be made from the first 5 natural numbers, using each digit only once? Show Answer

Q183) The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices. Show Answer

Q184) From 6 gentlemen and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done if there is no restriction in its formation? Show Answer

Q185) From 4 officers and 8 jawans in how many ways can 6 be chosen to include exactly one officer? Show Answer

Q186) From 4 officers and 8 jawans in how many ways can 6 be chosen to include at least one officer? Show Answer

Q187) The number of ways in which 6 British and 5 French can dine at a round table if no two French are to sit together is given by : Show Answer

Q188) A cricket team of 11 players is to be formed form 2o players including 6 bowlers and 3 wicketkeepers. Find the number of ways in which a team can be formed having exactly 4 bowlers and 2 wicketkeepers : Show Answer

Q189) Three boys and three girls are to be seated around a circular table. Among them one particular boy Rohit does not want any girl neighbor and one particular girl Shaivya does not want any boy neighbor. How many such arrangements are possible? Show Answer

Q190) Words with five letters are formed from ten different letters of an alphabet. Then the number of words which have at least one letter repeated is Show Answer

Q191) The number of parallelograms that can be formed if 7 parallel horizontal lines intersect 6 parallel vertical lines is : Show Answer

Q192) How many four - digit numbers, each divisible by 4 can be formed using the digits 1, 2, 3, 4 and 5 (repetitions allowed)? Show Answer

Q193) A student is to answer 10 out of 13 questions in a test such that he/she must choose at least 4 from the first five questions. The number of choices available to him is : Show Answer

Q194) The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed from a meeting consisting of 8 ladies and 7 gentlemen. If Mrs. Pushkar refuses to serve in a committee if Mr. Modi is its member is Show Answer

Q195) Two different series of a question booklet for an aptitude test are to be given to twelve students. In how many ways can the students be placed in two rows of six each so that there should be no identical series side by side and that the students sitting one behind the other should have the same series? Show Answer

Q196) The letters of the word PROMISE are arranged so that two of the vowels should come together. The total number of arrangements is : Show Answer

Q197) Find the remainder left after dividing 1! + 2! + 3! + ... + 1000! by 7. Show Answer

Q198) In the McGraw-Hill Mindworkzz mock test paper, there are two sections, each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any section. In how many ways can 5 questions be selected? Show Answer

Q199) A bag contains 10 balls out of which 3 are pink and rest are orange. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 pink balls are included in the sample and no sample has all the 6 balls of the same colour? Show Answer

Q200) There is one grandfather, 5 sons and daughters and 8 grandchildren in a family. They are to be seated in a row for dinner. The grandchildren wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. Find the number of ways in which the family can be made to sit : Show Answer

Q201) In a group photograph at the Patna Women's College, all the seven teachers should sit in the first row and all the twenty students should sit in the second row. The two corners of the second row are reserved for the two tallest students, interchangeable only between them and if the middle seat of the front row is reserved for the principal. Find the number of possible arrangements : Show Answer

Q202) In a certain town, all telephone numbers have six digits, the first two digits always being 53 or 54 or 56 or 82 or 84. The number of telephone numbers having all the six digits distinct is : Show Answer

Q203) There are 4 applicants for the post of the Indian cricket captain and one of them is to be selected by the votes of the 5 wise men (also called as the selectors). The number of ways in which the votes can be given is : Show Answer

Q204) In a Football Tournament, there were 171 matches played. Every two teams played one match with each other. The number of teams participating in the Tournament is : Show Answer

Q205) Seven points lie on a circle. How many chords can be drawn by joining these points? Show Answer

Q206) Ten different letters of an alphabet are given. Words with 5 letters are formed from these given letters. Find the number of words which have at least one letter repeated : Show Answer

Q207) There are eight chairs marked A to H. Two girls and three boys wish to occupy one chair each. First, the girls chose the chairs from amongst the chairs marked A to D, then the boys selected the chairs from amongst the remaining, marked E to H. The number of possible arrangements is : Show Answer

Q208) Prabhjeet a fan of poker, wants to play poker every night for the maximum number of nights possible. The key constraint for him is that he has only 8 friends who are willing to play with him and he wants to hold poker games with distinct groups of friends. His mother has put the condition that in case the same group is repeated on any day, she would stop his poker games and make him study - something that he should be doing anyway. Being a mathematically - oriented person, Prabhjeet calculates the maximum number of nights on which he can play poker without violating his mother's condition. What is the value that he has calculated? Show Answer

Q209) A five digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways this can be done is : Show Answer

Q210) There are 6 equi-distant points A, B, C, D, E and F marked on a circle with radius M. How many convex pentagons of distinctly areas can be drawn using these points as vertices? Show Answer

Q211) Five men A, B, C, D and E occupy seats in a row such that C and D sit next to each other. In how many possible ways can these five men sit? Show Answer

Q212) The number of zero at the end of 60! is Show Answer

Q213) A department had 8 male and female employees each. A project team involving 3 male and 3 female members needs to be selected from the department employees. How many different project teams can be formed? Show Answer

Q214) From a group of 7 men and 6 women, 5 persons are to be chosen to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? Show Answer

Q215) The number of different ways that the letters of the word STALLION can be arranged so that the vowels always come together is : Show Answer

Q216) If a polygon has 54 diagonals, then find the number of its sides. Show Answer