Practice Test

1) 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

2) Letter of the word COMPUTER can be arranged in

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

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

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

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

7) 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

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

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

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

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

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

13) 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

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

15) 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

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

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

18) 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

19) 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

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

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

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

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

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

25) 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?

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

27) 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?

28) 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?

29) 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?

30) 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?

31) 5 persons can sit on 8 chairs in a row in

32) 7 books can be arranged on a shelf in

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

34) Number of arrangements of letter of the word EQUATION which begin with and end with consonant is

35) Number of arrangements of letter of the word FAILURE in which consonants occupy even places is

36) Number of arrangements of letter of the word VOWEL in which vowels occupy even places is

37) Number of arrangements of letter of the word MOBILE in which consonants occupy odd places is

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

39) 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

40) 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

41) 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

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

43) 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

44) 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

45) 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

46) Number of distinct (distinguishable) permutations of letter of the word MISSISSIPPI is

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

48) When the product (a+b) (c+d+e) (f+g+h) (i+j) is simplified, the number of terms will be

49) 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

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

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

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

53) Inn how many ways can 7 persons seat along a round table so that two particular persons are never together?

54) 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

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

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

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

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

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

60) 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

61) 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

62) 8 points are marked on a circumference of a circle. Number of chords obtained by joining these points is

63) Number of parallelograms formed from a set of 4 parallel lines intersecting another set of 3 parallel lines is

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

65) Number of diagonals in a decagon is

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

67) Number of ways of selecting a cricket eleven from 14 players is

68) 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

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

70) 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

71) 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.

72) 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.

73) 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

74) 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

75) 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

76) 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

77) 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

78) 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

79) 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

80) 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

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

82) Number of diagonals of an octagon is

83) If a polygon has 44 diagonals, then the number of its sides is

84) If the number of diagonals of a polygon equals its number of sides, then the polygon is a

85) 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

86) 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

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

88) Number of other ways in which the letters of the word SIMPLETON can be arranged is

89) If (n+1)!=12.(n-1)!, then: n is

90) If n!=1, then: n is

91) If m! = n!, then