Maths: Important Topic: 
Self Assessment Test

Permutation-And-Combination
QNo.1    A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems? 0
63
511
1023
15
QNo.2    In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected? 0
400
500
600
20
QNo.3    In how many ways can three consonants and two vowels be selected from the letters of the word “TRIANGLE”? 0
25
13
40
30
QNo.4    A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag? 0
⁹C₂
³C₂
¹⁶C₂
¹²C₂
QNo.5    How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9} 0
60
360
120
240
QNo.6    How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)? 0
360
60
300
180
QNo.7    The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is_________?
(6!)2
6! * ⁷P₆
2(6!)
6! * 7
QNo.8    A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most__________? 0
216
243
215
729
QNo.9    A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons? 0
165
185
205
225
QNo.10    What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected? 0
100
60
30
20
QNo.11    A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee? 0
150
200
250
300
QNo.12    The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places? 0
720
144
120
36
QNo.13    Using all the letters of the word “NOKIA”, how many words can be formed, which begin with N and end with A? 0
3
6
24
120
QNo.14    Using all the letters of the word “THURSDAY”, how many different words can be formed? 0
8
8!
7!
7
QNo.15    How many three letter words are formed using the letters of the word TIME? 0
12
20
16
24
QNo.16    A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt? 0
21
12
9
108
QNo.17    In how many different ways can the letters of the word ‘OPTICAL’ be arranged so that the vowels always come together? 0
120
720
4320
2160
QNo.18    In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together? 0
10080
4989600
120960
None of these
QNo.19    How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed? 0
40
400
5040
2520
QNo.20    In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women? 0
63
90
126
45
QNo.21    In how many different ways can four books A, B, C and D be arranged one above another in a vertical order such that the books A and B are never in continuous position? 0
9
12
14
18
QNo.22    There are two identical red, two identical black, and two identical white balls.In how many different ways can the balls be placed in the cells (Each cell to contain one ball) shown above such that balls of the same colour do not occupy any two consecutive cells? 0
15
18
24
30
QNo.23    A two number committee comprising of one male and the female number is to be constituted out of five male and 3 females. Amongst the females, Ms. A refused to be number committee in which Mr.B is taken as the number of how many different ways can the committee be constituted? 0
11
30
14
20
QNo.24    A selection is to be made for one post of principal and two posts of vice-principal amongst the six candidates called for the interview only two are eligible for the post of principal while they all are eligible for the post of vice-principal. The number of possible combinations of selectees is___________? 0
4
12
18
None of these
QNo.25    A student has to opt for 2 subjects out of 5 subjects for a course. Namely commerce, economics, statistics, mathematics 1 and Mathematics 2, Mathematics 2 can be offered only if mathematics 1 has also opted. The number of different combinations of two subjects which can be opted is_________? 0
5
6
7
18
QNo.26    2 men and 1 woman board a bus of which 5 seats are vacant, one of these 5 seats is reserved for ladies. A woman may or may not sit on the seat reserved for ladies, In how many different ways can the five seats be occupied by these passengers? 0
15
36
48
60
QNo.27    Three dice (each having six faces with each face having one number from 1 or 6) are ralled. What is the number of possible outcomes such that atleast one dice shows the number 2? 0
36
81
91
116
QNo.28    A mixed doubles tennis game is to be played two teams(each consists of one male and one female) There are four married couples. No team is to consist a husband and his wife. What is the maximum number of games that can be played? 0
12
48
36
42
QNo.29    In how many different ways can six players be arranged in a line such that two of them, Asim and Raheem are never together? 0
120
240
360
480
QNo.30    Groups each containing 3 boys are to be formed out of 5 boys. A, B, C, D and E such that no group can contain both C and D together. What is the maximum number of such different groups? 0
5
6
7
8
QNo.31    Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points? 0
29
32
55
30
QNo.32    A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors? 0
¹²C₅ * 10
¹²C₇ * 10
¹²C₇ * ¹⁰C₅
12 * ¹⁰C₅
QNo.33    A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group? 0
300
450
600
750
QNo.34    A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group? 0
300
600
750
900
QNo.35    Find the number of ways of arranging the letters of the word “MATERIAL” such that all the vowels in the word are to come together? 0
720
1440
1860
2160
QNo.36    The number of new words that can be formed by rearranging the letters of the word ‘ALIVE’ is__________? 0
24
23
119
120
QNo.37    A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation? 0
20
54
42
60
QNo.38    The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is -. 0
4000
2160
4320
5300
QNo.39    In how many ways can live boys and three girls sit in a row such that all boys sit together? 0
4800
5760
2880
15000