1 .
From amongst 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done ?
A.  1260
B.  1250
C.  1240
D.  1800
E.  None of these
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2 .
A boy has 3 library cards and 8 books of his interest in the library. Of these 8, he does not want to borrow chemistry part II unless Chemistry part I is also borrowed. In how many ways can he choose the three books to be borrowed ?
A.  56
B.  27
C.  26
D.  41
E.  None of these
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3 .
In how many ways can six different rings be worn on four fingers of one hand ?
A.  10
B.  12
C.  15
D.  16
E.  None of these
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4 .
In how many ways can 7 persons be seated at a round table if 2 particular persons must not sit next to each other ?
A.  5040
B.  240
C.  480
D.  720
E.  None of these
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5 .
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together ?
A.  10080
B.  4989600
C.  120960
D.  12960
E.  None of these
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6 .
In an examination 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 particular section. In how many ways can 5 questions be selected ?
A.  24
B.  48
C.  96
D.  None of these
E.  108
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7 .
There are 4 candidates for the post of a lecturer in Mathematics and one is to be selected by votes of 5 men. The number of ways in which the votes can be given is
A.  24
B.  36
C.  40
D.  48
E.  None of these
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8 .
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by
A.  6 ! $\times$ 5 !
B.  5 ! $\times$ 4 !
C.  30
D.  7 ! $\times$ 5 !
E.  None of these
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9 .
A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
A.  140
B.  280
C.  196
D.  346
E.  None of these
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10 .
There are 100 students in a college class of which 36 are boys studying statistics and 13 girls not studying statistics. If there are 55 girls in all, then the probability that a boy picked up at random is not studying statistics, is
A.  $3 \over 5$
B.  $2 \over 5$
C.  $1 \over 5$
D.  $4 \over 5$
E.  None of these
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11 .
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by :
A.  6! $\times$ 5!
B.  30
C.  5! $\times$ 4!
D.  7! $\times$ 5!
E.  None of these
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12 .
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:
A.  ${16_C}_{11}$
B.  ${16_C}_{5}$
C.  ${16_C}_{9}$
D.  ${20_C}_{9}$
E.  None of these
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13 .
In how many different ways can the letters of the word 'PRETTY' be arranged?
A.  120
B.  36
C.  360
D.  720
E.  None of these
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14 .
Three boys and three 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. How many such arrangements are possible ?
A.  5
B.  6
C.  4
D.  2
E.  None of these
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15 . Answer these questions on the basis of the information given below :

From a group of 6 men and 4 women a Committee of 4 persons is to be formed.
In how many different ways can it be done so that the committee has at least one woman?
A.  210
B.  225
C.  195
D.  185
E.  None of these
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16 . Answer these questions on the basis of the information given below :

From a group of 6 men and 4 women a Committee of 4 persons is to be formed.
In how many different ways can it be done, so that the committee has at least 2 men?
A.  210
B.  225
C.  15
D.  185
E.  None of these
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17 . Answer these questions on the basis of the information given below :

From a group of 6 men and 4 women a Committee of 4 persons is to be formed.
In how many ways can 5 persons be chosen from 6 boys and 4 girls so as to include exactly one girl?
A.  252
B.  210
C.  126
D.  90
E.  60
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18 . Answer these questions on the basis of the information given below :

From a group of 6 men and 4 women a Committee of 4 persons is to be formed.
In how many different ways can the letters of the word CORPORATION be arranged?
A.  3326400
B.  1663200
C.  831600
D.  415800
E.  207900
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19 .
In how many different ways can the letters of the word 'COUNTRY' be arranged in such a way that the vowels always come together?
A.  720
B.  1440
C.  2880
D.  5040
E.  None of these
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20 .
In how many different ways can the letters of the word 'PROBLEM' be arranged ?
A.  5060
B.  720
C.  5040
D.  980
E.  None of these
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21 .
Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
A.  864
B.  865
C.  863
D.  1728
E.  None of these
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22 .
In how many different ways can the letters of the word 'OFFICES' be arranged?
A.  2520
B.  5040
C.  1850
D.  1680
E.  None of these
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23 .
In how many different ways can the letters of the word 'ARMOUR' be arranged?
A.  720
B.  300
C.  640
D.  350
E.  None of these
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24 .
There are six teachers. Out of them, two are primary teachers and two are secondary teachers. They are to stand in a row, so as the primary teachers, middle teachers and secondary teachers are always in a set. The number of ways in which they can do so, is
A.  52
B.  48
C.  34
D.  37
E.  None of these
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25 .
In how many different ways can 4 boys and 3 girls be arranged in a row such that all boys stand together and all the girls stand together?
A.  75
B.  576
C.  288
D.  24
E.  None of these
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26 .
In how many ways can a committee of 4 people be chosen out of 8 people ?
A.  110
B.  32
C.  70
D.  126
E.  None of these
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27 .
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
A.  564
B.  645
C.  735
D.  756
E.  None of these
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28 .
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
A.  360
B.  480
C.  720
D.  5040
E.  None of these
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29 .
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?
A.  5
B.  10
C.  15
D.  20
E.  None of these
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30 .
How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes?
A.  256
B.  12
C.  81
D.  89
E.  None of these
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Percentage 2 Pipes and cisterns


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