PERMUTATIONS
1.
(i) If nP4 = 360,
then what is the value of n? [Ans.
(a) 6]
(a) 6
(b) 7 (c)
5 (d)
9 (e)
None of these
(ii) If nP3
= 9240, then what is the value of n? [Ans.
(c) 22]
(a) 20
(b) 21 (c) 22 (d)
24 (e)
None of these
(iii) If 2nP3
= 100. nP2, then what is the value of n[Ans. (c)
13]
(a) 10 (b)
11 (c) 13 (d)
15 (e)
None of these
(iv)
If nP5 = 95040, then what is the value of n?
[Ans. (d) 12]
(a) 15 (b) 11 (c) 10 (d) 12 (e)
None of these
(v)
If 2n+1Pn-1: 2n-1Pn = 3 : 5, then
what is the value of n?
[Ans. (c) 4]
(a) 10
(b) 11 (c) 4
(d) 9 (e) None of these
2.
(i) If 10Pr = 720, then what is the value of rAns.
(e) 3)]
(a) 6
(b) 4 (c) 5 (d)
2 (e)
None of these
(ii)
If 9Pr = 3024, then what is the value of r? [Ans. (a) 4]
(a) 4
(b) 5 (c) 3 (d)
2 (e)
None of these
(iii) If 11Pr
= 12Pr-1, then what is the value of r? [Ans. (c) 9]
(a) 10
(b) 11 (c) 9 (d) 12
(e) None of these
(iv)
If 2n+1Pn-1 : 2n-1Pn = 3 : 5, then
what is the value of n? [Ans.
(c) 4]
(a) 10
(b) 11 (c) 4
(d) 9 (e) None of these
3. (i) There are three nails
on a wall to hang pictures. Seven different pictures are to be hung. In how
many ways can all the pictures be hung on all the nails? [Ans. (a) 210]
(ii)
In a railway compartment, 6 seats are vacant. In how many ways can 3 passengers
sit on them? [Ans. (e) None (120)]
(a) 110 (b) 720 (c) 140 (d)
160 (e) None of these
4. (i) In how many different ways can the letters of
the word RUMOUR be arranged? [Ans. (a) 180]
(a) 180
(b) 720 (c)
30 (d)
90 (e)
None of these
(ii) How many different
letter arrangements can be made from the letters of the word RECOVER? [Ans. (a) 1260]
(a) 1260 (b) 1200 (c) 1210 (d) 5040 (e) None of these
(iii)
In how many ways can the letters of the word CIVILIZATION be rearranged? [Ans.
(b) 12!/4! – 1]
(a) 12!/4! (b) 12!/4!
– 1 (c) 13!/4! – 1 (d)
13!/4! (e) None
(iv)
How many words can be formed from the letters of the work SIGNATURE, so
that the vowels always come together? [Ans.
(e) (17280)]
(a) 720
(b) 1440 (c)
3600 (d) 2880 (e)
None of these
(v) In how many different ways can the letters of the
word CORPORATION be arranged in such a way that the vowels always come
together? [Ans. (e) 50,400)]
(a) 840
(b) 86,400 (c)
8,400 (d) 1440 (e
None of these
(vi) Letters of the word DIRECTOR
are arranged in such a way that all the vowels come together. Find out the
total no. of ways for making such arrangement? [Ans. (d)
2160]
(a) 4320 (b) 2720
(c) 1120 (d) 2160 (e)
None of these
(vii)
In how many different ways can the letters of the word JUDGE be arranged
so that the vowels always come together? [Ans. (a) 48]
(a) 48 (b)
24 (c) 120 (d) 60
(e) None of these
(viii) How many different
words can be formed with the letters of the word UNIVERSITY, so that all
the vowels come together? [Ans. (e) None of these
(60480)]
(a) 6400 (b) 60000 (c) 36480 (d) 6088 (e) None of these
(ix) In how many different
ways can the letters of the word DESIRE be rearranged in such a way that
the vowels always come together? [Ans. (b) 71]
(a) 24
(b) 72 (c)
144 (d) 360 (e) 10
(x) In how many ways can the
letters of the word DIRECTOR be arranged so that all the three
vowels never come together? [Ans. (e) None of these (18000)]
(a) 1800 (b) 16000 (c)
18080 (d) 9000 (e)
None of these
(xi)
In how many ways can the letters of the word DAUGHTER be arranged
so that all the three vowels never come together? [Ans.
(a) 36000]
(a) 36000 (b) 6300 (c) 26000 (d) 4320 (e) None of these
(xii) In how many different
ways can the letters of the work ORGANISE be arranged in such a way that
all the vowels always come together and all the consonants always come
together?[Ans. (b) 1152]
(a) 576
(b) 1152 (c) 2880 (d)
1440 (e) None of these
5.
(i) How many numbers can be made with the digits 1, 2, 3, 4, 5 and 6, taken all
together when there is no restriction? [Ans. (d) 720]
(a) 520 (b) 716 (c)
680 (d)
720 (e)
None of these
(ii)
How many numbers each lying between 100
and 1000 can be made with the digits 0, 2, 3, 4, 8 and 9? [Ans.
(a) 100]
(a) 100
(b) 95 (c) 180 (d)
120 (e)
None of these
(iii)
How many numbers between 400 and 1000 can be made with the digits 2, 3, 4, 5, 6
and 0? [Ans. (c) 60]
(a) 120
(b) 48 (c) 60 (d)
90 (e)
None of these
(iv)
How many numbers between 300 and 3000 can be made with the digits 0, 1, 2, 3, 4
and 5, no digit being repeated in any number? [Ans. (c) 180]
(a) 220 (b)
90 (c) 180
(d) 120 (e)
None of these
(v)
How many odd numbers of three-digits can be formed with the digits 1, 2, 3, 4,
5 and 6, no digit being repeated in any number? [Ans. (b) 60]
(a) 90
(b) 60 (c)
160 (d) 120 (e)
None of these
(vi)
How many odd numbers of three-digits can be formed with the digits 1, 2, 3, 4,
5 and 6, the repetition of digits is allowed? [Ans. (c) 108]
(a) 90
(b) 180 (c)
108 (d) 120 (e)
None of these
(vii)
How many even numbers of four-digits can be formed with the digits 0, 1, 2, 3,
4, 5 and 6, no digit being repeated in any number? [Ans. (a) 420]
(a) 420
(b) 360 (c)
560 (d) 120
(e) None of these
(viii)
How many numbers of four-digits greater than 2300 can be formed with the digits
0, 1, 2, 3, 4, 5 and 6; no digit being repeated in any number? [Ans.
(e) none of these (560)]
(a) 620
(b) 360 (c)
540 (d) 440 (e)
None of these
(ix)
How many positive numbers can be formed by using any number of the digits 0, 1,
2, 3 and 4; no digit being repeated in any number? [Ans.
(b) 260]
(a) 420
(b) 260 (c)
360 (d) 120 (e)
None of these
6.
(i) In how many ways can 12 examination
papers be arranged so that the best and the worst papers always come
together. [Ans.
(a) 2! ´ 11!]
(a) 2! ´ 11! (b) 3 ´ 11! (c) 2 ´ 12! (d) 12! (e) None
(ii)
In how many ways can 10 examination papers be arranged so that the best and the
worst papers never come together? [Ans.
(d) 8 ´ 9!]
(a) 8! ´ 9! (b) 9 ´ 9! (c) 8 ´ 10! (d) 8 ´ 9! (e) None of
these
(iii) 4 boys and 2 girls are
to be seated in a row in such a way that two girls are always together. In how
many different ways can they be seated? [Ans. (d) 240]
(iv)
There are 5 boys and 3 girls. In how many ways can they be seated in a row so
that all the three girls sit together? [Ans. (d) 4320]
(a) 4230 (b) 4340
(c) 5320 (d)
4320 (e) None of these
(v) 2 girls and 4 boys are to be seated in a row in
such a way that the girls do not sit together. In how may different ways can it
be done? [Ans. (b) 480]
(a) 720
(b) 480 (c)
360 (d) 240 (e)
None of these
(vi)
There are 5 boys and 3 girls. In how many ways can they be seated in a row so
that all the three girls do not sit together? [Ans. (a) 36000]
(a) 36000 (b) 6300 (c) 26000 (d) 4320
(e) None of these
7.
(i) In how many ways can 9 Indians, 5 Americans and 4 Englishmen be seated in a
row so that all the persons of the same nationality sit together? [Ans. (a) 3! ´ 9! ´ 5! ´ 4!]
(a)
3! ´ 9! ´ 5! ´ 4! (b) 9! ´ 5! ´ 4! (c) 3 ´ 9! ´ 5! ´ 4! (d) 3! ´ 8! ´ 5! ´ 4! (e) None of these
(ii)
There are 21 books of which 5 are single volume and the others are books of 8,
5 and 3 volumes respectively. In how many ways can all these books be arranged
on a shelf so that the volumes of the same book are not separated? [Ans. (e)
None of these (8! ´ 8! ´ 5! ´ 3!)]
(a)
8! ´ 9! ´ 5! ´ 3! (b) 8! ´ 5! ´ 3! (c) 8 ´ 8! ´ 5! ´ 3! (d) 4! ´ 8! ´ 5! ´ 3! (e) None of these
(iii)
A library has two books each having three copies and three other books each
having two copies. In how many ways can all these books be arranged in a shelf
so that copies of the same book are not separated? [Ans. (e) None of these (120)]
(a)
110 (b) 720 (c) 140
(d) 160 (e) None of these
8.
(i) In how many ways can 7 I. A. and 5 I. Sc. Students be seated in a row so that no
two of the I. Sc. Students may sit together? [Ans.
(c) (8! ´ 7!)/ 3!]
(a) (9! ´ 7!)/ 3! (b) (8! ´ 7!)/ 3 (c) (8! ´ 7!)/ 3! (d) (8! ´ 8!)/ 3! (e) None of these
(ii)
In a class of 10 students, there are 3 girls. In how many different ways can
they be arranged in a row such that no two of the three girls are
consecutive? [Ans. (d) (8! ´ 7!)/ 5!]
(a) (8! ´ 7!)/ 3! (b) (8! ´ 7!)/ 5 (c) (8! ´ 9!)/ 3! (d) (8! ´ 7!)/ 5! (e) None of these
9.(i)
In how many ways 5 boys and 4 girls can be seated in a row so that they are
alternate? [Ans. (a) 2880]
(a) 2880 (b) 2800 (c) 2680 (d) 2408 (e) None of these
(ii)
In how many ways 9 boys and 10 girls can be seated in a row so that they are
alternate? [Ans. (e) None of these (9! ´ 10!)]
(a) 11! ´ 9! (b) 9 ´ 10! (c) 9! ´ 11! (d) 8! ´ 9! (e) None
(iii)
In how many ways 5 boys and 5 girls can be seated in a row so that they are
alternate? [Ans. (b) 28800]
(a) 28080 (b) 28000
(c) 2880 (d) 38800 (e) None of these
(iv) In how many ways 3 boys
and 3 girls can be seated in a row so that they are alternate? [Ans. (b) 72]
(a) 272 (b)
72 (c) 127 (d) 92
(e) None of these
10. (i) In how many ways can
6 Indians and 6 Americans can be seated along a circle so that they are
alternate? [Ans.
(a) 5! ´ 6!]
(a) 5! ´ 6! (b) 5 ´ 6! (c) 6 ´ 6! (d) 12 ´ 6 (e) None of
these
(ii) In how many ways can 4
Indians and 4 Russians can be seated along a circle so that they are alternate? [Ans.
(a) 144]
(a) 144 (b) 1440 (c) 72
(d) 184 (e) None of these
(iii)
A round table conference is to be held between 15 delegates of 15 countries. In
how many ways can they be seated if two particular delegates are always to sit
together? [Ans. (e)
None of these (2! ´ 13!)]
(a) 2! ´ 15! (b) 14! ´ 15! (c) 2! ´ 14! (d) 15! (e) None of these
11.
(i) Find the number of ways in which 9 different beads can be arranged to form
a necklace? [Ans. (b) 8!/2]
(a) 8! (b) 8!/2
(c) 9! (d) 9!/2!
(e) None of these
(ii)
Find the number of ways in which 5 different beads can be arranged to form a
necklace? [Ans. (c) 12]
(a) 12! (b)
5! (c)
12 (d) 5!/2! (e) None of these
12.
(i) There are 10 true-false type questions in an examination. How many
sequences of answers are possible? [Ans. (d) (210 = 1024)]
(a) 512
(b) 100 (c)
1125 (d) 1024 (e)
None of these
(ii)
A servant has to post 5 letters and there are 4 letter-boxes. In how many ways
can he post the letters? [Ans. (c) (45 = 1024)]
(a) 612 (b)
102 (c) 1024
(d) 1126 (e)
None of these
(iii)
A gentleman has 6 friends to invite. In how many ways can he send invitation
cards to them if he has three servants to carry the cards. [Ans. (b) (36
= 729)]
(a) 216 (b) 729
(c) 261 (d) 36
(e) None of these
(iv) In how many ways 3
prizes can be given away to 7 boys when each boy is eligible for any of the
prizes. [Ans. (c) (73 = 343)]
(v)
A telegraph has 5 arms and each arm is capable of 4 distinct positions,
including the position of rest. What is the total number of signals that can be
made? [Ans. (a) (45 - 1= 1023)]
(a) 1023 (b) 1024 (c) 3125 (d)
3124 (e) None of these
(vi)
A letter lock consists of three rings each marked with 10 different letters. In
how many ways it is possible to make an unsuccessful attempt to open the
lock. [Ans. (d) (103 - 1= 999)]
(a) 1000 (b) 59049 (c) 59048 (d)
999 (e) None of these
(vii)
How many numbers greater than 1000 but not greater than 4000 can be formed with
the digits 0,1, 2, 3, 4; repetition of digits being allowed. [Ans. (c) (3 ´ 53 = 375)]
(a) 625 (b) 187 (c)
375 (d) 135 (e) None of these
No comments:
Post a Comment