JEE Mathematics - Permutation and Combinations Chapter Sample Question Paper With Answer Key
Exam Duration: 60 Mins Total Questions : 50
The total number of ways in which six '+' and four '-' signs can be arranged in a line such that no two '-' signs are together, is
- (a)
35
- (b)
15
- (c)
30
- (d)
NONE OF THESE
There are five letters and five addressed envelopes, then the number of ways in which no letter is placed in correct envelop, is
- (a)
9
- (b)
33
- (c)
44
- (d)
119
Out of n objects p are alike of one kind, q are alike of another kind and r are alike of a third kind and the rest all are different; then number of permutations when all the n objects are taken at a time is
- (a)
n! p! q! r!
- (b)
\(n!\over p! q! r!\)
- (c)
\(p! q! r!\over n!\)
- (d)
NONE OF THESE
Out of 10 white, 9 black and 7 red balls, the number or ways in which selection of one or more balls can be made is
- (a)
881
- (b)
891
- (c)
879
- (d)
892
Given five different green dyes, four diferent blue dyes and three different red dyes, the number of combinations that can be chosen, taking at least one green and one blue dye, are
- (a)
31
- (b)
15
- (c)
8
- (d)
3720
Number of divisors of the form \(4n+2(n\ge 0)\) of the integer 240, is
- (a)
4
- (b)
8
- (c)
10
- (d)
3
The number of ways in which 6 men and 6 women can be seated around a round table, so that no two women sit together is
- (a)
6!6!
- (b)
6!5!
- (c)
5!5!
- (d)
NONE OF THESE
There are 10 lamps in a hall each one of which can be switched on independently. The number of ways in which the hall can be illuminated, is
- (a)
103
- (b)
1023
- (c)
210
- (d)
10!
A round table conference is to be held among 20 delegates of 20 countries. The number of ways they can be seated, if two particular delegates are never sit together, is
- (a)
17.18!
- (b)
18.19!
- (c)
\(20!\over 2\)
- (d)
19!.2
A group of 6 is chosen from 10 men and 7 women. The number of ways this can be done, if two particular women refuse to serve on the same group, is
- (a)
8000
- (b)
7800
- (c)
7600
- (d)
7200
Let Tn be the number of all possible triangles formed by joining vertices of n-sided regular polygon. If Tn+1-Tn=10, then the value of n is
- (a)
7
- (b)
5
- (c)
10
- (d)
8
Statement I :The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty, is 9C3.
Statement II: The number of ways of choosing any 3 places from 9 different places is 9C3
- (a)
Statement I is true, Statement II is true; Statement II is the correct explanation for statement I.
- (b)
Statement I is true, statement II is true; Statement II is not the correct explanation for statement I.
- (c)
Statement I is true, statement II is false.
- (d)
Statement I is false, statement II is true.
How many different words can be formed by jumbling the letters in the word 'MISSiSSIPPI' in which no two S are adjacent?
- (a)
7.6C4.8C4
- (b)
8.6C4.7C4
- (c)
6.7.8C4
- (d)
6.8.7C4
How many ways are there, to arrange the letters in the word 'GARDEN' with the vowels in alphabetical order?
- (a)
360
- (b)
240
- (c)
120
- (d)
480
The lock of safe consists of five discs each of which features the digits 0, 1, 2, ...., 9. The safe can be opened by dialing a special combination of the digits. The number of days sufficient enough to open the safe, if the workday lasts 13 hands 5 s are needed to dial one combination of digits is
- (a)
9
- (b)
10
- (c)
11
- (d)
12
The maximum number of points intersection of 8 straight lines, is
- (a)
8
- (b)
16
- (c)
28
- (d)
56
The number of ways in which 7 persons can be seated at a round table, if two particular persons are not to sit together, is
- (a)
120
- (b)
480
- (c)
600
- (d)
720
Six identical coins are arranged in a row. The total number of ways in which the number of heads is equal to the number of tails, is
- (a)
9
- (b)
20
- (c)
40
- (d)
120
The total number of numbers that can be formed by using all the digits 1, 2, 3, 4, 3, 2, 1, so that the odd digits always occupy the odd places, is
- (a)
3
- (b)
6
- (c)
9
- (d)
18
Total number of words formed by using 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
- (a)
60
- (b)
120
- (c)
720
- (d)
none of the above
The total number of 3 digit even numbers that can be composed from the digits 1,2,3,....,9 when the repetition of digits is not allowed, is
- (a)
224
- (b)
280
- (c)
324
- (d)
405
Two straight lines intersect at a point O. Points A1, A2,..., An are taken on one line and points B1, B2,..., Bn on the other. If the point O. is not to be used, the number of triangles that can be drawn using these points as vertices is
- (a)
n ( n -1 )
- (b)
n ( n - 1 )2
- (c)
n2 ( n - 1 )
- (d)
n2 ( n - 1 )2
There are n points in a plane of which no three are in a straight line except 'm' which are all in a straight line. Then the number of different quadrilaterals, that can be formed with the given points as vertices. is
- (a)
nC4 - mC3n-m+1C1-mC4
- (b)
nC4 - mC3n-mC1+mC4
- (c)
nC4 - mC3n-mC1-mC4
- (d)
nC4 - nC3.mC1
The number of numbers less than 1000 that can be formed out of the digits, 0, 1, 2, 4 and 5, no digit being repeated is
- (a)
69
- (b)
68
- (c)
130
- (d)
none of these
If the ( n + 1 ) numbers a, b, c, d, ..., be all different and each of them a prime number, then the number of different factors (other than 1) of am, b, c, d, ..., is
- (a)
m - 2n
- (b)
( m + 1 )2n
- (c)
( m + 1 )2n - 1
- (d)
none of these
The number of six digit numbers that can be formed from the digits 1, 2, 3, 4, 5, 6 and 7, so that digits do not repeat and the terminal digits are even is
- (a)
144
- (b)
72
- (c)
288
- (d)
720
In the next world cup of cricket, there will be 12 teams, divided equally in two groups. Teams of each group will play a match against each other. From each group, 3 top teams will qualify for the next round. In this round, each team will play against others once. Four top teams of this round will qualify for the semifinal round when each team will play against the others once. Two top teams of this round will go to the final round, where they will play the best of t~ree matches. The minimum number of matches in the next world cup will be
- (a)
54
- (b)
53
- (c)
52
- (d)
none of these
If 33 ! is divisible by 2n, then the maximum value of n is equal to
- (a)
33
- (b)
32
- (c)
31
- (d)
30
The number of zeros at the end of 100 ! is
- (a)
54
- (b)
58
- (c)
24
- (d)
47
The number of ways in which a mixed double game can be arranged from amongst 9 married couples. If no husband and wife play in the same game is
- (a)
756
- (b)
1512
- (c)
3024
- (d)
none of these
In a college examination, a candidate is required to answer 6 out of 10 questions which are divided into two sections each containing 5 questions further the candidate is not permitted to attempt more than 4 questions from either of the section. The number of ways in which he can make up a choice of 6 questions is
- (a)
200
- (b)
150
- (c)
100
- (d)
50
If the number of arrangements of ( n - 1 ) things taken from n different things k times the number of arrangements of ( n - 1 ) things taken from n things in which two things are identical, then the value of k is
- (a)
1/2
- (b)
2
- (c)
4
- (d)
none of these
Suppose a lot of n objects contains n 1 objects of one kind, n 2 objects of second kind, n3 objects of third kind,....., nk objects of kth kind. Such that n1 + n2 + n3 + ... + nk = n, then the number of possible arrangements/permutations of r objects out of this lot is the coefficient of xr in the expansion of \(r!\Pi \left( \overset { { n }_{ 1 } }{ \underset { \lambda =0 }{ \Sigma } } \frac { { x }^{ \lambda } }{ \lambda ! } \right) \)
The number of permutations of the letters of the word INDIA taken three at a time must be
- (a)
27
- (b)
30
- (c)
33
- (d)
57
Suppose a lot of n objects contains n 1 objects of one kind, n 2 objects of second kind, n3 objects of third kind,....., n k objects of kth kind. Such that n1 + n2 + n3 + ... + n k = n, then the number of possible arrangements/permutations of r objects out of this lot is the coefficient of x r in the expansion of \(r!\Pi \left( \overset { { n }_{ 1 } }{ \underset { \lambda =0 }{ \Sigma } } \frac { { x }^{ \lambda } }{ \lambda ! } \right) \)
If n1 + n2 + n3 + ... + nk = r, then number of permutations must be
- (a)
nCr
- (b)
nPr
- (c)
( k + r )!
- (d)
\(\frac {r!}{{n_1}!{n_2}!...{n_k}!}\)
Different words are being formed by arranging the letters of the word "SUCCESS". All the words obtained by written in the form of a dictionary.
The number of words in which the relative positions of vowels and consonants unaltered is
- (a)
20
- (b)
60
- (c)
180
- (d)
540
Compute \(\cfrac { 7! }{ 5! } \)
- (a)
42
- (b)
40
- (c)
43
- (d)
44
find the value of n such that \({ { n }_{ P } }_{ 5 }=42\quad { { n }_{ P } }_{ 3, }n>4\)
- (a)
10
- (b)
15
- (c)
12
- (d)
20
All the letters of the world 'EAMCOT' are arranged in different possible ways. The number of such arrangements in which not two vowels are adjacent to each other is
- (a)
360
- (b)
144
- (c)
72
- (d)
54
The sum of all the five digit numbers formed with the 1,2,3,4,5 taken all at time is
- (a)
15(5!)
- (b)
3999960
- (c)
3990000
- (d)
none of these
The sum of 5 digit numbers in which only odd digits occur without any repetition is
- (a)
2777775
- (b)
555550
- (c)
1111100
- (d)
6666600
If\(\cfrac { { { n }_{ P } }_{ r-1 } }{ a } =\cfrac { { { n }_{ P } }_{ r } }{ b } =\cfrac { { { n }_{ P } }_{ r+1 } }{ c } ,\)then
- (a)
b2=a(b+c)
- (b)
\(\cfrac { 1 }{ a } +\cfrac { 1 }{ b } +\cfrac { 1 }{ c } =1\)
- (c)
a2=c(a+b)
- (d)
abc=1
Find the number of arrangements of the letters of the word INDEPENDENCE when words begin with I and end in P.
- (a)
12400
- (b)
12420
- (c)
12600
- (d)
12620
The number of permutations letters a,b,c.d,e,f,g so that neither the pattern beg not nor cad appears is
- (a)
\(\cfrac { 7! }{ 3!3! } \)
- (b)
\(\cfrac { 7! }{ 2!3!3! } \)
- (c)
4806
- (d)
None of these
If n-1C3+n-1C4>nC3 then
- (a)
n>5
- (b)
n>6
- (c)
n>7
- (d)
None of these
There were two women participants in a chess tournament. The number of games the men played between themselves exceeded by 52 the number of games they played with women. If each player played one game with each other, the number of men in the tournament ,was
- (a)
10
- (b)
11
- (c)
12
- (d)
13
For a game in which two patterns play against two other patterns,six persons are available. If every possible pair must play with every other possible pair, then the total number of games played is
- (a)
90
- (b)
45
- (c)
30
- (d)
60
The number of ways in which 20 rupees can be distributed among 5 people such that each person gets atleast Rs.3 is
- (a)
26
- (b)
63
- (c)
125
- (d)
126
The number of arrangements that can be made taking 4 letters,at a time out of the letters of the word PASSORT is
- (a)
606
- (b)
626
- (c)
666
- (d)
686
If m points of one straight line are joined to n points on another straight. The number of points of intersection of the line segment thus formed is
- (a)
\(\cfrac { { { m }_{ C } }_{ 2 }.{ { n }_{ C } }_{ 2 } }{ 4 } \)
- (b)
\(\cfrac { mn\left( m-1 \right) \left( n-1 \right) }{ 4 } \)
- (c)
\(\cfrac { { { m }_{ C } }_{ 2 }.{ { n }_{ C } }_{ 2 } }{ 2 } \)
- (d)
mC2+nC2
12 persons are to be arranged to a round table. If two particular persons among them are not to be side by side, the total number of arrangements is A.9!. Find A.
- (a)
70
- (b)
80
- (c)
90
- (d)
100