Mathematics - Permutations and Combinations
Exam Duration: 45 Mins Total Questions : 30
A question paper is divided into two parts A and B. Each part contains 5 questions. The number of ways in which candidate can answer 6 questions selecting at least two questions from each part is
- (a)
50
- (b)
100
- (c)
200
- (d)
NONE OF THESE
n-1Pr.+ rn-1Pr-1, equals
- (a)
nPr
- (b)
nCr
- (c)
n-1Pr+1
- (d)
NONE OF THESE
There are 10 true-false questions in an examination. Then these questions can be answered in
- (a)
20 ways
- (b)
100 ways
- (c)
512 ways
- (d)
1024 ways
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
In a class of 10 students, there are 3 girls. The number of ways they can be arranged in a row, so that no 2 girls are consecutive is k.8!, where k is equal to
- (a)
12
- (b)
24
- (c)
36
- (d)
42
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
4 points out of 8 points in a plane are collinear. Number of different quadrilaterals that can be formed by joining them is
- (a)
56
- (b)
53
- (c)
76
- (d)
60
Number of words of 4 letters that can be formed with the letters of the word IITJEE is
- (a)
42
- (b)
82
- (c)
102
- (d)
142
The total number of ways in which 9 different toys can be distributed among three different children, so that the youngest gets 4, the middle gets 3 and the oldest gets 2, is
- (a)
137
- (b)
236
- (c)
1240
- (d)
1260
The sides AB, BC and CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles that can be constructed using these interior points as vertices, is
- (a)
205
- (b)
208
- (c)
220
- (d)
380
The total number of 5 digit telephone numbers that can be composed with distinct digits, is
- (a)
10P2
- (b)
10P5
- (c)
10C5
- (d)
none of these
The number of positive integers with the property that they can be expressed as the sum of the cubes of 2 positive integers in two different ways is
- (a)
1
- (b)
100
- (c)
infinite
- (d)
0
A is a set containing n elements. A subset P1 is chosen and A is reconstructed by replacing the elements of P1. The same process is repeated for subsets P1, P2, ...., pm with m > 1. The number of ways of choosing P1, P2,..., Pm, so that \({ P }_{ 1 }\cup { P }_{ 2 }\cup ....\cup { P }_{ m }=A\) is
- (a)
(2m - 1)mn
- (b)
(2n - 1)m
- (c)
m + nCm
- (d)
none of these
The number of non-negative integral solutions of x1 + x2 + x3 + 4x4 = 20 is
- (a)
530
- (b)
532
- (c)
534
- (d)
536
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
The number of ways in which 30 coins of one rupee each be given to six persons, so that none of them receives less than 4 rupees is
- (a)
231
- (b)
462
- (c)
693
- (d)
924
If \(\alpha ={x}_{1}{x}_{2}{x}_{3}\) and \(\beta = {y}_{1}{y}_{2}{y}_{3 }\) be two three digits numbers, the number of pairs of \(\alpha\) and \(\beta\) can be formed so that \(\alpha\) can be subtracted from \(\beta\) without borrowing is
- (a)
2!10!10!
- (b)
(45)(55)2
- (c)
32 .53 .112
- (d)
136125
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 rank of the word 'SUCCESS' in the dictionary is
- (a)
328
- (b)
329
- (c)
330
- (d)
331
Let \(f(n)\) denotes the number of different ways the positive integer n can be expressed as the sum of 1's and 2's. For example
\(f(4)=5\)
ie, 4=1+1+1+1
=1+1+2
=1+2+1
=2+1+1
=2+2
The value of \(f(6)\) is
- (a)
10
- (b)
13
- (c)
16
- (d)
19
Different words are being formed by arranging the letters of the word 'ARRANGE'. All the words obtained are written in the form of a dictionary.
The number of words in which at least one vowel is in between two consonant is
- (a)
18
- (b)
36
- (c)
624
- (d)
836
i) How many numbers are there between 99 and 1000 having 7 in the units place?
(ii) How many numbers are there between 99 and 1000 having at least one of their digits is 7?
- (a)
90,253
- (b)
90,258
- (c)
90,252
- (d)
90,352
Find the number of arrangements of the letters of the world INDEPENDENCE. In how many of these arrangements, do the word with P?
- (a)
1663200,138600
- (b)
163000,135600
- (c)
160000,138650
- (d)
None of these
How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that odd digits occupy even positions?
- (a)
16
- (b)
60
- (c)
60
- (d)
180
In how many ways can 5 children be arranged in a line such that (i) two particular children are always together (ii) two particular children are never together?
- (a)
47,73
- (b)
48,72
- (c)
48,72
- (d)
49,72
The straight lines l1,l2 and l3 are parellel and lie in the same plane. a total numbers of m points on l3 .The maximum number of triangle formed with verticals at these points are
- (a)
(m+n+k)C3
- (b)
(m+n+k)C3-mC3-nC3-kC3
- (c)
mC3+nC3+kC3
- (d)
mC3XnC3XkC3
A crocodile is known to have not more than68 teeth. The total number of crocodiles with different set of teeth, are
- (a)
68
- (b)
68!
- (c)
1617
- (d)
6868
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 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
In how many ways football team of 11 players be selected from 16 players? How many of them will
(i) include 2 particular players?
(ii) exclude 2 particular players?
- (a)
16C9,14C11
- (b)
14C9,14C11
- (c)
14C9,16C11
- (d)
None of these
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