JEE Main Mathematics - Permutations and Combinations
Exam Duration: 60 Mins Total Questions : 30
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
The number of ways in which five identiocal balls can be distributed among ten identical boxes such that no box contains more than one ball is
- (a)
10!
- (b)
\(10!\over (5!)\)
- (c)
\(10!\over (5!)^2\)
- (d)
NONE OF THESE
A polygon has 44 diagnols; then the number of its sides is
- (a)
11
- (b)
7
- (c)
8
- (d)
NONE OF THESE
Five balls of different colours are to be placed in 3 boxes of different sizes. Each box can hold all the five balls. The number of different ways of placing these balls in these boxes so that no box is empty are
- (a)
90
- (b)
15
- (c)
150
- (d)
NONE OF THESE
The number of ways of diving equally a pack of 52 cards amongst 4 players is
- (a)
\(52!\over13!\)
- (b)
\(52!\over (13!)^2\)
- (c)
\(52!\over (13!)^3\)
- (d)
\(52!\over (13!)^4\)
The number of ways in which 20 rupees can be distributed amongst 5 persons in such a way that no person gets less than 3 rupees :
- (a)
26
- (b)
63
- (c)
126
- (d)
256
In how many ways the letters of the word 'ARRANGE' can be arranged without altering the relative positions of vowels and consonants?
- (a)
36
- (b)
26
- (c)
62
- (d)
None of the above
In an examination of 9 papers, a candidate has to pass in more papers, then the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful, is
- (a)
255
- (b)
256
- (c)
193
- (d)
319
In a steamer, there are stalls for 12 animals and there are horses, cows and calves (not less than 12 each) ready to be shipped. In how many ways, can the ship load be made?
- (a)
312-1
- (b)
312
- (c)
(12)3-1
- (d)
(12)3
If \({^nP_{r-1}\over{a}}={{^nP_r}\over b}={{^nP_{r-1}}\over c }\), then
- (a)
b2=a(b+c)
- (b)
c2=a(b+c)
- (c)
ab=a2+bc
- (d)
bc=a3+b2
Let X={1,2,3,4,5}. The number of different ordered pairs (Y,Z) that can be formed such that \(Y\subseteq X, \ Z\subseteq X\) and \(Y\cap Z\) is empty, is
- (a)
52
- (b)
35
- (c)
25
- (d)
53
The number of permutations of the letters a, b, c, d such that b does not follow a, and c does not follow band d does not follow c, is
- (a)
9
- (b)
11
- (c)
13
- (d)
14
The number of triangles that can be formed joining the angular points of decagon, is
- (a)
30
- (b)
45
- (c)
90
- (d)
120
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 sum of the digits in the unit's place of all the numbers formed with the digits 5, 6,7,8 when taken all at a time, is
- (a)
104
- (b)
126
- (c)
127
- (d)
156
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
We are required to form different words with the help of the letters of the word INTEGER. Let m1 be the number of words in which 1and N are never together and m2 be the number of words which beginning with I and end with R, then m1/m2 is given by
- (a)
42
- (b)
30
- (c)
6
- (d)
1/30
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
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 class tournament when the participants were to plat one game with another, two class players fell ill, having played 3 games each. If the total number of games played is 84, the number of participants at the beginning was
- (a)
15
- (b)
30
- (c)
6C2
- (d)
48
Total number of ways of giving at least one coin out of three 25 paise and two 50 paise coins to a beggar is
- (a)
32
- (b)
12
- (c)
11
- (d)
12P1 -1
Let N denote the greatest number of points in which m straight lines and n circles intersect, then
- (a)
m | (N - mC2 - nP2)
- (b)
n | ( N - mC2 - nP2)
- (c)
N - mC2 - nP2 is an ever integer
- (d)
N - mC2 - nP2 is an odd integer
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 \(r!\Pi \left( \overset { { n }_{ 1 } }{ \underset { \lambda =0 }{ \Sigma } } \frac { { x }^{ \lambda } }{ \lambda ! } \right) \)
- (a)
2214
- (b)
1422
- (c)
5424
- (d)
2454
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 consonants appear in alphabatic order is
- (a)
42
- (b)
40
- (c)
420
- (d)
280
If eleven members of a committee sit at a round table so that the President and Secretary always sit together, then the numbers of arrangements is
- (a)
10! X 2
- (b)
10!
- (c)
9! X2
- (d)
11! X2!
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
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 15 members of a council sit along a circular table, when the Secretary is to sit on one side of the Chairman and the Deputy Secretary on the other side?
- (a)
2X12!
- (b)
24
- (c)
2X15!
- (d)
None of these
The number of ways in which the letters x1,x2...,x10x,y1,y2,...y15 can be arranged in a line such that the suffixes of x and those of y are in ascending order magnitude is
- (a)
25C1010!15!
- (b)
25C15
- (c)
25C10
- (d)
both (b) and (c)