Quantitative Aptitude - Permutations and Combinations
Exam Duration: 45 Mins Total Questions : 30
(n-1)Pr+ r.(n-1)P(r-1) is equal to
- (a)
nCr
- (b)
\({\underline{|n}\over ^np_r}/(\underline{|r} \ \underline{|n-r})\)
- (c)
nPr
- (d)
None of these
\(\underline{|0}\) is equal to
- (a)
0
- (b)
1
- (c)
\(\infty\)
- (d)
-1
\(0!\times 5!\over 2!\) is equal to
- (a)
60
- (b)
0
- (c)
120
- (d)
None of these
In how many ways the words 'failure' can be arranged so that the consonants occupy only the odd positions?
- (a)
4!
- (b)
(4!)2
- (c)
7!\(\div\)3!
- (d)
None
In how many ways it is possible to write the word 'ZENITH' in a dictionary?
- (a)
6P6
- (b)
6C6
- (c)
6P0
- (d)
None
In how many ways the vowels of the word "ALLAHABAD" will occupy the even places
- (a)
120
- (b)
60
- (c)
30
- (d)
None
The number of numbers lying between 100 and 1,000 can be formed with the digits 1,2,3,4,5,6,7 is
- (a)
210
- (b)
200
- (c)
110
- (d)
None of these
Find the number of divisors of 21,600 excluding 1 and the number itself
- (a)
72
- (b)
142
- (c)
35
- (d)
70
In how many different ways can seven persons stand in a line for a group photograph?
- (a)
7 x 6!
- (b)
6!
- (c)
7
- (d)
24
The total number of sitting arrangements of 7 persons in a row if 2 persons occupy the end seats is
- (a)
5!
- (b)
6!
- (c)
2! x 5!
- (d)
None
Let S be the collection of eight points in the plane with no three points on the straight line. Find the number of triangles that have points of S as vertices
- (a)
52 choices
- (b)
55 choices
- (c)
48 choices
- (d)
56 choices
Six Persons A, B, C, D, E and F to be seated at a circular table. In how many ways can this be done, if A must always have either B or C on his right and B must always have either C or D on his right?
- (a)
3
- (b)
6
- (c)
12
- (d)
18
Which one is true
- (a)
nCr<n Cn-r
- (b)
nCr>n Cn-r
- (c)
nCr=n Cn-r
- (d)
nCr\(\neq\) n Cn-r
The value of 7C1 is
- (a)
1
- (b)
7
- (c)
6
- (d)
8
The value of 8C3 is
- (a)
48
- (b)
65
- (c)
24
- (d)
56
5C1 +5C2 +5C3+5C4+5C5 is equal to
- (a)
30
- (b)
31
- (c)
32
- (d)
25
If (n+ 1)Cr-1 : nc1 : n-1Cr-1 = 8:3:1 then find the value of n
- (a)
14
- (b)
15
- (c)
16
- (d)
17
If 10Pr= 6,04,800 and 10Cr = 120 ; find the value of r,
- (a)
12
- (b)
7
- (c)
8
- (d)
9
Find r if 12C5+212C4 + 12C3= 14Cr
- (a)
5,9
- (b)
4,9
- (c)
5,8
- (d)
4,8
If nC r-1 = 56, nCr= 28 and nCr+1= 8, then r is equal to
- (a)
8
- (b)
6
- (c)
5
- (d)
None of these
A committee is to be formed of 3 persons out of 12. Find the number of ways of forming such Committee
- (a)
220
- (b)
240
- (c)
36
- (d)
4
In forming a committee of 5 out of 5 males and 6 females how many choices you have to make if there are 2 males?
- (a)
150
- (b)
200
- (c)
1
- (d)
461
In forming a committee of 5 out of 5 males and 6 females how many choices you have to make if there is at least one female?
- (a)
150
- (b)
200
- (c)
1
- (d)
461
A person has 8 friends. The number of ways in which he may invite one or more of them to a dinner is
- (a)
250
- (b)
255
- (c)
200
- (d)
None of these
A building contractor needs three helpers and ten men apply. In how many ways can these selections take place?
- (a)
120 ways
- (b)
30 ways
- (c)
150 ways
- (d)
240 ways
A party of 6 is to be formed from 10 men and 7 women as so as to include 3 men and 3 women. In how many ways the partly can be formed if two particular women refuses to join it?
- (a)
4,200
- (b)
600
- (c)
1200
- (d)
None
How many different numbers can be formed by using any three out of five digits 1, 2, 3, 4, 5, no digit being repeated in any number? How many of these will begin with a specified digit?
- (a)
8
- (b)
10
- (c)
12
- (d)
18
A committee is to be formed of 2 teachers and 3 students out of 10 teachers and 20 students. The number of ways in which this can be done is
- (a)
10C2x 20C3
- (b)
9C1x 20C3
- (c)
10C2x 19C3
- (d)
None
The number of ways in which 15 mangoes can be equally divided among 3 students is
- (a)
\(\underline{|15}/ \underline{(5)^4}\)
- (b)
\(\underline{|15}/ \underline{(5)^3}\)
- (c)
\(\underline{|15}/ \underline{(5)^2}\)
- (d)
None
Find the number of ways of selecting 4 letters from the word EXAMINATION.
- (a)
140 ways
- (b)
136 ways
- (c)
152 ways
- (d)
128 ways