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Permutation and Combination Questions

NA
SHSTTON
31
Solv. Corr.
43
Solv. In. Corr.
74
Attempted
0 M:0 S
Avg. Time

81 / 100

Choose the correct option.

105 shake hands were exchanged in a meeting, each person shakes hands with every other person only once.How many people were present in the meeting?


A14

B8

C56

D15

Answer: Option D

Explanation:

Let n be the number of persons in the party. Number of hands shake = 105; Total number of hands shake is given by nC2.

Now, according to the question,

nC2 = 105;
=> n!/[2!*(n-2)!] = 105;
=> n*(n-1)/2 = 105;
=> n2-n = 210;
=> n2-n-210 = 0;
=> n = 15, -14 (Negative Value);

So, n = 15 i.e. number of persons in the party = 15.

Workspace

NA
SHSTTON
33
Solv. Corr.
30
Solv. In. Corr.
63
Attempted
0 M:0 S
Avg. Time

82 / 100

Choose the correct option.

A password consists of two letters of the alphabet followed by three digits chosen from 0 to 9. Repeats are allowed. How many different possible passwords are there?


A492,804

B650,000

C676,000

D1,757,600

Answer: Option C

Explanation:

For the first Letter you have 26 possible letters
For the second letter you have 26 possible letters
For the first number you have 10 possible numbers

For the second number you have 10 possible numbers
For the third number you have 10 possible numbers
Times all of the possibilities together to get:

26*26*10*10*10 = 676000
Which means their are 676,000 possible passwords

Workspace

NA
SHSTTON
8
Solv. Corr.
4
Solv. In. Corr.
12
Attempted
0 M:0 S
Avg. Time

83 / 100

Choose the correct option.

There are 20 persons sitting in a circle. In that there are 18 men and 2 sisters. How many arrangements are possible in which the two sisters are always separated by a man?


A18! * 2

B17!

C17! * 2

D12!

Answer: Option A

Explanation:

Here 2 sisters can be assumed 1 sister,
In this way there are total of 19 member,

Formula for circular seating arrangement: (n-1)!

So, (19-1)! = 18!

2 sisters can sit in 2 ways.
Hence answer is 18! *2

Workspace

NA
SHSTTON
30
Solv. Corr.
11
Solv. In. Corr.
41
Attempted
0 M:0 S
Avg. Time

84 / 100

Choose the correct option.

In how many possible ways can you write 1800 as a product of 3 positive integers a,b and c.


A340

B360

C260

D45

Answer: Option B

Explanation:

Formula (n+r-1) C (r-1)
where n=power
r=no of integers
1800=3^2*5^2*2^3
hence (2+3-1) C (3-1)=6
(2+3-1) C (3-1)=6
(3+3-1) C (3-1)=10
=> 6*6*10=360

Workspace

NA
SHSTTON
4
Solv. Corr.
11
Solv. In. Corr.
15
Attempted
0 M:0 S
Avg. Time

85 / 100

Choose the correct option.

Two students have to be chosen as montiors from a class of 36 students. In how many different ways can this be done?


A72

B630

C1260

D71

E71.5

Answer: Option B

Explanation:

The way = 36C2
=> 36*35/2*1 = 630

Workspace

NA
SHSTTON
3
Solv. Corr.
8
Solv. In. Corr.
11
Attempted
0 M:0 S
Avg. Time

86 / 100

Choose the correct option.

There are 10 person among whom two are brother. The total number of ways in which these persons can be seated around a round table so that exactly one person sit between the brothers , is equal to:


A7!*2*8

B14

C7!*8

D7!*2!

Answer: Option A

Explanation:

Two brothers can be arranged = 2 ways.
The way in the middle of 2 brothers, any of 8 other person can sit = 8 ways.
The rest 7 people can be arranged in 7! Ways.
So,Total = 7!*2*8

Workspace

NA
SHSTTON
6
Solv. Corr.
16
Solv. In. Corr.
22
Attempted
0 M:0 S
Avg. Time

87 / 100

Choose the correct option.

In a staircase , there are 10 steps . A child is attempting to climb the staircase. Each time, she can either make 1 or 2 steps. In how many different ways can she climb the staircase?


A21

B26

C10

DNone of these

Answer: Option D

Explanation:

Child can clim in a+2b = 10 ways (a is 1 step and b is taking 2 steps)
So, if she is making 0 1steps den she has take 5 2steps for reaching 10th step den combination is 5c5 =1
Again for (2,4) : 6c4 =15
And for (4,3) : 7c3=35
For (6,2) : 8c2= 28
For (8,1) : 9c1 =9
For (10,0) 10c10=1
So total 1+15+35+28+1 = 89

Workspace

NA
SHSTTON
3
Solv. Corr.
10
Solv. In. Corr.
13
Attempted
0 M:0 S
Avg. Time

88 / 100

Choose the correct option.

What is the maximum value of n such that 146! is perfect divisible by 5n ?


A12

B32

C35

D43

Answer: Option C

Explanation:

= [146/5] + [146/52] + [146/53];
= 29+5+1.
= 35.

Workspace

NA
SHSTTON
5
Solv. Corr.
10
Solv. In. Corr.
15
Attempted
0 M:0 S
Avg. Time

89 / 100

Choose the correct option.

There is a 3*3 matrix . you have 2 colors red and blue. In how many ways you can fill the colors in the boxes so that if u rotate the matrix by 180 degree we get the same matrix ?


A31 ways

B32 ways

C41 ways

DNone of these

Answer: Option B

Explanation:

for 3*3 matrix if we rotate 180 degrees , there are 32 ways

Workspace

NA
SHSTTON
14
Solv. Corr.
26
Solv. In. Corr.
40
Attempted
0 M:0 S
Avg. Time

90 / 100

Choose the correct option.

Find the no. of ways in which 4 particular persons a,b,c,d and 6 more persons can stand in a queue so that A always stand before B. B always stand before C, And C always stand before D.


A6!

B7!

C1006*6!

D10046!

Answer: Option B

Explanation:

a,b,c,d are grouped ie consider them as one and remaining as 6.
Total 6+1 = 7! Ways

Workspace

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