Permutations and Combinations Test 9

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Permutations and Combinations Test 9

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Weekly Quiz Competition

Question 1
1 / -0

In a chess tournament each of six players will play every other player exactly once. How many matches will be played during the tournament?

A
36

B
30

C
15

D
12

Solution

First player can play 5 matches with other five players. Second player can play 4 matches with other four players and proceeding this way, the fifth player will play only one match with sixth player.
$$\displaystyle \therefore $$ Total number of matches played = 5 +4 + 3 + 2 + 1 = 15.
Short cut : Number of matches played by n players = $$\displaystyle \frac { n\left( n+1 \right) }{ 2 } $$
Question 2
1 / -0

If the area of the triangle formed by $$ (-2,5), (x,-3) $$ and $$(3,2)$$ is $$14 $$ square units, then $$x=$$ ____.

A
1

B
2

C
-2

D
-1

Solution

Area of triangle having vertices $$(x_1,y_1), (x_2,y_2)$$ and $$(x_3,y_3)$$ is given by
$$ = \dfrac{1}{2} \times [ x_1 (y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) ] $$
$$\therefore \displaystyle Area=\frac{1}{2}\left [ -2\left ( -3-2 \right )+x\left ( 2-5 \right )+3\left ( 5+3 \right ) \right ]$$
$$\displaystyle =\frac{1}{2}\left [ 10-3x+24 \right ]=\frac{34-3x}{2}$$
$$\displaystyle \therefore \frac{34-3x}{2}=14$$ or x = 2
Question 3
1 / -0

ab _ bc _ c _ ba _ c

A
baac

B
aabb

C
caab

D
aaab

Solution

Pattern is abc/bca/cab/abc
Thus letters are written in a cyclic order
Question 4
1 / -0

If CAT is $$48$$, Z is $$52$$ Then what is TEA equal to ?

A
$$48$$

B
$$52$$

C
$$60$$

D
$$50$$

Solution

Alphanumeric coding type
Word Code value Final code
(alphabet series)
CAT C=3,A=1,T=20 24X2=48
3+1+20=24
Z 26 24X2=52
TEA T=20,E=5,A=1 26X2=52
20+5+1=26
Question 5
1 / -0

I think of a decimal number. After I have subtracted 2.9 from it, then multiplied by 3 and then added 0.15, I get 10.5. What is the decimal number?

A
4.5

B
15.66

C
20.10

D
6.35

Solution

Let the decimal number be x.
$$3(x-2.9)+0.15=10.5$$
$$3x-8.7+0.15=10.5$$
$$3x-8.7=10.35$$
$$3x=19.05$$
$$x=6.35$$.
Question 6
1 / -0

I thought of a decimal number. After I had multiplied it by 2, then added 1.5 and then divided by 3, I got 3.5. What was the decimal number?

A
7.1

B
5.6

C
5.8

D
4.5

Solution

Let the decimal number be $$x.$$
$$\dfrac{x\times 2+1.5}{3}=3.5$$
$$2x+1.5=3.5\times 3$$
$$2x+1.5=10.5$$
$$2x=9$$
$$x=\dfrac{9}{2}$$
$$x=4.5$$
Hence, correct option is D.
Question 7
1 / -0

In a class there are 18 boys who are over 160 cm tall If these constitute three-fourths of the boys and the total number of boys is tow-third of the total number of students in the class what is the number of girls in the class?

A
6

B
12

C
18

D
24

Solution

Given in class there are 18 boys who over 160 cm tall and these are three- fourths of total boys
Then total boys in class=$$18\div \frac{3}{4}= 18\times \frac{4}{3}=24$$
And total no of student in class=$$24\times \frac{3}{2}=36$$
Then number of girls=36-24=12
Question 8
1 / -0

Out of 100 students 50 fail in English and 30 in Maths. If 12 students fail in both English and Maths, then the number of students passing both the subjects is

A
26

B
28

C
30

D
32

Solution

Total number of students=100
Number of students fail in English=(50-12)=38
Number of students fail in Maths=(30-12)=18
Number of students fail in both=12
Therefore total failing students=(38+18+12)=68
Pass in both the subjects=(100-68)
=32 students
32 students have passed in both subjects
Question 9
1 / -0

At the end of a business conference, the ten people present all shake hands with each other once. How many handshakes will there be altogether?

A
20

B
45

C
55

D
90

Solution

Total number of handshakes=10×92=45
Question 10
1 / -0

Answer the following set of questions by reading the above pitctograph. Number of TV sets sold in the year 2005 is

A
$$1000$$

B
$$500$$

C
$$50$$

D
$$2000$$

Solution

In the given pictogram the year 2005 depicts only one television figure.
When each television figure represents 500 TV sets, number of TV sets sold in the year 2005 is 500.
So, option B is the correct answer.

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Re-Attempt Weekly Quiz Competition

Permutations and Combinations Test 9

Result

Permutations and Combinations Test 9

Score

-

Rank

-

SHARING IS CARING

Question 1

36

30

15

12

Solution

Question 2

1

2

-2

-1

Solution

Question 3

baac

aabb

caab

aaab

Solution

Question 4

$$48$$

$$52$$

$$60$$

$$50$$

Solution

Question 5

4.5

15.66

20.10

6.35

Solution

Question 6

7.1

5.6

5.8

4.5

Solution

Question 7

6

12

18

24

Solution

Question 8

26

28

30

32

Solution

Question 9

20

45

55

90

Solution

Question 10

$$1000$$

$$500$$

$$50$$

$$2000$$

Solution

User

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