Sequences and Series Test 8

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Sequences and Series Test 8

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Weekly Quiz Competition

Question 1
1 / -0

On the eve of Diwali festival, a group of 12 friends greeted every other friend by sending greeting cards. Find the number of cards purchased by the group.

A
156

B
144

C
132

D
72

E
66

Solution

There being 12 friends in the group, each friend must have purchased (12 - 1) i.e. 11 cards for sending greeting to rest of his 11 friends. Thus total number of cards purchased by all the friends together is 12 x 11 i.e. 132. '
Question 2
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 3
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 4
1 / -0

If the area of the triangle formed by the points $$(-2,3), (4,-5)$$ and $$(-3,y)$$ is 10 square units then $$y =$$

A
$$\dfrac{19}{3}$$

B
$$\dfrac{21}{3}$$

C
$$\dfrac{23}{3}$$

D
$$\dfrac{25}{3}$$

Solution

Area of triangle having vertices $$(x_1,y_1), (x_2,y_2)$$ and $$(x_3,y_3)$$ is given by
$$ = \dfrac{1}{2} \times [ x_1 (y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) ] $$
$$\displaystyle \text{Area} =\frac{1}{2}\left [ -2\left ( -5-y \right )+4\left ( y-3 \right )-3\left ( 3+5 \right ) \right ]$$
$$\displaystyle =\frac{1}{2}\left ( 10+2y+4y-12-24 \right )$$
$$\displaystyle =\frac{1}{2}\left ( 6y-26 \right )=3y-13$$
$$\displaystyle 3y-13=10\ \mathrm{sq. unit}$$
$$\displaystyle y=\frac{23}{3}$$
Question 5
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 6
1 / -0

How many numbers of four digits can be formed from the digits 0, 1, 2, 3, and 4?

A
48

B
64

C
96

D
100

Solution

The first box can be filled in four ways, because we cannot put 0 in the first box. The second box can also be filled in four ways, because we cannot put 0. The third box can be filled in three ways and the fourth in two ways. Therefore,
Total numbers = $$\displaystyle 4\times 4\times 3\times 2=96$$
Question 7
1 / -0

A group of 1200 persons consisting of captains and soldiers is travelling in a train. For every 15 soldiers there is one captain. The number of captains in the group is:

A
85

B
80

C
75

D
70

Solution

Out of 16 men, there is a captain.
Number of captains in 1200 men = $$\displaystyle \\ 1200\div 16=75$$.
Question 8
1 / -0

A car driver knows four different routes from Delhi to Amritsar. From Amritsar to Pathankot, he knows three different routes and from Pathankot to Jammu he knows two different routes. How many routes does he know from Delhi to Jammu?

A
4

B
8

C
12

D
24

E
36

Solution

The car driver can reach Amritsar in 4 ways.From each of these four ways, he can reach Pathankot in 3 different ways and so he can reach from Delhi to Pathankot in $$\displaystyle \left( 4\times 3 \right) $$ i.e 12 ways. Again from Pathankot to Jammu, there are 2 ways. Hence he can reach Jammu from Delhi in $$\displaystyle \left( 12\times 2 \right) $$ i.e. in 24 ways.
Question 9
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 10
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

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Re-Attempt Weekly Quiz Competition

Sequences and Series Test 8

Result

Sequences and Series Test 8

Score

-

Rank

-

SHARING IS CARING

Question 1

156

144

132

72

66

Solution

Question 2

6

12

18

24

Solution

Question 3

26

28

30

32

Solution

Question 4

$$\dfrac{19}{3}$$

$$\dfrac{21}{3}$$

$$\dfrac{23}{3}$$

$$\dfrac{25}{3}$$

Solution

Question 5

20

45

55

90

Solution

Question 6

48

64

96

100

Solution

Question 7

85

80

75

70

Solution

Question 8

4

8

12

24

36

Solution

Question 9

36

30

15

12

Solution

Question 10

1

2

-2

-1

Solution

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Question Analysis

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Rank

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