Test paper -3
1) A bar graph is drawn to the scale 1cm= k units, then a bar of length k cm represents
a) 1 unit b) k units c) 2k units d) k² units
2) A bar graph is drawn to the scale of 1 cm = x units. If the length of a bar representing a quantity of 702 units is 3.6cm, then x=
a) 165 b) 175 c) 185 d) 195
3) In figure
bar graph represents sales of two wheelers and four wheelers in a mega city from 2013 to 2016. In which year the difference between the sales of two wheelers and four wheelers is less ?
a) 2013 b) 2014 c) 2015 d) 2016
4) In the figure, the total number of vehicles (two wheelers and four wheelers ) sold in the year 2013 and 2014 is
a) 26100 b) 28500 c) 25100 d) 27500
5) In figure, the maximum difference between sales of two wheelers and that of four wheelers, in any year, in the given period is :
a) 1500 b) 1700 c) 1800 d) 2000
6) In figure, the total number of two wheelers sold in four years is
a) 26000 b) 27000 c) 31000 d) 32000
7) in a bar graph, the height of a bar is 5cm and it represent 40 units . The height of the bar representing 56 units is:
a) 11.2cm b) 5.6cm c) 7cm d) 8cm
8) in a bar graph, length of a bar is 6.4cm and it represent 256 units. The number of units represented by a bar of length 5.3cm is
a) 228 b) 196 c) 212 d) 224
9) In a bar graph, the height of a bar is proportional to the
a) width of the bar b) range of the data c) value of the component d) number of observation in the data.
10) Which one of the following is not the graphical representation of statistical data ?
a) bar graph b)?histogram c) frequency polygon d) cumulative frequency distribution
11) In a frequency distribution, ogives are graphical representation of
a) frequency b) relative frequency c) cumulative frequency d) raw data.
12) A frequency polygon is constructed by plotting frequency of the class interval and the
a) upper limit of the class b) lower limit of the class c) mid value of the class d) any values of the class
13) In a Instagram the area of each rectangle is proportional to
a) the class marks of the corresponding class interval.
b) the class size of the corresponding class interval
c) frequency of the corresponding class interval.
d) cumulative frequency of the corresponding class interval .
14) In the 'less than' type of ogive the cumulative frequency is plotted against
a) the lower limit of the concerned class interval.
b) the upper limit of the concerned class interval .
c) the mid value of the concerned class interval.
d) any value of the concerned class interval.
15) In a histogram the class interval or the groups are taken along
a) y-axis b) x-axis c) both of x-axis and y-axis d) in between x and y-axis .
16) A histogram is a pictorial representation of the grouped data in which class intervals and frequency are represpectively taken along
a) vertical axis and horizontal Axis
b)!vertical access only
c) horizontal Axis only
d) horizontal axis and vertical axis.
17) In a histogram, each class rectangle is constructed with base as
a) frequency b) class intervals c) range d) size of the class
18) Consider the following frequency distribution :
Class interval Frequency
5-10 6
10-15 12
15-25 10
25-45 8
45-75 15
To draw a histogram to represent the above frequency distribution the adjusted frequency for the class 25-44 is
a) 6 b) 5 c) 3 d) 2
19) Figure shows the bar graph of number of boys and number of girls in a school from 2014 to 2017.
In which year the difference between the number of boys and the number of girls was more ?
a) 2014 b) 2015 c) 2016 d) 2017
20) In figure, total number of students in the year 2015 was
a) 1160 b) 1270 c) 1380 d) 1490
21) In figure , the minimum difference between the number of boys and girls in any year in the given period was
a) 90 b) 70 c) 50 d) 30
22) In figure, in which year the number of girls more than the number of boys?
a) 2014 b) 2015 c) 2016 d) 2017
23) In figure , the ratio between the number of student in the year 2016 and 2017 was
a) 107 :145 b) 127 : 145 c) 29 :36 d) 107: 127
CASE STUDY
1) Following bar graph represents the sales of the cold drinks of two companies A and B from 2015 to 2018.
Read the above bar graph and answer the following questions :
i) The year in which the difference between the sells of two companies was highest, was
a) 2018 b) 2015 c) 2016 d) 2017
ii) Total sales of A and B in the year 2016 was
a) 1160000 b) 1270000 c) 1380000 d) 1490000
iii) The minimum difference between the sales of company A and B in any year in the given period was
a) 90000 b) 70000 c) 50000 d) 300000
iv) In which year was the sales of company B more than the sales of company A?
a) 2015 b) 2016 c) 2017 d) 2018
v) The ratio of the total sales in the year 2017 and that in 2018 was
a) 107 :145 b) 29:36 c) 127: 145 d) 107: 127
2) Read the following bar graph and answer the following questions:
i) In the which year was the difference between sales of the scooters and the sales of cars the least ?
a) 2015 b) 2016 c) 2017 d) 2018
ii) Total number of the vehicles (scooters and cars) sold in the year 2015 and 2016 was
a) 26100 b) 28500 c) 25100 d) 27500
iii) The maximum difference between the sales of scooters and cars , in the given period was
a) 1500 b) 1700 c) 1800 d) 2000
iv) The total number of scooters sold in the 4 years was
a) 26000 b) 27000 c)!31000 d) 32000
v) The ratio between the total number of vehicles sold (scooters and cars) in the year 2016 that in the year 2018.
a) 41: 46 b) 69: 91 c) 147 :182 d) 46: 49
3) Population census in India is conducted every 10 years. The first complete census was taken in 1881 and 15th decennial census taken in 2011. The 16th decennial census was to be conducted in 2021 but due to the COVID it will be taken in 2022. The data obtained from the census of a town has been represented by a bar graph shown in figure. It represents the number of persons living in various age groups in the town. Observe the bar graph and answer the following questions:
i) What is the total of persons living in the town in the age-groups 10-15 and 60-65 ?
a) 2000 b) 2200 c) 2100 d) 1900
ii) How many persons are more in the age group 10 to 15 than in the age group 30 to 35 ?
a) 200 b) 250 c) 300 d) 350
iii) What is the total population of the town ?
a) 6700 b) 6400 c) 7700 d) 6600
iv) What is the number of persons in the age-group of 60-65 ?
a) 900 b) 750 c) 850 d) 800
v) What is the age group of exactly 1200 persons living in the town ?
a) 10 to 15 b) 20-25 c) 30-35 d) 40-45
4) A healthcare survey was done by the State Health and Family Welfare Care Board of the State of Punjab. The data is collected by forming age groups i.e.,10 - 15, 20 -25, 30 -35, 40 -45, 50 -55, 60- 65, 70-75. The overall data from a town is the given below in the form of a bar graph. Read the data carefully and answer the question that follow :
i) How many persons are more in the age group 10 - 15 than the age group 30-35?
ii) What is the age group of exactly 1200 persons living in the town?
iii) What is the percentage of the youngest age group persons over those in the oldest age group?
iv) What is the total population of the town ?
EXERCISE -O
1) If A={1,2,3},
B={1,3,5,7},
C={1,3,5,7} then find
(i) A∪B (ii) A∩C (iii) B∩C
2) If A={1,2,3,4,5,6}, B={2,3,4,7,8}
and C= {3,4,5,6} then find
i) A∪B∪C ii) A∩B∩C iii) A∪B∩C
3) If A={1,3,4}, B={2,5,7},C={2,4,6} then prove
a) (A∪B)∪C=A∪(B∪C)
b) (A∩B)∪(A∩C)=A∩(B∪C)
4) Given A={1,2,3}, B={2,4,5},C={1,3}
then Find
i) A∩B ii) A∩C
iii) (A∩B)∪(A∩C) iv) B∪C
v) A∩(B∪C)
Hence, verify
A∩(B∪C)= (A∩B)∪(A∩C)
5) If A, B, C be three subset S when
S={1,2,3,4,5,6,7}
A={1,3,5,6} , B∩C={1,2,6} find
i) (A∪B)∩(A∪C) ii) (A∩B)∪(A∩C)
6) Let A={x|x∈N}, B={x| x= 2n, n∈N}, C={x| x= 2n -1, n∈ N} and D = {x| x is a prime natural number} . find
i) A∩B ii) A∩C iii) A∩ D
iv) B∪C v) B∩C v) B∩D
vi) C∪D vii) C∩D
7) If A={a,b,c,d,e}, B={a,c,e,g} and C={b,c,f,g} verify that
i) (A∪B)∩C=(A∩C)∪(B∩C)
(A∩B)∪C= (A∪C)∩(B∪C)
• Difference of Two Sets:
The difference of two sets A and B is the set A - B which contains only elements that are in A but not in B.
EXERCISE-- P
1) Let A= {13,6,12,15, 18, 21}
B= {4,8,12, 16, 20}
C={2, 4, 6, 8, 10, 12, 14, 16} and
D= {5, 10, 15, 20} Find
i) A - B ii) A - C iii) A - D
iv) B - A v) C - A vi) D - A
vii) B - C viii) B - D
2) Given A= {1, 2, 3, 4} , B={3,4,5}
C={1,4,5} verify
A - (B∪C)= (A -B)∩(A - C)
3) If A={1, 2,3,4} , B={2,3,4,5} , C={1,3,4,5,6,7} find
i) A - B ii) A - C
iii) verify A - (B∩C)= (A-B)∪(A-C)
4) If A={1,2,3,a ,b} and
B={a,b,c,d} find A-B , B-A
• Disjoint Sets:
Two sets A and B are said to be disjoint, if A ∩ B = θ.
• Symmetric Difference of Two Sets:
The symmetric difference of two sets A and B is the set
(A - B)∪(B - A) and is denoted by
A ∆ B. Thus, A ∆ B = (A - B) ∪(B-A)
• Complement of a Set:
The Complement of a set A with respect to the universal set U is the set of all elements of ∪ which are not in A.
It is denoted by A' or Aᶜ or U - A.
Thus A'= { x belongs to U: x ∉ A}
EXERCISE - Q
1) If S={1,2,3,4,5} be the universal set and A={4,5} prove A∪A′ = S
2) If S={0,1,2,3…..8,9} be the universal set A={1,3,5,7}, B{0,1,2,3}
find (a) A′ (b) A′∩B′
(c ) (A∪B)′ ( d) (A-B)′
3) If A={1,2,3},B={2,34,5},
C={3,4,5,6} prove
a) (A∩B)∪(A∩C)=A∩(B∪C)
b) A-(B∪C)=(A-B)∩(A-C)
4) Let the set A and B be given by,
A={1,2,3,4}, B={2,4,6,8,10} and the universal set S={1,2,3,4,5,6,7,7,8,10}
find i) (A∪B)′ ii) (A∩B)ᶜ
5) Let S={1,2,3,4,5} be the universal set and let A={3,4,5} and B={1,4,5}
verify (A∪B)′= A′ ∩B′
6) S={1,2,4,8,16,32} be the universal set and A={1,2,8,32}, B={4,8,32} verify i) (Aᶜ)ᶜ = A
ii) (A∩B)ᶜ=Aᶜ ∪ Bᶜ
iii) (A∪B)ᶜ = Aᶜ ∩ Bᶜ
EXERCISE -- R
1) If S={a,b,c,d,e,f} be the universal set A={a,c,d,f}, (B∩C)={a,b,f}, find i)(A∪B)∩(A∪C) ii) B′∪C′
2) If A={x | -1 ≤ x ≤2} and
B={x| 0 < y ≤4} Find
i) A∪B ii) A∩B
iii) A - B iv) A∪B - (A∩B)
3) Find the set A, B, C if
A∪B = {p,q,r,s}, A∪C={q,r,s,t},
A∩B= {q,r}, A∩C= {q,s}
4) If P={a,b,c,d,e,f} and Q={a,c,e,f}, prove that (P - Q)∪(P∩Q)=P
5) Given A = {1,2,3,4,5} and
B∪C= {3,4,5} find
i) (A∩B)∪(A∩C) ii) (A-B)∩(A-C)
6) Let Z be the set of integers and A={x | x= 6n, n∈ Z},
B={ x |x= 4n, n∈ Z} find A∩B
7) A={x | 2 ≤ x <5}, B={x | 3 < x <7} and iniversal set S={x |0 < x ≤10} verify (A∪B)ᶜ= Aᶜ∩Bᶜ
8) If U={a,b,c,d,e,f} be the universal set and A, B, C are three subset of U, where A={a,c,d} and B∪C={a,d,c,f}, find
i) (A∩B)∪(A∩C) ii) B′∩C′
9) Given X∪Y={1,2,3,4} ,
X ∪ Z={2,3,4,5}, X∩Y={2,3} and
X ∩ Z= {2,4} Find X, Y, Z
10) Let A={1,2,4,5}, B={2,3,5,6} and C={4,5,6,7} verify that
i) A∪(B∩C)=(A∪B)∩(A∪C)
A∩(B∪C)=(A∩B)∪(B∩C)
A∩(B - C)= (A∩B) - (A∩C)
A - (B∪C)=(A - B)∩(A -C)
A - (B∩C)=(A-B)∪(A-C)
A∩(B∆C)=(A∩B)∆(A∩C)
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