Exercise 19.1
Question 1
1.Take 1cm on y-axis = 5units
2.Take fruits on x -axis
3. Construct the rectangles corresponding to given data
The required histogram is shown below figure
(diagram should be added)
Question 2
(diagram should be added)
Question 3
(diagram should be added)
Question 4
(i) Expendiature of family on different items
(ii) Food
(iii) Clothing
(iv) True
Question 5
(i) Double bar graph representing the no. of boys and girls using different modes of transport for going to school
(ii) School bus
(iii) Bicycle
(v) walking
Question 6
(diagram should be added)
Question 7
(diagram should be added)
Question 8
(diagram should be added)
Question 9
(diagram should be added)
(i) 80 - 90 group
(ii) 26
(iii) 14
Question 10
(diagram should be added)
Question 11
(diagram should be added)
Question 12
(i) 18
(ii) 450-475
(iii) 34
(iv) 54
(v) 28
Question 13
(i) 4-5 hrs
(ii) 34
(iii) 14
(iv) 30
Question 14
(i) $10-15,15-20,20-25,25-30,30-35,35-40$
(ii) 5
(iii) 10-15
(iv) 15-20
Exercise 19.2
Question 1
To represent given data in pie chart , we have to find angles
Total animals = 40+ 10+30+ 15+25= 120
Animals no.of animals Angle
Deer 40 $\frac{40}{120} \times 360=120^{\circ}$
Tiger 10 $\frac{10}{120} \times 360=30^{\circ}$
Elephant 30 $\frac{30}{120} \times 360=90^{\circ}$
Reptiles 25 $\frac{25}{120} \times 360=75^{\circ}$
Giraffe 15 $\frac{15}{120} \times 360=45^{\circ}$
(Diagram should be added)
Question 2
To represent given data in pie chat we have to find angles
Total expenditure = 12500+5000+7500+10000+5000+10000=50,000
Item Expenditure Angle
1.Food 12500 $\frac{12500}{50000} \times 360=90$
2.House rent 5000 $\frac{5000}{50000} \times 360=36^{\circ}$
3.Education 7500 $\frac{7500}{50000} \times 360=54^{\circ}$
4.Sovings 10000 $\frac{10000}{50000} \times 360=72^{\circ}$
5.Health 5000 $\frac{5000}{50000} \times 360=36^{\circ}$
6. Others 10000 $\frac{10000}{50000} \times 360=72^{\circ}$
(Diagram should be added)
Question 3
To represent given data to pie chart we have to find angles
Total = $25+20+20+10+15+10=100 \%$
Item Expenditure Angle
Paper cost- 25% $\frac{25}{100} \times 360=90^{\circ}$
Printing cost 20% $\frac{20}{100} \times 360=72^{\circ}$
Binding 20% $\frac{20}{100} \times 360=72^{\circ}$
Royality 10% $\frac{10}{100} \times 360=36^{\circ}$
Transpotation cost 15% $\frac{15}{100} \times 360=54^{\circ}$
Promotion cost 10% $\frac{10}{100} \times 360=36^{\circ}$
(Diagram should be added)
Question 4
To represnt above data in pie chart we have to find angles
Total no. of students = 400+300+500+250+350=1800
Stream No. of Students Angle
Science 400 $\frac{400}{1800} \times 360^{\circ}=80^{\circ}$
Arts 300 $\frac{300}{1800} \times 360=60^{\circ}$
Commerce 500 $\frac{500}{1800} \times 360^{\circ}=100^{\circ}$
Law 250 $\frac{250}{1800} \times 360^{\circ}=50^{\circ}$
Managment 350 $\frac{350}{1800} \times 360^{\circ}=70^{\circ}$
(Diagram should be added)
Question 5
(i) $\frac{90^{\circ}}{360} \times 100=\frac{1}{4} \times 100=25$ %
(ii) Hockey - $75^{\circ}$
Tennis - 50'
Dictereu $=75-50=25^{\circ}$
$\frac{25^{\circ}}{360} \times 100=6.94$ %
(iii) Badminton -- 60
$\frac{60^{\circ}}{360} \times 100=16.67 t .$
Total Amount $=18000000$
Amount spend on Badminton $=\frac{16.67}{100} \times 18000000$
=30,00000
(iv)Hockey--- $75^{\circ}$
Cricket ---90'
h+ c= 75+90 = 165'
Both H and c = $\frac{165^{\circ}}{360} \times 100$ $=45.83 \%$.
Total amount 2,40,00,000
Amount spent on both hockey and cricket = $\frac{45.83}{100} \times 2,40,00,000$
= 11,000,000
Question 6
(i) Angle of class viii = $85^{\circ}$
% of class viii = $\frac{85}{360} \times 100=28.611 \%$
No. of students enrolled in class viii =$=\frac{28.61}{100} \times 1440$
$=340$
(ii) Angle of class ix = $75^{\circ}$
Angle of class x = $50^{\circ}$
Difference = $75-50=25^{\circ}$
% of Difference = $\frac{25}{360} \times 100=6.94$%
No. of Students enrolled more in class ix Then class x
is = $\frac{6.94}{100} \times 1440=100$
(iii) Angle of class viii = $85^{\circ}$
Angle of class vii = $70^{\circ}$
Sum = $85+70=155^{\circ}$
% of sum = $\frac{155}{360} \times 100=43.05 \%$
Total Students in class viii and class vii $=\frac{43.05}{100} \times 1440$
$=620$
(iv) Angle of class vi = $80^{\circ}$
Angle of class x = $50^{\circ}$
% of class vi = $\frac{80}{360} \times 100=22.22$%
% of class x = $\frac{50}{360} \times 100=13.88 \%$
No. of Students enrolled in class vi = $\frac{22.22}{100} \times 1440$
= 320
No. of Students enrolled in class x = $\frac{13.88}{100} \times 1440$
= 200
Ratio of students enrolled in Class vi to Class X = 320: 200
= 8:5
Exercise 19.3
Question 1
(i) A, A, A, B, C, D
(ii)W , R, B, G, Y
Question 2
(i) Total No. of Outcomes = $\{1,2,3,4,5,6\}=6$
Favorable Outcomes = $\{2,4,6\}=3$
Probability $=\frac{\text { no.of forverable outcomes }}{\text { Total no.of outcomes }}$
$\begin{aligned} & \frac{3}{6} \\=& 1 / 2 \end{aligned}$
(ii) Total No. of Outcomes = $\{1,2,3,4,5,6\}=6$
Favorable Outcomes= $\{3,6\}=2$
Probability $=\frac{\text { no.of forverable outcomes }}{\text { Total no.of outcomes }}$
=$\frac{2}{6}$
$=\frac{1}{3}$
(iii) No. of multiple of '3' = {1,2,4,5}= 4
Probability = $\frac{4}{6}=\frac{2}{3}$
Question 3
(i) Total Outcomes = $\{T T, TH, H T, H H\}=4$
Getting two tail = {T,T } = 1
Probability $=\frac{1}{4}$
(ii) Atleast One tail = {TH, HT, TT}= 3
Probability $=\frac{\text { no.of forverable outcomes }}{\text { Total no.of outcomes }}$
$=\frac{3}{4}$
(iii) No. tail = {H,H }= 1
Probability = $\frac{1}{4}$
Question 4
Total outcomes = {TTT, TTH , THT , HTT, THH, HHT,HTH, HHH}= 8
(i) At least two heads
Favorable outcomes = {TTT,TTH , THT, HTT} = 4
Probability $=\frac{4}{8}=\frac{1}{2}$
(ii) Atleast on tail
Favorable Outcomes = {TTT, TTH, THT, HTTT, THH, HHT,HTH}= 7
Probability = $\frac{7}{8}$
(iii) At most one tail
Favorable Outcomes = {HHH,THH, HTH,HHT}= 4
Probability $=\frac{4}{8}=\frac{1}{2}$
Question 5
When two dice rolled simultanlouly
Total no. of outcomes =36
(i) The sum as 7
Favorable Outcomes = {(11,6),(2,5),(3,4),(4,3),(5,2),(6,11)}
Probability $=\frac{6}{36}=\frac{1}{6}$
(ii) The sum as 3 or 4
Sum '3' = {(1,2),(2,1)}= 2
Sum '4' = {(1,3),(2,2),(3,1)}=3
Total = 2+3= 5
∴ Favorable Outcomes = 5
Probability = $\frac{5}{36}$
(iii) Prime number on both dice
Favorable Outcomes = {(2,2),(2,3),(2,5),(3,2),(3,3),(3,5),(5,2),(5,3),(5,5)}=9
probability $=\frac{9}{36}=\frac{1}{4}$
Question 6
Total Screws = 60
Rusted Screws= $600 \times \frac{1}{10}=60$
(i) A rusted Screw
No. of faborable outcomes = 60
Probability=$\frac{60}{600}=\frac{1}{10}=0.1$
(ii) Not a Rusted Screw
No of favorable outcomes = 600-60 = 540
Probability = $\frac{540}{60}=0.9$
Question 7
TRIANGLE
Vowels ----{I, A, E }= 3
Total letters = 8
Probability = $\frac{\text { no.of vowels }}{\text { total no. of letter}}$
$=\frac{3}{8}$
Question 8
Bag = {5 Red, 6 black, 4 white } = 15 Balls
(i) Getting white
No. of favorable outcomes = 4
probability $=\frac{4}{15}$
(ii) Not black
Mean either red or white
No. of favorable outcomes = 5+ 4= 9
probability=$\frac{9}{15}=\frac{3}{5}$
(iii) Red or black
No. of favorable Outcomes = 5+ 6= 11
Probability $4=\frac{11}{15}$
Question 9
Total Cards = 17 = {1,2,3,4,5,6.............10,11,12,13,14,15,16,17}
(i) odd
No. of favorable Outcomes = 9
Probabilily $=\frac{9}{17}$
(ii) Even
No. of favorable outcomes = 8
Probability $\frac{8}{17}$
(iii) Prime
No. f favorable Outcomes {2,3,5,9,11,13,17}= 7
probability $=\frac{7}{17}$
(iv) divisible by 3
No of favorable outcomes = {3,6,9,12,15}=5
Probability $=\frac{5}{17}$
(v) Divisible by 2 and 3 both
No.of Favorable Outcomes = {6,12}=2
Probability $=\frac{2}{17}$
Question 10
Total Cards = 52
(i) An ace
No. of favable Outcomes = 4
$\begin{aligned} \text { probability }=& \frac{4}{52} \\ &=\frac{1}{13} \end{aligned}$
(ii) A red card
No.of favorable Outcomes = 26
$\begin{aligned} \text { Probability } &=\frac{26}{52} \\ &=\frac{1}{2} \end{aligned}$
(iii) Neither a king nor a queen
No. of favorable outcome = $56-(4 \times 2)=56-8 =44$
Probability = $\frac{44}{52}$
=$\frac{11}{13}$
(iv) A Red face card
No.of favorable outcome= $3 \times 2=6$\
$\begin{aligned} \text { Probability } &=\frac{6}{52} \\ &=\frac{3}{26} \end{aligned}$
(v) A card of spade or an ace
No. of spades $=n(s)=13$
No.of Ace = n(A) = 4
No.of Ace or spade = $n(s \wedge A)=1$
$\begin{aligned} \therefore n(S \cup A) &=n(s)+n(A)-n (S \wedge A) \\ &=13+4-1 \end{aligned}$
$n(S \cup A)=16$
No.of favorable outcomes = 16
$\begin{aligned} \text { Probabilily } &=\frac{16}{54} \\ &=\frac{4}{13} \end{aligned}$
(vi) Non face card of red colour
No.of favourable outcomes = $26-(3 \times 2)=20$
Probability $=\frac{20}{54}$
$\frac{5}{13}$
Question 11
Total tickets $=5+955=1000$
No.of favorable outcomes = 5
Probability = $\frac{5}{1000}$
$=\frac{1}{200}$
∴ Probability that the person wins lottery is $\frac{1}{200}$
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