PSEB 9th Class Maths MCQ Chapter 15 Probability

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 15 Probability MCQ Questions with Answers.

PSEB 9th Class Maths Chapter 15 Probability MCQ Questions

Multiple Choice Questions and Answer

Answer each question by selecting the proper alternative from those given below each question to make the statement true:

Question 1.
When a balanced die is thrown, the probability of getting 3 is …………….. .
A. \(\frac{1}{3}\)
B. \(\frac{1}{2}\)
C. \(\frac{1}{4}\)
D. \(\frac{1}{6}\)
Answer:
D. \(\frac{1}{6}\)

PSEB 9th Class Maths MCQ Chapter 15 Probability

Question 2.
A card is drawn at random from a well shuffled pack of cards. The probability of that card being a king is …………………. .
A. \(\frac{1}{52}\)
B. \(\frac{1}{26}\)
C. \(\frac{1}{13}\)
D. 1
Answer:
C. \(\frac{1}{13}\)

Question 3.
A card is drawn at random from a well shuffled pack of cards. The probability of that card being a card other than picture cards is ……………….. .
A. \(\frac{4}{13}\)
B. \(\frac{10}{13}\)
C. \(\frac{3}{13}\)
D. \(\frac{1}{13}\)
Answer:
B. \(\frac{10}{13}\)

PSEB 9th Class Maths MCQ Chapter 15 Probability

Question 4.
When an unbiased coin is tossed thrice, the probability of receiving three heads is ………………… .
A. \(\frac{1}{8}\)
B. \(\frac{1}{4}\)
C. \(\frac{1}{2}\)
D. \(\frac{3}{8}\)
Answer:
A. \(\frac{1}{8}\)

Question 5.
When three unbiased coins are tossed simultaneously, the probability of receiving exactly one tail is ………………… .
A. \(\frac{1}{8}\)
B. \(\frac{1}{2}\)
C. \(\frac{1}{4}\)
D. \(\frac{3}{8}\)
Answer:
D. \(\frac{3}{8}\)

PSEB 9th Class Maths MCQ Chapter 15 Probability

Question 6.
When a balanced die is thrown, the probability of receiving an even number is ………………… .
A. \(\frac{1}{6}\)
B. \(\frac{5}{6}\)
C. \(\frac{1}{2}\)
D. \(\frac{1}{4}\)
Answer:
C. \(\frac{1}{2}\)

Question 7.
When a balanced die is thrown, the probability of receiving a prime number is ……………….. .
A. \(\frac{2}{3}\)
B. \(\frac{3}{4}\)
C. \(\frac{1}{3}\)
D. \(\frac{1}{2}\)
Answer:
D. \(\frac{1}{2}\)

PSEB 9th Class Maths MCQ Chapter 15 Probability

Question 8.
When two balanced dice are thrown simultaneously, the probability of getting the total of numbers on dice as 9 is ………………. .
A. \(\frac{1}{9}\)
B. \(\frac{1}{6}\)
C. \(\frac{1}{3}\)
D. \(\frac{1}{12}\)
Answer:
A. \(\frac{1}{9}\)

Question 9.
Out of 100 days, the forecast predicted by the wheather department proved to be true on 20 days. Chosen any one day from these 100 days, the probability that the forecast proved to be false is ………………… .
A. \(\frac{1}{3}\)
B. \(\frac{1}{4}\)
C. \(\frac{3}{4}\)
D. \(\frac{4}{5}\)
Answer:
D. \(\frac{4}{5}\)

PSEB 9th Class Maths MCQ Chapter 15 Probability

Question 10.
The probability of a month of January having 5 Sundays is ………………….. .
A. \(\frac{2}{7}\)
B. \(\frac{3}{7}\)
C. \(\frac{5}{7}\)
D. \(\frac{1}{7}\)
Answer:
B. \(\frac{3}{7}\)

PSEB 9th Class Maths Solutions Chapter 15 Probability Ex 15.1

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 15 Probability Ex 15.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1

Question 1.
In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.
Answer:
The batswoman played 30 balls. Hence, the total number of trials = 30. If the event that she did not hit a boundary is denoted by A, then. the number of trials when event A occured is 30 – 6 = 24.
∴ p(A) = \(\frac{\text { No. of trials in which event A occured }}{\text { The total number of trials }}\)
= \(\frac{24}{30}\)
= \(\frac{4}{5}\)
Thus, the probability that she did not hit a boundary is \(\frac{4}{5}\).

PSEB 9th Class Maths Solutions Chapter 15 Probability Ex 15.1

Question 2.
1500 families with 2 children were selected randomly, and the following data were s recorded:
PSEB 9th Class Maths Solutions Chapter 15 Probability Ex 15.1 1
Compute the probability of a family, chosen at random, having
(i) 2 girls
(ii) 1 girl
(iii) No girl. Also check whether the sum of these probabilities is 1.
Answer:
Here, the total number of families is 1500.
Hence, the total number of trials = 1500

(i) Let event A denote the event that the family chosen at random is having 2 girls.
Then, the number of trials when event A occured is 475.
∴ P(A) = \(\frac{\text { No. of trials in which event A occured }}{\text { The total number of trials }}\)
= \(\frac{475}{1500}\)
= \(\frac{19}{60}\)

(ii) Let event B denote the event that the family chosen at random is having 1 girl.
Then, the number of trials when event B occured is 814.
∴ P(B) = \(\frac{\text { No. of trials in which event B occured }}{\text { The total number of trials }}\)
= \(\frac{814}{1500}\)
= \(\frac{407}{750}\)

(iii) Let event C denote the event that the family chosen at random Is having no girl.
Then, the number of trials when event C occured is 211.
∴ p(C) = \(\frac{\text { No. of trials in which event } \mathrm{C} \text { occured }}{\text { The total number of trials }}\)
= \(\frac{211}{1500}\)
Now,
P(A) + P(B) + P(C) = \(\frac{19}{60}+\frac{407}{750}+\frac{211}{1500}\)
= \(\frac{475+814+211}{1500}\)
= \(\frac{1500}{1500}\)
= 1

PSEB 9th Class Maths Solutions Chapter 15 Probability Ex 15.1

Question 3.
Refer to sum no. 5 of “Sums to Enrich ‘Remember’” in chapter 14. Find the probability that a student of the class was born in August.
Answer:
From the Bar graph in the sum which is referred here, we get the following information:

Total number of students = 40 and the number of students born in August = 6.
Hence, if event A denotes the event that a student of the class is born in August, then the number of trials when event A occured is 6 and the total number of trials is 40.
∴ P(A) = \(\frac{\text { No. of trials in which event A occured }}{\text { The total number of trials }}\)
= \(\frac{6}{40}\)
= \(\frac{3}{20}\)

Question 4.
Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:
PSEB 9th Class Maths Solutions Chapter 15 Probability Ex 15.1 2
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.
Answer:
Here, the total number of trials = 200. If event A denotes the event that 2 heads come up, then the number of trials when event A occured is 72.
∴ P(A) = \(\frac{\text { No. of trials in which event A occured }}{\text { The total number of trials }}\)
= \(\frac{72}{200}\)
= \(\frac{9}{25}\)

PSEB 9th Class Maths Solutions Chapter 15 Probability Ex 15.1

Question 5.
An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below :
PSEB 9th Class Maths Solutions Chapter 15 Probability Ex 15.1 3
Suppose a family is chosen. Find the probability that the family chosen is ( i ) earning ? 10000- ? 13000 per month and owning exactly 2 vehicles.
(ii) earning ₹ 16000 or more per month and owning exactly 1 vehicle.
(iii) earning less than ₹ 7000 per month and does not .own any vehicle.
(iv) earning ₹ 13000 – ₹ 16000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle.
Answer:
Here, the total number of families is 2400. Hence, the total number of trials = 2400

(i) Let event A denote the event that the family is earning ₹ 10000 – ₹ 13000 per month and owning exactly 2 vehicles.
Then, the number of trials when event A occured = 29.
∴ P(A) = \(\frac{\text { No. of trials in which event A occured }}{\text { The total number of trials }}\)
= \(\frac{29}{2400}\)

PSEB 9th Class Maths Solutions Chapter 15 Probability Ex 15.1

(ii) Let event B denote the event that the family is earning ₹ 16000 or more per month and owning exactly 1 vehicle.
Then, the number of trials when even B occured = 579.
∴ P(B) = \(\frac{\text { No. of trials in which event B occured }}{\text { The total number of trials }}\)
= \(\frac{579}{2400}\)
= = \(\frac{193}{800}\)

(iii) Let event C denote the event that the family is earning less than ₹ 7000 per month and does not own any vehicle.
Then, the number of trials when event C occured = 10.
∴ P(C) = \(\frac{\text { No. of trials in which event C occured }}{\text { The total number of trials }}\)
= \(\frac{10}{2400}\)
= = \(\frac{1}{240}\)

(iv) Let event D denote the event that the family is earning ? 13000 -? 16000 per month and is owning more than 2 vehicles. Then, the number of trials when event D occured = 25.
∴ P(D) = \(\frac{\text { No. of trials in which event D occured }}{\text { The total number of trials }}\)
= \(\frac{25}{2400}\)
= \(\frac{1}{96}\)

(v) Let event E denote the event that the family is owning not more than 1 vehicle, i.e., 1 vehicle or no vehicle.
Then, the number of trials when event E occured.
= 10 + 160 + 0 + 305 + 1 + 535 + 2 + 469 + 1 + 579 = 2062
∴ P(E) = \(\frac{\text { No. of trials in which event E occured }}{\text { The total number of trials }}\)
= \(\frac{2062}{2400}\)
= \(\frac{1031}{1200}\)

PSEB 9th Class Maths Solutions Chapter 15 Probability Ex 15.1

Question 6.
Refer to table 7 of sum no. 7 in “Sums to Enrich ‘Remember’” in chapter 14.
(i) Find the probability that a student obtained less than 20 marks in the mathematics test.
(ii) Find the probability that a student obtained marks 60 or above.
Answer:
According to the table referred here, the total number of students = 90.
Hence, the total number of trials = 90.
(i) According to the same table, the number of students who obtained less than 20 marks in the mathematics test is 7. So, if the event that a student obtained less than 20 marks in mathematics test is called event A, then the number of trials when event A occured is 7.
∴ P(A) = \(\frac{\text { No. of trials in which event A occured }}{\text { The total number of trials }}\)
= \(\frac{7}{90}\)

(ii) Let event B denote the event that a student obtained 60 or more marks. Then, , according to the same table, the number of trials when event B occured = 15 + 8 = 23.
∴ P(B) = \(\frac{\text { No. of trials in which event B occured }}{\text { The total number of trials }}\)
= \(\frac{23}{90}\)

Question 7.
To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table:

Opinion Number of students
Like 135
Dislike 65

Find the probability that a student chosen at random
(i) Likes statistics,
(ii) Does not like it.
Answer:
Here, the total number of students = 200.
Hence, the total number of trials = 200.

PSEB 9th Class Maths Solutions Chapter 15 Probability Ex 15.1

(i) Let event A denote the event that a student likes statistics.
Then, the number of trials when event A occured = 135
∴ P(A) = \(\frac{\text { No. of trials in which event A occured }}{\text { The total number of trials }}\)
= \(\frac{135}{200}\)
= \(\frac{27}{40}\)

(ii) Let event B denote the event that a student does not like statistics. Then, the number of trials when event B occured = 65.
∴ P(B) = \(\frac{\text { No. of trials in which event B occured }}{\text { The total number of trials }}\)
= \(\frac{65}{200}\)
= \(\frac{13}{40}\)

Question 8.
Refer to sum no. 2, Exercise 14.2. What is the empirical probability that an engineer lives:
(i) less than 7 km from her place of work ?
(ii) more than or equal to 7km from her place of work ?
(iii) within \(\frac{1}{2}\)km from her place to work?
Answer:
The total number of observations in the question referred here is 40.
Hence, the total number of trials = 40.

(i) Let event A denote the event that the distance between her residence and the place of work is less than 7 km. Then there are 9 such observations, viz., 5, 3, 2, 3, 6, 5, 6, 2, 3.
Hence, the number of trials when event A occured = 9.
∴ P(A) = \(\frac{\text { No. of trials in which event A occured }}{\text { The total number of trials }}\)
= \(\frac{9}{40}\)

PSEB 9th Class Maths Solutions Chapter 15 Probability Ex 15.1

(ii) Let event B denote the event that the said distance is 7 km or more than 7 km. Then, all the remaining 31(40-9) observations refer to event B.
Hence, the number of trials when event B occured = 31
∴ P(A) = \(\frac{\text { No. of trials in which event A occured }}{\text { The total number of trials }}\)
= \(\frac{31}{40}\)

(iii) Let event C denote the event that the engineer lives within \(\frac{1}{2}\) km from her place of work. There is no observation which is \(\frac{1}{2}\) or less than \(\frac{1}{2}\).
Hence, the number of trials when event C occured = 0.
∴ P(C) = \(\frac{\text { No. of trials in which event C occured }}{\text { The total number of trials }}\)
= \(\frac{0}{40}\)
= 0

Question 9.
Activity: Note the frequency of two-wheelers, three-wheelers and four-wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two-wheeler.
Answer:
Note: Students should do this Activity themselves.

Question 10.
Activity: Ask all the students in your class to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by her / him is divisible by 3 ? Remember that a number is divisible by 3, if the sum of its digits is divisible by 3.
Answer:
Note: Students should do this Activity themselves.

Question 11.
Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg) :
4.97 5.05 5.08 5.03 5.00 5.06 5.08 4.98 5.04 5.07 5.00
Find the probability that any of these bags chosen at random contains more than 5 kg of flour.
Answer:
The total number of bags = 11.
Hence, the total number of trials = 11.
Let event A denote the event that a bag contains more than 5 kg of flour.
There are 7 bags weighing more than 5 kg.
Their weights (in kg) are 5.05, 5.08, 5.03, 5.06, 5.08, 5.04 and 5.07. Hence, the number of trials when event A occured = 7.
∴ P(A) = \(\frac{\text { No. of trials in which event A occured }}{\text { The total number of trials }}\)
= \(\frac{7}{11}\)

PSEB 9th Class Maths Solutions Chapter 15 Probability Ex 15.1

Question 12.
In sum no. 5, Exercise 14.2, you were asked to prepare a frequency distribution table, regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12 – 0.16 on any of these days.
Answer:
In sum no. 5, Exercise 14.2, total number of days is 30.
Hence, the total number of trials = 30.
In the table prepared there, we see that the frequency of class 0.12 – 0.16 is 2.
Hence, during 2 days the concentration of sulphur dioxide (in ppm) was in the interval 0.12 – 0.16.
Let event A denote the event that the concentration of sulphur dioxide (in ppm) is in the interval 0.12 – 0.16.
Hence, the number of trials when event A occured = 2.
∴ P(A) = \(\frac{\text { No. of trials in which event A occured }}{\text { The total number of trials }}\)
= \(\frac{2}{30}\)
= \(\frac{1}{15}\)

Question 13.
In sum no. 1, Exercise 14.2, you were asked) to prepare a frequency distribution table regarding the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group AB.
Answer:
In sum no. 1, Exercise 14.2, the total number of students is 30.
Hence, the total number of trials = 30.
Let event A denote the event that a student has blood group AB. The number of students having blood group AB is 3.
Hence, the number of trials when event A occured = 3.
∴ P(A) = \(\frac{\text { No. of trials in which event A occured }}{\text { The total number of trials }}\)
= \(\frac{3}{30}\)
= \(\frac{1}{10}\)

PSEB 9th Class Maths MCQ Chapter 14 Statistics

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 14 Statistics MCQ Questions with Answers.

PSEB 9th Class Maths Chapter 14 Statistics MCQ Questions

Multiple Choice Questions and Answer

Answer each question by selecting the proper alternative from those given below each question to make the statement true:

Question 1.
The marks scored by Kavya in 10 tests of Mathematics are 35, 18, 41, 24, 45, 10, 28, 32, 40, 15. Then, the range of the data is …………….. .
A. 45
B. 10
C. 35
D. 28.8
Answer:
C. 35

Question 2.
The average of the observations 3, 4, 5, 8, 12, 10, 13, 16, 18, 11 is …………………. .
A. 100
B. 10
C. 18
D. 3
Answer:
B. 10

PSEB 9th Class Maths MCQ Chapter 14 Statistics

Question 3.
The mean of first five odd natural numbers is ……………….. .
A. 3
B. 5
C. 4
D. 25
Answer:
B. 5

Question 4.
The mean of first four even natural numbers is ……………….. .
A. 5
B. 10
C. 20
D. 4
Answer:
A. 5

PSEB 9th Class Maths MCQ Chapter 14 Statistics

Question 5.
The mean of first five prime numbers is
A. 28
B. 2.8
C. 5.6
D. 1.4
Answer:
C. 5.6

Question 6.
If the mean of 2x, 5, 3x, 12, 5x, 17 and 6 is 20, then x = ………………….. .
A. 10
B. 20
C. 15
D. 40
Answer:
A. 10

PSEB 9th Class Maths MCQ Chapter 14 Statistics

Question 7.
The mean of the following distribution is ………………. .
PSEB 9th Class Maths MCQ Chapter 14 Statistics 1
A. 3.9
B. 7.8
C. 78
D. 39
Answer:
A. 3.9

Question 8.
If the mean of 12, 13, x, 17, 18 and 20 is 16, then x = ………………. .
A. 8
B. 4
C. 16
D. 32
Answer:
C. 16

PSEB 9th Class Maths MCQ Chapter 14 Statistics

Question 9.
For a given frequency distribution, n = 20 and Σf<sub>i</sub>x<sub>i</sub> = 140, then X̄ = ………………… .
A. 20
B. 14
C. 7
D. 28
Answer:
C. 7

Question 10.
The mean of \(\frac{2}{5},\), \(\frac{5}{7},\), \(\frac{3}{5},\) and \(\frac{2}{7},\) is ……………… .
A. \(\frac{1}{2},\)
B. \(\frac{3}{5},\)
C. \(\frac{5}{7},\)
D. 2
Answer:
A. \(\frac{1}{2},\)

PSEB 9th Class Maths MCQ Chapter 14 Statistics

Question 11.
The median of 14, 6, 2, 13, 9, 15 and 12 is …………………. .
A. 12
B. 10
C. 2
D. 15
Answer:
A. 12

Question 12.
The median of 21, 17, 13, 33, 19, 23 is ………………… .
A. 21
B. 20
C. 33
D. 19
Answer:
B. 20

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.4

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 14 Statistics Ex 14.4 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.4

Question 1.
The following number of goals were scored by a team in a series of 10 matches:
2, 3. 4, 5, 0. 1, 3, 3, 4, 3
Find the mean, median and mode of these scores.
Answer:
Here, n = 10.
Mean X̄ = \(\frac{\Sigma x_{i}}{n}\)
= \(\frac{2+3+4+5+0+1+3+3+4+3}{10}\)
= \(\frac{28}{10}\)
= 2.8
Thus, the mean of the given scores is 2.8 goals.

Arranging the observations in the ascending order, we get:
0, 1, 2, 3, 3, 3, 3, 4, 4, 5
Since n = 10 is an even number, \(\frac{n}{2}\) = 5 and \(\frac{n}{2}\) + 1 = 6.

Median M
= \(\frac{\left(\frac{n}{2}\right) \text { th observation }+\left(\frac{n}{2}+1\right) \text { th observation }}{2}\)
= \(\frac{5 \text { th } \text { observation }+6 \text { th } \text { observation }}{2}\)
= \(\frac{3+3}{2}\) = 3
Thus, the median of the given scores is 3 goals.
In the given data, observation 3 occurs most frequently (4 times). Hence, the mode of the data is 3 goals.

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.4

Question 2.
In a mathematics test given to 15 students, the following marks (out of 100) are recorded :
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60
Find the mean, median and mode of this data.
Answer:
Here, n = 15.
Mean X̄ = \(\frac{\Sigma x_{i}}{n}\)
= \(\begin{gathered}
41+39+48+52+46+62+54+40 \\
+96+52+98+40+42+52+60 \\
\hline 15
\end{gathered}\)
= \(\frac{822}{15}\) = 54.8
Thus, the mean of the data is 54.8 marks.
Arranging the observations in the ascending order, we get:
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98
Here, n = 15 is an odd number.
Median M = \(\left(\frac{n+1}{2}\right)\)th observation
= \(\left(\frac{15+1}{2}\right)\)th observation
= 8 th observation
= 52
Thus, the median of the data is 52 marks.
In the given data, observation 52 occurs most frequently (3 times). Hence, the mode of the data is 52 marks.

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.4

Question 3.
The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95
Answer:
Here, the median = 63 and n = 10.
∴ \(\frac{n}{2}\) = 5 and \(\frac{n}{2}\) + 1 = 6

Median M
= \(\frac{\left(\frac{n}{2}\right) \text { th observation }+\left(\frac{n}{2}+1\right) \text { th observation }}{2}\)
∴ 63 = \(\frac{5 \text { th } \text { observation }+6 \text { th } \text { observation }}{2}\)
∴ 63 = \(\frac{(x)+(x+2)}{2}\)
∴63 × 2 = x + x + 12
∴126 = 2x + 2
∴ 2x = 124
∴ x = 62

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.4

Question 4.
Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.
Answer:
Here, just by simple observation, it is clearly seen that observation 14 occurs most frequently, i.e., 4 times.
Hence, the mode of the data is 14.

Question 5.
Find the mean salary of 60 workers of a factory from the following table:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.4 1
Answer:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.4 2

Mean X̄ = \(\frac{\Sigma f_{i} x_{i}}{n}\)
= \(\) = \(\frac{3,05,000}{60}\) = 5083.33
Thus, the mean salary is ₹ 5083.33.

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.4

Question 6.
Give one example of a situation in which
(i) the mean is an appropriate measure of central tendency.
Answer:
For the students studying in the same class, usually their level of knowledge and understanding would be more or less equal. There would be a few student having this level low and there would be a few students having this level high. Their level of knowledge and understanding would be reflected in the marks scored by them at an examination. Hence, the mean of marks scored by them at an examination is an appropriate measure of central tendency.

(ii) the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.
Answer:
If we consider the monthly income of the people of certain region, the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 14 Statistics Ex 14.3 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.3

Question 1.
A survey conducted by an organisation for the cause of illness and death among the women between the ages 15-44 (in years) worldwide, found the following figures (in %):

Causes Female fatality rate (%)
1. Reproductive health conditions 31.8
2. Neuropsychiatric conditions 25.4
3. Injuries 12.4
4. Cardiovascular conditions 4.3
5. Respiratory conditions 4.1
6. Other causes 22.0

(i) Represent the information given above graphically.
Answer:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3 1

(ii) Which condition is the major cause of women’s ill health and death worldwide?
Answer:
‘Reproductive health conditions’ is the major cause of womens ill health and death worldwide.

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3

(iii) Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause.
Answer:
‘Malnutrition’ and ‘Lack of necessary medical facilities’ can be considered as two other factors which play a major role in female fatality.

Question 2.
The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below:

Section Number of girls per thousand bays
Scheduled Caste (SC) 940
Scheduled Tribe (ST) 970
Non-SC/ST 920
Backward districts 950
Non-backward districts 920
Rural 930
Urban 910

(i) Represent the information above by a bar graph.
(ii) In the classroom discuss what conclusions can be arrived at from the graph.
Answer:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3 2

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3

Question 3.
Given below are the seats won by different political parties in the polling outcome of a state assembly elections:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3 3
(i) Draw a bar graph to represent the polling results.
Answer:
Seats won by different political parties
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3 4

(ii) Which political party won the maximum number of seats?
Answer:
Political party: A won the maximum number of seats.

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3

Question 4.
The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:

Length (in mm) Number of leaves
118-126 3
127-135 5
136-144 9
145-153 12
154-162 .5
163-171 4
172-180 2

(i) Draw a histogram to represent the given data. [Hint: First make the class intervals continuous.]
(ii) Is there any other suitable graphical representation for the same data?
(iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?
Answer:
Making the class intervals continuous, we get the following table:

Length (in mm) Number of leaves
117.5-126.5 3
126.5- 135.5 5
135.5-144.5 9
144.5-153.5 12
153.5- 162.5 5
162.5-171.5 4
171.5-180.5 2

(i) Length of leaves in millimetre
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3 5

(ii) Yes. The given data can also be represented by ‘Frequency polygon’.

(iii) It is not correct to conclude that the maximum number of leaves are 153 mm long, because even if the frequency of class 145-153 is 12, we do not have the information about the length of each of those 12 leaves individually.

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3

Question 5.
The following table gives the life times of 400 neon lamps:

Life time (in hours) Number of lamps
300 – 400 14
400 – 500 56
500 – 600 60
600 – 700 86
700 – 800 74
800 – 900 62
900 – 1000 48

(i) Represent the given information with the help of a histogram.
Answer:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3 6

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3

(ii) How many lamps have a life time of 700 hours or more than 700 hours ?
Answer:
The-frequencies of classes 700-800, 800-900 and 900-1000 are 74, 62 and 48 respectively.
Hence, the life time of 184 (74 + 62 + 48) lamps is 700 hours or more than 700 hours.

Question 6.
The following table gives the distribution of students of two sections according to the marks obtained by them:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3 7
Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.
Answer:
To draw the frequency polygons of both the sections, we find the class marks of each class and prepare the following tables:

Section A

Marks Class mark Frequency
0-10 5 3
10-20 15 9
20-30 25 17
30-40 35 12
40-50 45 9

Section B

Marks Class mark Frequency
0-10 5 5
10-20 15 19
20-30 25 15
30-40 35 10
40-50 45 1

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3 8
Comparing the performance of both the sections from the frequency polygons, we observe that the performance of students of section A is better than the performance of students of section B.

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3

Question 7.
The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:

Number of balls Team A Team B
1-6 2 5
7-12 1 6
13-18 8 2
19-24 9 10
25-30 4 5
31-36 5 6
37-42 6 3
43-48 10 4
49-54 6 8
55-60 2 10

Represent the data of both the teams on the same graph by frequency polygons.
[Hint: First make the class intervals continuous.]
Answer:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3 9

Number of runs made by Team A and Team B in first 60 balls.
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3 10

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3

Question 8.
A random survey of the number of children of various age groups playing in a park was found as follows:

Age (in years) Number of children
1-2 5
2-3 3
3-5 6
5-7 12
7-10 9
10-15 10
15-17 4

Draw a histogram to represent the data above.
Answer:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3 11

Children of various age groups playing in a park
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3 12

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3

Question 9.
100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:

Number of letters Number of surnames
1-4 6
4-6 30
6-8 44
8-12 16
12-20 4

(i) Draw a histogram to depict the given information.
(ii) Write the class interval in which the maximum number of surnames lie.
Answer:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3 13

(i) Information regarding the number of surnames having given number of letters
Answer:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3 14

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.3

(ii) Write the class interval in which the maximum number of surnames lie.
Answer:
The maximum number of surnames lie in the class interval 6-8.

PSEB 9th Class Maths Solutions Chapter 12 Heron’s Formula Ex 12.2

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 12 Heron’s Formula Ex 12.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2

Question 1.
A park, in the shape of a quadrilateral ABCD has ∠C = 90°, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?
Answer:
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 1

In ∆ BCD, ∠C = 90°
∴ BD2 = BC2 + CD2
= (12)2 + (5)2
= 144 + 25
= 169
= (13)2
∴ BD = 13 m

In ∆ BCD, a = 5 m, b = 12 m and c = 13 m
∴ Semiperimeter s = \(\frac{a+b+c}{2}\)
= \(\frac{5+12+13}{2}\) = \(\frac{30}{2}\) = 15 m
Then, s – a = 15 – 5 = 10m,
s – b = 15 – 12 = 3m and
s – c = 15 – 13 = 2 m.

Area of ∆ BCD = \(\sqrt{s(s-a)(s-b)(s-c)}\)
= \(\sqrt{15 \times 10 \times 3 \times 2}\) m2
= \(\sqrt{900}\) m2
= 30 m2

Note: ∆ BCD is a right triangle.
∴ Area of ∆ BCD = \(\frac{1}{2}\) × BC × CD
= \(\frac{1}{2}\) × 12 × 5 = 30 m2

Now, in ∆ ABD, a = 9 m, b = 13 m arid c = 8 m
∴ Semiperimeter s = \(\frac{a+b+c}{2}\)
= \(\frac{9+13+8}{2}\) = \(\frac{30}{2}\) = 15 m
Then,
s – a = 15 – 9 = 6m,
s – b = 15 – 13 = 2m and
s – c = 15 – 8 = 7 m.

Area of ∆ ABD = \(\sqrt{s(s-a)(s-b)(s-c)}\)
= \(\sqrt{15 \times 6 \times 2 \times 7}\) m2
= \(\sqrt{5 \times 3 \times 3 \times 2 \times 2 \times 7}\) m2
= 6 √35 m2
= 35.5 m2 (approx.)
Then, the area of park in the shape of quadrilateral ABCD
= Area of ∆ BCD + Area of ∆ ABD
= (30 + 35.5) m2 (approx.)
= 65.5 m2 (approx.)
Thus, the area of the park is 65.5 m2 (approx.)

PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2

Question 2.
Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.
Answer:
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 2
In ∆ ABC, a = 3 cm; b = 4 cm and c = 5 cm
∴ Semiperimeter s = \(\frac{a+b+c}{2}\)
= \(\frac{3+4+5}{2}\)
= \(\frac{12}{2}\) = 6 cm
Then,
s – a = 6 – 3 = 3 cm,
s – b = 6 – 4 = 2 cm and,
s – c = 6 – 5 = 1 cm.
Area of ∆ ABC = \(\sqrt{s(s-a)(s-b)(s-c)}\)
= \(\sqrt{6 \times 3 \times 2 \times 1}\) cm2
= 6 cm2
Note: Proving that ∆ ABC is a right triangle, Area of ∆ ABC = \(\frac{1}{2}\) × 3 × 4 = 6 cm2 can be obtained easily.
In ∆ ACD, a = 4 cm; b = 5 cm and c = 5 cm
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 3
Area of quadrilateral ABCD
= Area of ∆ ABC + Area of ∆ ACD
= (6 + 9.2) cm2 (approx.)
= 15.2 cm2 (approx.)

PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2

Question 3.
Radha made a picture of an aeroplane with coloured paper as shown in the given figure, s Find the total area of the paper used. ;
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 4
Answer:
The sides of the triangle in part 1 measure 5 cm, 5 cm and 1 cm.
∴ a = 5 cm, b = 5 cm and c = 1 cm
∴ Semiperimeter s = \(\frac{a+b+c}{2}\)
= \(\frac{5+5+1}{2}\) = \(\frac{11}{2}\) cm
Area of part 1
= Area of triangle
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 5
The length and breadth of rectangle in part II are 6.5 cm and 1 cm respectively.
Area of part II = Area of rectangle
= length × breadth
= (6.5 × 1) cm2
= 6.5 cm2
For the trapezium in part III, the parallel sides measure 1 cm and 2 cm, while both the non-parallel sides measure 1 cm each.
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 6
Drawing DM ⊥ AB and CN ⊥ AB. we get
AM = BM = \(\frac{2-1}{2}\) = \(\frac{1}{2}\) cm.
In ∆ DMA, ∠M = 90°
Area of trapezium ABCD
= \(\frac{1}{2}\) × Sum of parallel sides X Distance between parallel sides
= \(\frac{1}{2}\) × (AB + CD) × DM
= \(\frac{1}{2}\) × (2 + 1) × \(\frac{\sqrt{3}}{2}\)cm2
= \(\frac{1}{2}\) × 3 × \(\frac{\sqrt{3}}{2}\) cm2
= 1.3 cm2 (approx.)
For the right triangle in part IV the sides forming the right angle measure 6 cm and 1.5 cm.
Area of right triangle in part IV.
= \(\frac{1}{2}\) × Product of sides forming the right angle
= \(\frac{1}{2}\) × 6 × 1.5 cm2
= 4.5 cm2
The right triangle in part V is congruent to the right triangle in part IV.
∴ Area of right triangle in part V = 4.5 cm2
Now, total area of the paper used
= Areas of figures in part I to part V
= (2.5 + 6.5 + 1.3 + 4.5 + 4.5) cm2
= 19.3 cm2

PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2

Question 4.
A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
Answer:
In the given triangle, a = 26 cm, b = 28 cm and c = 30 cm
∴ Semiperimeter s = \(\frac{a+b+c}{2}\)
= \(\frac{26+28+30}{2}\) = \(\frac{84}{2}\) = 42 cm
Area of triangle
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 7
= 7 × 6 × 4 × 2 cm2
= 336 cm2
The area of the triangle and the area of the parallelogram are equal.
∴ Area of the parallelogram = 336 cm2
∴ Base × Corresponding altitude = 336 cm2
∴ 28 cm × Corresponding altitude = 336 cm2
∴ Corresponding altitude = \(\frac{336}{28}\) cm
∴ Corresponding altitude = 12 cm
Thus, the height of the parallelogram is 12 cm.

Question 5.
A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?
Answer:
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 8
Rhombus ABCD in the given figure represents the field.
A diagonal of a rhombus divides it into two congruent triangles.
∴ Area of rhombus ABCD = 2 × Area of ∆ ABC
In ∆ ABC, a = 30 m; b = 30 m; and c = 48 m.
∴ Semiperimeter s = \(\frac{a+b+c}{2}\)
= \(\frac{30+30+48}{2}\) = \(\frac{108}{2}\) = 54 cm
Area of ∆ ABC
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 9
= 3 × 6 × 24 m2
= 432 m2
Now, area of the field
= area of rhombus ABCD
= 2 × area of ∆ ABC
= 2 × 432 m2
= 864 m2
Now, area of grass field available for 18 cows to graze = 864 m2
∴ Area of grass field available for 1 cow to graze = \(\frac{864}{18}\) m2 = 48 m2
Thus, each cow gets 48 m2 of grass field to graze.

PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2

Question 6.
An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see the given figure), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 10
Answer:
Out of 10 triangular pieces, 5 are dark coloured and 5 are light coloured.
For each triangle, a = 20 cm, b = 50 cm and c = 50 cm
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 11
Hence, the total area of 5 dark coloured cloth pieces = 5 × 200 √6 cm2 = 1000 √6 cm2
Similarly, the total area of 5 light coloured cloth pieces = 5 × 200 √6 cm2 = 1000 √6 cm2

PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2

Question 7.
A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in the given figure. How much paper of each shade has been used in it?
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 12
Answer:
Let us name the square part as ABCD and the triangular part as CMN.
Suppose the length of square ABCD is xcm.
∴ In ∆ ABD, AB = AD = x cm and ∠A = 90°
The length of hypotenuse BD is given to be 32 cm.
AB2 + AD2 = BD2 (Pythagoras’ theorem)
∴ (x)2 + (x)2 = (32)2
∴ 2x2 = 1024
∴ x2 = 512
∴ x = √512
∴ x = \(\sqrt{256 \times 2}\)
∴ x = 16√2
Thus, the length of each side of square ABCD is 16 √2 cm.
Area of part I = Area of ∆ ABD
= \(\frac{1}{2}\) × AB × AD (∠A is a right angle.)
= \(\frac{1}{2}\) × 16 √2 × 16 √2 cm2
= 256 cm2
Area of part II = Area of A BCD
= \(\frac{1}{2}\) × BD × CD (∠A is a right angle.)
= \(\frac{1}{2}\) × 16 √2 × 16 √2 cm2
= 256 cm2
Note: Here, area of square ABCD can easily be found as below:
Area of square ABCD = \(\frac{(\text { Hypotenuse })^{2}}{2}\)
= \(\frac{(32)^{2}}{2}\)
= \(\frac{1024}{2}\)
= 512 cm2
To find the area of part III, we find the area of ∆ CMN.
In ∆ CMN, a = 6 cm, b = 8 cm and c = 6 cm.
∴ Semiperimeter s = \(\frac{a+b+c}{2}\)
= \(\frac{6+8+6}{2}\) = \(\frac{20}{2}\) = 10 cm

Area of part III
= Area of ∆ CMN
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 13
= 8 × 2.24 cm2 (approx.)
= 17.92 cm2 (approx.)

PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2

Question 8.
A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm (see the given figure). Find the cost of polishing the tiles at the rate of 50 p per cm2.
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 14
Answer:
For each of 16 triangular tiles,
a = 9 cm; b = 28 cm and c = 35 cm
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 15
= 88.2 cm2 (approx.)
∴ Area of 16 tiles = 16 × 88.2 cm2
= 1411.2 cm2
50 paise = ₹ 0.50
Cost of polishing 1 cm2 region = ₹ 0.50
∴ Cost of polishing 1411.2 cm2 region
= ₹ (1411.2 × 0.50)
= ₹ 705.60

PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2

Question 9.
A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.
Answer:
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 16
In the given figure, trapezium ABCD represents the field in which AB || CD,
AB = 25 m, BC = 14 m, CD = 10 m and DA = 13 m.
Through C, draw a line parallel to DA to intersect AB at E.
In quadrilateral AECD, AE || CD and DA || CE
∴ AECD is a parallelogram.
∴ CE = DA = 13 m and AE = CD = 10 m
Now, BE = AB – AE = 25 – 10 = 15 m
In ∆ CEB, a = 13 m; b = 15 m and c = 14 m
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.2 17
In ∆ CEB, draw CM ⊥ BE.
Area of ∆ CEB = \(\frac{1}{2}\) × BE × CM
∴ 84 m2 = \(\frac{1}{2}\) × 15 m × CM
∴ CM = \(\frac{84 \times 2}{15}\) m
∴ CM = 11.2 m
Area of parallelogram AECD
= Base × Corresponding altitude
= AE × CM
= 10 × 11.2 m2
= 112 m2
Hence, area of the field
= Area of trapezium ABCD
= Area of ∆ CEB + Area of parallelogram AECD
= 84 m2 + 112 m2
= 196 m2
Note: After finding CM = 11.2m, the area of . the field can also be found as below:
Area of the field
= Area of trapezium ABCD
= \(\frac{1}{2}\) × sum of parallel sides × distance between parallel sides
= \(\frac{1}{2}\) × (AB + CD) × CM
= \(\frac{1}{2}\) × (25 + 10) × 11.2 m2
= \(\frac{1}{2}\) × 35 × 11.2 m2
= 196 m2

PSEB 9th Class English Paragraph Writing

Punjab State Board PSEB 9th Class English Book Solutions English Paragraph Writing Exercise Questions and Answers, Notes.

PSEB 9th Class English Paragraph Writing

1. My Father

My father is an able person. He is a farmer. He is not well-educated. But he knows his work well. He is very hard-working. He is truthful and honest. So people respect him. They greet him respectfully. My father has an open mind. He tries to settle the quarrels among the people of the village. He is the wisest man of the village. He leads a simple and clean life. He does not lose temper with anybody. He is respected by one and all. I am proud of my father.

2. My Mother

Shrimati Asha is my mother. She is 40 years old. She is a kind and noble lady. She is active and smart. She is an M.A. She is a very simple lady. She has good habits. She gets up early in the morning. Then she cleans the house. She takes a bath and prays to God. She goes to temple daily. She prepares food for us. She looks after us all. She helps me in my studies. At night, she tells us stories. She loves me very much. I am proud of my mother. May she live long !

PSEB 9th Class English Paragraph Writing

3. My Younger Brother

Surinder is my younger brother. He is twelve years old. He is strong and healthy. He is tall for his age. He is very intelligent. He is honest. He never tells a lie. He is hard-working and obedient. He reads in the 6th class. He is the monitor of his class. He stands first in his class. He does his homework daily. He does not mix with bad boys. All the teachers love him. He is very fond of cricket. He is a member of the school cricket team. He is a good singer also. He is fond of reading storybooks. We are proud of him.

4. The Person I Dislike Most

Mr. Chaudhry, our next-door neighbour, is the person I dislike most. He has made our life miserable. Whenever he sees that we are studying, he switches on his TV at full volume. He has a big dog. He keeps it unchained. Many a time the dog bites people going through the street. Mr. Chaudhry’s wife is a very quarrelsome lady. She quarrels over trifles. She has six children. They make mischiefs all the day. Their mother never scolds them. These children are very rude. They know no manners. They write dirty words on the walls. But nobody dares complain against them to their parents. It is really a curse to have such a neighbour.

5. My School

I read in Arya High School, Ludhiana. It is a very big school. It has one huge gate. It has two storeys. There are fifty rooms. The rooms are airy. Each room has two electric fans. The hall of our school is very big. The school has two big playgrounds. It has a beautiful garden also. There are ten classes in our school.

PSEB 9th Class English Paragraph Writing

Each class has four sections. Each section has about sixty students. Our Headmaster is very able. He is very kind to the students. He is very hardworking. The teachers of our school are also able and hard-working. They love the students and the students respect them. Our school shows very good results every year. I love my school. I am proud of it. May it propser day and night!

6. Our Headmaster

Sh. Sohan Lal is the headmaster of our school. He is forty years old. He is tall and strong. He is active and smart. He is an M.A., B.Ed. Our headmaster is true to his duty. He is very punctual. He comes to school in time. He sits in his office. He works very hard. He plans his work well. He is very intelligent. He watches the working of the school. All the teachers and students respect him. He is a good teacher. He is a good speaker. He is a good writer also. He has written many books. He is a good player. He plays games in the evening. He is all in all in our school. We are proud of him. May he live long !

7. The Prize Distribution Function

The prize distribution function of our school was held on the seventh of March this year. The Education Minister presided over the function. The Minister took his seat and the function began. The Headmaster spoke a few words to welcome the guests and the Minister. Then the Headmaster requested the Minister to give away the prizes. The Minister shook hands with the prize-winners. All the prize-winners were loudly cheered. After giving away the prizes, the Minister made a short speech. He congratulated the prize-winners. He congratulated the Headmaster and the staff on their excellent work. In the end, the Headmaster thanked the Minister and the function was over. Tea was served to the guests and the prize-winners.

8. Our School Peon

Ramu is our school peon. He is twenty-five years old. He is tall and strong. He wears a khaki uniform. He is obedient and honest. He is true to his duty. He respects the teachers. He always speaks the truth. He knows his job well. Ramu lives in the school. He gets up early in the morning. He sweeps the school. He dusts the office. He rings the bell at the right time. He is busy the whole day. He is loyal to the school. He looks after the school property. His duty is hard, but his pay is small. I pity his lot.

9. A Postman

The postman is a very useful public servant. His duty is very hard. He has to do his duty in sun and rain. He goes to the Head Post Office in the morning. There he gets the dak. He arranges the letters. He puts them in a bag. Then he goes on his beat. He goes from door to door. He is eagerly waited for. He brings good as well as bad news. He helps to bring the world closer. A postman has to work hard. But his pay is small. He can hardly make both ends meet. I pity his lot.

PSEB 9th Class English Paragraph Writing

10. A Rickshaw-Puller 

The life of a rickshaw-puller is very hard. He lives by the sweat of his brow. He pulls heavy loads. He pulls men, women and children. It is very painful to look at him. A rickshaw-puller hardly gets as much as he deserves. People try to give him as little as possible. He has to work in sun and rain from morning till evening. Even then, he gets very little to eat. He is in rags. It is unlucky that even in this age of science men have to work like beasts of burden to earn their bread.

11. The Diwali Festival

Diwali is an important Indian festival. It falls in the month of October or November. It comes twenty days after Dussehra. Shri Ram came back to Ayodhya on this day. Shri Guru Hargobind was set free by the Mughal Emperor on this day. This festival is celebrated in every village and town. Houses and shops are painted in new colours. People light their homes with candles and electric lights. They buy sweets and toys. They distribute gifts among friends and relatives. Children enjoy fireworks at night. On this day, people worship goddess Lakshmi Some people gamble on this day. It is evil. It should be ended.

12. The Dussehra Festival

Dussehra is an important Hindu festival. It comes off in October. Rama defeated Ravar on this day. It marks the victory of good over evil. The festival lasts for ten days. Ram Lila staged at night. Many people come to see this Lila. On the last day, a fair is held. Many people come to see the fair. Everyone looks happy. Effigies of Ravana, Meghnada and Kumbhakarn are set up. Rama shoots arrows at the effigies. At about sunset, Hanumana sets them on fire After this people come back to their homes. They feel happy.

13. The Independence Day

India became a free country on August 15, 1947. So, August 15 is called the Independence Day of India. The British rule came to an end on this day. It is a red-letter day in the history of the country. It is celebrated all over the country with great enthusiasm. On this day, all schools, colleges and offices remain closed. It is a national holiday. Public meetings are held in all towns and cities. A big function is held in Delhi. The Prime Minister unfurls the national flag at the Red Fort. Our freedom is a hard-won freedom. We should protect it.

14. The Republic Day

India became a Republic on January 26, 1950. The Constitution of the country came into force on this day. India became a secular democratic country. The power of government passed into the hands of the common people. All castes, creeds and religions are to be equal in the eyes of the law. It is a red-letter day in the history of the country. It is celebrated all over the country with great enthusiasm. The national flag is unfurled at all the public buildings. A big function is held in Delhi. The President of the country presides over this function. It is worth seeing. This day is a national holiday.

15. Mahatma Gandhi

Mahatma Gandhi was born on October 2, 1869. He was unlike other boys. He was very gentle. He loved truth. He respected his teachers. After doing law he started practice in India. He did not take up false cases. He went to Africa to fight a case. There he saw the poor Indians. The English treated them badly. Gandhiji fought for their rights for ten years. Then he came back to India. He fought for the freedom of India. He gave us a new way of fighting. It was ‘ahimsa’. It was more powerful than violence. He was able to free India in 1947. He was a real Mahatma. He led a very simple life. He is called the Father of our Nation. A mad person shot him dead on January 30, 1948. Gandhiji’s name will always be remembered.

16. An Ideal Student

An ideal student is a knowledge-seeker in the real sense. He obeys his teachers. He has full confidence in them. He is regular and punctual. He works hard at studies. But he takes part in games also. He does not read cheap and dirty literature. He reads only good and useful books. An ideal student believes in simple living and high thinking. He knows the value of discipline. He does not waste the hard-earned money of his parents. An ideal student is a true patriot. In short, he has all the qualities of head and heart.

PSEB 9th Class English Paragraph Writing

17. The Recess Period

The recess is the period of enjoyment. In this period, the students feel happy. They enjoy freedom for some time. As soon as the recess period begins, students rush out of their classrooms. Some of them run to the vendors. They buy things to eat. Others go to the taps to drink water. There is great rush in the playground. Some love to play there while others like to sit under the shady trees. They talk about their friends and teachers. Soon the bell goes. Students run back to their classes. The students feel fresh and start their studies once again.

18. A One-Day Cricket Match

Last Sunday, a one-day cricket match was played between our school and Arya High School. Each team played 40 overs. The match started at 10 a.m. We won the toss. We decided to bat first. Mohan and Gopal were our openers. Mohan made 30 runs and was out. Now Raja came in to bat. He did not play well. He was out for a duck. The next four players made 60 runs. Our team was out at 120 runs. Now it was the turn of Arya High School. They had good openers. They made 60 runs. Their third batsman was a hitter. He made 30 runs. But the other players were soon out. Their team could make only one hundred runs. We won the match by 20 runs. It was really a very interesting match.

19. A Football Match

Last Monday, a football match was played between our school and Khalsa School. It was played on our school grounds. Sh. Jaswant Singh was the referee. He blew the whistle. There was a toss. We won the toss. We chose our side. The match began. At first, the game was slow, but soon it became brisk. All the players played well. Our defence was very strong. There was no goal. The referee blew the whistle for interval. In the second half, Vinod passed the ball on to me. I ran with it into the Then I kicked it hard. It went through the poles. It was a goal. There were loud cheers. The referee blew the whistle. The game was over. We won the march by one goal.

20. A Kabaddi Match

I saw a kabaddi match last Sunday. It was played between our school and New High School. Sh. Mohan Lal was the referee. Many people came to see the match. There was a toss. We won the toss. We chose our side. Then the match began. First of all, our captain went running to the other side. He shouted, “Kabaddi, Kabaddi.” He came back. There was no point. Now it was the turn of New High School.

PSEB 9th Class English Paragraph Writing

One of their players came to our side. He was caught. He could not go back. We scored a point. There were loud cheers. We scored more points. New High School team got only 8 points. We had gained 20 points. The referee blew a long whistle. The match came to an end. We won the match by 12 points. It was an interesting match.

21. Morning Walk

Morning walk is the best form of exercise. It costs nothing. It is very useful for our health. It refreshes our mind. It strengthens our body. It saves us from many diseases. Morning walk keeps us fresh for the whole day. It develops in us the habit of rising early. It brings pure thoughts in our mind. The dew drops, the fresh flowers, the chirping birds and the rustling leaves charm our mind. We start loving these objects of natural beauty. Thus, morning walk is useful not only for our body but for our mind also.

22. A Journey by Bus

Last Sunday, I went to Delhi by bus. I went to the bus stand and bought a ticket. A bus bound for Delhi was standing there. I got in and took the front seat. The conductor gave a whistle and the bus started. ‘We were soon out of the city. The driver drove very fast. But he was very good at his job. We felt quite safe. He left many buses behind. I saw farmers working in their fields. Here and there, I saw carts going on the road. The conductor was a jolly fellow. He made the journey pleasant by his witty talk. The bus reached Delhi at 6 p.m. It was a very pleasant journey.

23. A Journey by Train

Last year, I went to Delhi by train. I packed my luggage. I hired a rickshaw. I reached the station. I bought a ticket. I went to the platform. Soon the train arrived. I got into it. There was a great rush. But I was lucky. I got a seat near the window. The train started. I saw many things on the way. Farmers were ploughing the fields. Children were playing. A ticket-checker came. He checked our tickets. A young man was without ticket. He was fined. The train stopped at many stations. I bought a newspaper, I read it. It was 10 a.m. The train reached Delhi. It was a happy journey.

24. A Visit to a Zoo

There is a zoo in our city. I visited it last Sunday. I went with my parents. We bought tickets and went in. First of all, we saw birds. There were many beautiful and rare kinds of birds. We saw parrots, canaries, swallows, peacocks, ducks, cranes, herons, gulls and geese. Then we saw some wild beasts. A lioness and her cub were basking in the sun. They roared now and then. We also saw wolves, tigers, elephants and rhinos. When we were coming back, we saw a muddy pond. There were many big snakes in it. It was fearful to look at them. We stayed in the zoo for about three hours. Then we came back home.

25. A Visit to a Fair 

I went to see a fair last Tuesday. This fair is held every year in our town. It is held in the memory of a pious faqir. Many people go to see this fair. They include men of all religions and faiths. This year I went to see the fair with my parents. We offered flowers at the faqir’s tomb.

PSEB 9th Class English Paragraph Writing

Then we went round the fair. There was a temporary bazaar. Stalls were arranged on either side. There was a great hustle and bustle. Sweets were in great demand. Children were enjoying rides in merry-go-rounds. A big shamiana was set up on one side of the fair. Qawalis were being sung there. We sat there for some time. Then we came back home.

26. A Visit to a Circus

A circus came to our town last month. I went to see it with my parents. We bought tickets and went in. We took our seats in the front row. First of all, a young girl came in. She had an umbrella in her hand. She walked on a rope. Then some more girls joined her. They showed various feats in gymnastics. They looked like rubber dolls. One of the girls jumped through a fire ring. Then there were animal shows. An elephant drank water from a bottle. A lion and a goat played with each other. A monkey drove a mini-cycle. The show came to an end at 7 p.m. I liked it very much.

27. A Visit to a Historical Place

During the last spring holidays, I went to Agra. There I visited the Taj. It is built outside the city on the bank of the Yamuna. A large gateway of red stone provides the entrance. The Taj is a large and beautiful building. It stands on a raised platform. In the middle of the platform, there is a splendid white dome. At its four corners, there are four stately towers. Underneath the white dome are the marble tombs of Mumtaz Mahal and Shah Jahan. The whole building is surrounded by a garden on three sides. On the fourth side, the river Yamuna grazes it. No words can describe the beauty of the Taj.

28. A Scene at the Railway Station

Last Sunday, my father went to Delhi. I went to the station to see him off. I bought a ticket and a platform ticket. We went to the platform. There was great hustle and bustle. Some men were buying books at the bookstall. The hawkers were going up and down the platform. The coolies were busy. People were waiting for the train. Soon the train arrived. There was a great rush in it. Some passengers got down. Others got in and took their seats. I got a seat for my father. The engine gave a whistle. The guard waved a green flag. The train again whistled and steamed off. Now there was all quiet on the platform. I came back home.

29. A Scene at the Bus Stand

Last Monday, I went to the bus stand to see off my uncle. The bus stand was humming with life. There were separate parking stands for different routes. A bus was parked at each stand. Men behind the counter were issuing tickets. The conductors were shouting to attract passengers for their respective buses. As soon as a bus was full, the conductor blew his whistle and the bus moved out of the stand. Another one immediately took its place. This activity was going on endlessly. I bought a ticket for my uncle, got him a good seat and then came back home.

30. A House on Fire

It was Sunday. I was sitting in my room with my friend, Atul. Suddenly, we saw clouds of smoke rising in the sky. There was a big fire in the next street. People were running to the site of fire. Children were shouting for help. People brought buckets of water. We also joined them. We threw sand and water on the flames. The fire was put out after half an hour. It was the house of a carpenter. The poor man suffered a big loss. All his wood, grain and money were gone. The house was reduced to ashes. He was very sad at his loss. People felt sorry for him. They gave him food, clothes and some money. The poor carpenter thanked them with folded hands.

PSEB 9th Class English Paragraph Writing

31. A Bus Accident

Last Monday, I was travelling from Panipat to Delhi by bus. We had hardly gone twenty kilometres when a dreadful accident took place. All of a sudden a scooterist, coming from a side-road, came in front of the bus. The driver at once applied the brakes, and also turned the bus to one side. All the passengers were thrown off their seats. In no time, the bus went off the road and fell into a ditch. There were loud cries. Many passengers were badly wounded. I, too, got a deep cut on my forehead. Many people gathered there. They helped us to get out of the bus. Luckily there was no death. The scooterist had sped away. I reached home with a bandaged head.

32. A Street Quarrel

Last evening, I was sitting near the window of my room. I saw two children playing in the street. Suddenly, they fell out. Other boys of the street gathered there. None tried to separate them. They kept looking on. Soon, the mothers of both the children reached there. They started abusing each other. They used very dirty words for each other. From hot words, they came to blows. They pulled each other’s hair. Luckily, an elderly woman came there. She separated the fighting ladies. She spoke to them very wisely. The two women realised their mistake. They went back to their homes. Both the children started playing together once again.

33. A Rainy Day

It was the month of July last year. One day, it was very hot. Men and animals were panting. All were perspiring. We longed for a shower of rain. In the afternoon, some clouds appeared in the east. Soon the whole sky was overcast with dark clouds. It started raining heavily. Streets and bazaars were flooded with water. Little children came out and played in the rain. They splashed water over one another. The rain stopped after two hours. It became very cool and pleasant. Streets and bazaars were washed clean. The city gave a fresh look.

34. Life in a Village

The three words that can amply describe the life in a village are — Simple, Pure and Fresh. The villagers are very simple-hearted people. They know no cunning. They are pure in their thoughts and actions. They are very hospitable. They live simply and happily. They have no anxiety. Life in a village is very calm and peaceful. It is free from the noise and din of cities. The air is fresh and health-giving. Says Leo Tolstoy in one of his stories, “A villager’s life is not a fat one, but it is a long one.” He may never grow rich, but he has always enough to eat. In short, we can say that life in a village is worth living.

35. How I Celebrated My Birthday

I gave a party on my birthday. I invited all my friends. The party was held at my house. The party began at 6 p.m. A big cake was placed on a table. All my friends stood round the table. I cut the cake with a knife. My friends and parents chanted three times : ‘Happy Birthday To You.’ Then everybody set to eating. The cake was served to all. It was very tasty. There were many things to eat. Everybody ate to their heart’s content. There was singing and dancing also. Everyone enjoyed the party. It was over by 8 p.m. My friends congratulated me once again and went back to their homes.

36. A Drowning Tragedy

One day, I was picnicking with some of my friends on the riverbank. A boy named Kamal fell into the river. He didn’t know how to swim. I saw him struggling with water. It was a painful sight. I at once jumped into the river. I swam to him and brought him out with great difficulty. He had swallowed a lot of water. He was unconscious. We, at once called a doctor. Someone ran to inform Kamal’s parents. The doctor pressed out the water from Kamal’s belly. Kamal opened his eyes. We felt great relief. After some time Kamal’s parents reached the place. They thanked me and the doctor again and again.

PSEB 9th Class English Paragraph Writing

37. The Golden Temple

Amritsar is also called Guru-ki-nagri. It is famous for the Golden Temple. The Temple is situated in the city. It is surrounded by many narrow lanes. The golden shrine built in the middle of the sarover shines at sunrise and sunset. It was built by Guru Arjun Dev Ji. It is a unique experience when Granth Sahib is brought out from the Akal Takhat Sahib amidst chanting of hymns and blowing of bugles.

The Akal Takhat Sahib, facing the Harmandir Sahib, was built by Guru Hargobind Ji. It was used for holding courts. The complex has a museum of rare paintings, books, shashtras, etc. The lives of the Gurus are described through them. There is a big bazaar near Darshani Deori. Gutakas, karas and other articles related to the Sikh religion are sold there. Home-made papad-varian, chura-bangles, dry fruit are also sold in many shops. There are number of hotels and guest houses near the Temple for tourists to stay. There is a sarai also for pilgrims in the Temple. The Golden Temple is indeed a worth-visiting place.

38. Canada

Canada is one of the largest country of the world. Its area is 9,976,139 sq. km. and population is about 32 million. The capital city of Canada is Ottawa. The currency of the country is Canadian dollar. English and French are the official languages of Canada. In winter, the climate of Canada is bitterly cold. In some regions, the mercury may dip to -65°C. The average temperature in Ottawa is from -15°C to -6°C in January.

In July, the average temperature is 15°C to 26°C. The main products of Canada are fruit, vegetables, livestock, tobacco, copper, zinc, iron, salt, oil and natural gas. And major industries of the country are agriculture, forestry, food processing, transport, chemicals, oil and gas refining and cement. Vehicles, machinery, food stuffs, natural gas, meat, coal and timber are exported to other countries. Canada is one of the most developed nations of the world.

39. Aruna Asif Ali

Aruna Asif Ali is known as the Grand Old Lady of India. She took active part in the Independence movement. She was born in an orthodox Hindu Bengali family in 1909 at Kalka. She married a Muslim, Mr. Asif Ali, thus breaking all conventions regarding marriage. Her husband, Mr. Asif Ali, was also involved in the freedom struggle. Aruna Asif Ali took part in Salt Satyagrah under the leadership of Gandhiji.

She addressed many public meetings and led processions for the cause of India’s independence from the British rule. As a result, she was sentenced to one-year imprisonment. But she didn’t give up the cause for which she was fighting against the British rule. She was again sentenced to jail.

She became the editor of the newspaper ‘Inquilab’. After Independence, she became a social worker. She fought for the rights of women. In 1992 she received Nehru Award for International Understanding. She passed away in July 1996. She was honoured with Bharat Ratna posthumously.

40. The Tribals of Odisha 

There are many tribal groups in Odisha. They live in remote places. One such group lives in the forests of Kalahandi. These people are one of most backward tribes in the world. They have dark skin and black hair. The women wear bright-coloured saris while the men wear nothing but loincloth.

They still believe that India is ruled by kings. These people are illiterate as they do not have any facility of schooling, means of transportation and proper motorable roads. As a result, they are cut off from the rest of the world. They do not have any idea of currency notes. They still use barter system.

PSEB 9th Class English Paragraph Writing

They usually live in groups and each group has common property. They cure diseases with herbs and set bones by rubbing oils. The government should launch schemes to educate them and bring them to the mainstream of the nation.

41. An Incident of Burglary

Mr. Ramanathan is an affluent businessman of our town. One day, he with his family went out of the town to attend a wedding. There was nobody at home and the house was locked from outside. A thief broke into the house at night. He decamped with the jewellery, valuables and money.

But the neighbours had seen the lights on and they informed the police about it. The police came along with a dog. They found the thief’s glove. The dog sniffed the scent of the thief. It took the policemen to the thief’s place. Thus the thief was arrested and the case was solved. The policemen were rewarded by the department for their efficiency.

42. Floods in Mumbai

On July 26, 2005, I was busy shopping in a famous crowded market, although it was raining. Gradually, it started raining heavily. Now, it was impossible to go from there. Therefore, I took shelter in a shop. Soon, the place got flooded and water started entering the shops. The articles in the shops started floating in the water and the shopkeeper tried to retrieve valuable articles. The entire area was submerged in the flood water.

Many vehicles couldn’t move in the flood water. The people had to stay in them. Some other people took shelter in shops and houses. Suddenly, it started raining like hell. Now water in the shops and houses rose up to 6-7 feet. The people had to move to first floor. In no time the army swung into action. The volunteers of many NGO’s started helping the affected people with food and water. All this went on for more than 24 hours. It was really a horrifying experience which I can never forget.

43. The Lohri Festival

Lohri is a festival of fun and frolic. It is generally celebrated on 13th of January every year. This festival is related to the folklore of Dulla Bhatti. At sunset, people light up bonfires in the open in front of their houses. Lohri is celebrated with more enthusiasm in the families where there is a newborn son or a newly married person.

Giddha or Bhangra is performed to the beats of the drums. On the day of Lohri, children go singing from house to house asking for money and sweets. Lohri is a busy festival. People meet their friends and relatives and exchange greetings and gifts.

44. How to Make Papier-mache -Toys

In order to make toys with papier-mache, old newspaper sheets are taken. They are torn into small pieces. These pieces are soaked in water overnight. Next day, the mixture is boiled for half an hour. After that, the mixture is whipped till it becomes soft and pulpy.

PSEB 9th Class English Paragraph Writing

The water is squeezed out from the mixture and two tablespoons of white gum are added into it. The mixture is stirred well and then the toys are made from it. These toys are left to dry overnight or more. Then they are painted with water-based colour. To make these toys waterproof, two or three coats of lacquer are given on them. Masks can also be made in the same manner.

45. How to Make Gajrela

It is very easy to make gajrela at home. Take three kilograms of large carrots and wash them properly. Then grate the carrots. Mix 242 litres milk with the carrots. After that put the mixture in a pan and boil it till the mixture becomes very thick. Add 3/4 cup of sugar and 250 gm of khoya in the mixture.

Stir the mixture till it becomes thick. Stir it continuously as the mixture should not stick to the pan. Now remove the pan from the fire. Add nuts to it. Your gajrela is ready. Let it cool before serving. It can also be served hot.

PSEB 9th Class Maths Solutions Chapter 12 Heron’s Formula Ex 12.1

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 12 Heron’s Formula Ex 12.1 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.1

Question 1.
A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
Answer:
In equilateral ∆ ABC, the length of each side is a.
∴ a = a, b = a, c = a
and semiperimeter s = \(\frac{a+b+c}{2}\) = \(\frac{a+a+a}{2}\) = \(\frac{3}{2}\)a
Now,
s – a = \(\frac{3}{2}\)a – a = \(\frac{1}{2}\)a,
s – b = \(\frac{3}{2}\)a – a = \(\frac{1}{2}\)a, and
s – c = \(\frac{3}{2}\)a – a = \(\frac{1}{2}\)a,
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.1 1
Now, the perimeter of equilateral ∆ ABC is 180 cm.
∴ Length of each side = \(\frac{180}{3}\) = 60 cm and
semiperimeter s = \(\frac{180}{2}\) = 90 cm.
Here, a = b = c = 60 cm and s = 90 cm
∴ s – a = 90 – 60 = 30 cm,
s – b = 90 – 60 = 30 cm and
s – c = 90 – 60 = 30 cm.
Area of ∆ ABC = \(\sqrt{s(s-a)(s-b)(s-c)}\)
= \(\sqrt{90 \times 30 \times 30 \times 30}\) cm2
= \(\sqrt{3 \times 900 \times 900}\) cm2
= 30 × 30 × √3 cm2
= 900 √3 cm2

PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.1

Question 2.
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m and 120 m (see the given figure). The advertisements yield an earning of ₹ 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.1 2
Answer:
For triangular side wall of the flyover,
a = 122 m, b = 120 m and c = 22 m.
Semiperimeter s = \(\frac{a+b+c}{2}\)
= \(\frac{122+120+22}{2}\)
= \(\frac{264}{2}\)
= 132 m
Area of triangular side wall
= \(\sqrt{s(s-a)(s-b)(s-c)}\)
= \(\sqrt{132(132-122)(132-120)(132-22)}\) m2
= \(\sqrt{132 \times 10 \times 12 \times 110}\) m2
= \(\sqrt{12 \times 11 \times 10 \times 12 \times 11 \times 10}\) m2
= 12 × 11 × 10 m2
= 1320 m2
∴ Annual rent of one wall = ₹ (1320 × 5000)
∴ Rent of one wall for 3 months
= ₹ (1320 × 5000 × \(\frac{3}{12}\))
= ₹ 16,50,000

PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.1

Question 3.
There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see the given figure). If the sides of the wall are 15 m, 11m and 6 m, find the area painted in colour.
PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.1 3
Answer:
The lengths of the triangular side wall are
15 m, 11m and 6 m.
∴ a = 15 m, b = 11m, c = 6m and
semiperimeter s = \(\frac{a+b+c}{2}\) = \(\frac{15+11+6}{2}\) = \(\frac{32}{2}\) = 16 cm
Then, s – a = 16 – 15 = 1 m,
s – b = 16 – 11 = 5 m, and
s – c = 16 – 6 = 10m.
Area of the triangular region painted in colour
= \(\sqrt{s(s-a)(s-b)(s-c)}\)
= \(\sqrt{16 \times 1 \times 5 \times 10}\) m2
= \(\sqrt{16 \times 5 \times 5 \times 2}\) m2
= 4 × 5 × √2 m2
= 20√2 m2

PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.1

Question 4.
Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
Answer:
Here, perimeter of the triangle = 42 cm
∴ Semiperimeter s = \(\frac{42}{2}\) = 21 cm.
Now, a = 18 cm and b = 10 cm.
s = \(\frac{a+b+c}{2}\)
∴ 21 = \(\frac{18+10+c}{2}\)
∴ 42 = 28 + c
∴ c = 14 cm
Now,
s – a = 21 – 18 = 3 cm,
s – b = 21 – 10 = 11 cm and
s – c = 21 – 14 = 7 cm.
Area of a triangle = \(\sqrt{s(s-a)(s-b)(s-c)}\)
= \(\sqrt{21 \times 3 \times 11 \times 7}\) cm2
= \(\sqrt{21 \times 21 \times 11}\) cm2
= 21√11 cm2

PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.1

Question 5.
Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.
Answer:
Suppose the sides of the triangle measure 12x cm, 17x cm and 25x cm.
Perimeter of a triangle = Stun of three sides
∴ 540 = 12x + 17x + 25x
∴ 540 = 54x
∴ x = 10
Then, the measures of the sides of the triangle are,
a = 12 × 10 = 120 cm,
b = 17 × 10 = 170 cm and
c = 25 × 10 = 250 cm.
Now, s – a = 270 – 120 = 150 cm,
s – b = 270 – 170 = 100 cm and
s – c = 270 – 250 = 20 cm.
Area of a triangle
= \(\sqrt{s(s-a)(s-b)(s-c)}\)
= 7\(\sqrt{270(150)(100)(20)}\) cm2
= \(\sqrt{270 \times 30 \times 5 \times 100 \times 5 \times 4}\) cm2
= \(\sqrt{8100 \times 25 \times 400}\) cm2
= \(\sqrt{(90)^{2} \times(5)^{2} \times(20)^{2}}\) cm2
= 90 × 5 × 20 cm2
= 9000 cm2

PSEB 9th Class Maths Solutions Chapter 12 Heron's Formula Ex 12.1

Question 6.
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Answer:
Let, the sides of the isosceles triangle be a = 12 cm, b = 12 cm and c cm.
Perimeter of triangle = Sum of three sides
∴ 30 = 12 + 12 + c
∴ 30 = 24 + c
∴ c = 6 cm
Now, semiperimeter s = \(\frac{\text { Perimeter }}{2}\) = \(\frac{30}{2}\) = 15 cm
Then, s – a = 15 – 12 = 3 cm,
s – b = 15 – 12 = 3 cm and
s – c = 15 – 6 = 9 cm.
Area of a triangle = \(\sqrt{s(s-a)(s-b)(s-c)}\)
= \(\sqrt{15 \times 3 \times 3 \times 9}\) cm2
= \(\sqrt{15 \times 9 \times 9}\) cm2
= 9 √15 cm2

PSEB 9th Class Maths Solutions Chapter 11 Constructions Ex 11.2

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 11 Constructions Ex 11.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 11 Constructions Ex 11.2

Question 1.
Construct a triangle ABC in which BC = 7cm, ∠B = 75° and AB + AC = 13cm.
Answer:
PSEB 9th Class Maths Solutions Chapter 11 Constructions Ex 11.2 1

Steps of construction:

  1. Draw any ray BX. With centre B and radius 7 cm draw an arc to intersect BX at C.
  2. At B, construct ∠YBC with measure 75°.
  3. With centre B and radius 13 cm, draw an arc to intersect BY at M.
  4. Draw line segment MC. Draw the perpendicular bisector of MC to intersect BM at A.
  5. Draw line segment AC.
    Then, ∆ ABC is the required triangle.

PSEB 9th Class Maths Solutions Chapter 11 Constructions Ex 11.2

Question 2.
Construct a triangle ABC in which BC = 8 cm, ∠B = 45° and AB – AC = 3.5 cm.
Answer:
PSEB 9th Class Maths Solutions Chapter 11 Constructions Ex 11.2 2

Steps of construction:

  1. Draw any ray BX and from that obtain the line segment BC of length 8 cm.
  2. At B, draw ray BY such that ∠YBC = 45°.
  3. With centre B and radius 3.5 cm, draw an arc to intersect ray BY at D.
  4. Draw line segment DC. Draw the perpendicular bisector of DC to intersect ray BY at A.
  5. Draw line segment AC.
    Then, ∆ ABC is the required triangle.

PSEB 9th Class Maths Solutions Chapter 11 Constructions Ex 11.2

Question 3.
Construct a triangle PQR in which QR = 6 cm, ∠Q = 60° and PR – PQ = 2 cm.
Answer:
PSEB 9th Class Maths Solutions Chapter 11 Constructions Ex 11.2 3

Steps of construction:

  1. Draw any ray QX and from that obtain the line segment QR of length 6 cm.
  2. At Q, construct ray QY such that Z YQR = 60°.
  3. Produce ray QY on the side of Q to obtain ray QZ. Obtain point S on ray QZ such that QS = 2 cm.
  4. Draw line segment RS. Draw the perpendicular bisector of RS to intersect QY at E
  5. Draw line segment PR.
    Then, ∆ PQR is the required triangle.

PSEB 9th Class Maths Solutions Chapter 11 Constructions Ex 11.2

Question 4.
Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm.
Answer:
PSEB 9th Class Maths Solutions Chapter 11 Constructions Ex 11.2 4

Steps of construction:

  1. Draw any ray AP and from that obtain the line segment AB of length 11 cm.
  2. Construct ray AL such that ∠LAB = 30°.
  3. Construct ray BM such that ∠MBA = 90°.
  4. Draw the bisectors of ∠LAB and ∠MBA to intersect each other at X.
  5. Draw line segment XB. Draw the perpendicular bisector of XB to intersect AB at Z.
  6. Draw line segment XA. Draw the perpendicular bisector of XA to intersect AB at Y.
  7. Draw line segments XY and XZ.
    Then, ∆ XYZ is the required triangle.

PSEB 9th Class Maths Solutions Chapter 11 Constructions Ex 11.2

Question 5.
Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm.
Answer:
PSEB 9th Class Maths Solutions Chapter 11 Constructions Ex 11.2 5

Steps of construction:

  1. Draw any ray BX and from that obtain the line segment BC of length 12 cm.
  2. Construct ray BY such that ∠YBC = 90°.
  3. Taking B as centre and radius 18 cm, draw an arc to intersect BY at M.
  4. Draw line segment CM. Draw the perpendicular bisector of CM to intersect BM at A.
  5. Draw line segment AC.
    Then, ∆ ABC is the require triangle in which ∠B is a right angle, BC = 12 cm and AB + AC = 18 cm.

PSEB 9th Class English Letter Writing

Punjab State Board PSEB 9th Class English Book Solutions English Letter Writing Exercise Questions and Answers, Notes.

PSEB 9th Class English Letter Writing

Important Applications

Application For Marriage Leave

Suppose you are Gopal Singh. You are a student of IX-A class of A.S. High School, Khanna. Write an application to the Headmaster of your school for marriage leave.
Answer:
The Headmaster
A.S. High School
Khanna
Sir
I beg to say that my elder brother’s marriage takes place next week. I have much work to do. So I cannot come to school. Kindly grant me leave for five days. I shall be very thankful to you for this kindness.
Yours obediently
Gopal Singh
Roll No. 25
IX-A
15 March 20_ _.

PSEB 9th Class English Letter Writing

Application For Leave
Due To Urgent Work

Suppose you are Gopal. You are a student of IX-A class of A.B. Sr. Sec. School, Ludhiana.You have an urgent piece of work at home. Write an application for leave to your Principal.
Answer:
The Principal
A.B. Sr. Sec. School
Ludhiana
Sir.
I beg to say that I have an urgent piece of work at home. So I cannot come to school. Kindly grant me leave for today. I shall be thankful to you for this kindness.
Yours obediently
Gopal
Roll No. 25
IX-A
5 March 20_ _.

Application For Remission Of Fine

Suppose you are Satish Kumar. You are a student of IX-B class of Govt. High School, Amritsar. Write an application to your Headmaster for the remission of fine.
Answer:
The Headmaster
Govt. High School.
Amritsar
Sir
Our English teacher gave us a test on Monday. That day, I was suffering from high fever. So I could not take the test. The teacher fined me ten rupees. I wanted to take the test, but couldn’t due to my illness. Kindly remit my fine and oblige.
Yours obediently
Satish Kumar
Roll No. 52
IX-B
5 February 20_ _.

Application For Full Fee-Concession

Suppose you are Sham Singh. You are a student of IX-B class of Govt. High School, Ludhiana. Write an application to the Headmaster of your school, requesting him to grant you full fee-concession.
Answer:
The Headmaster
Govt. High School !
Ludhiana
Sir
I am a student of IX-B of your school. My father is a peon. His pay is very small. He cannot pay my school fees. I am good at my studies. I am also a member of the Football Eleven. My teachers are pleased with me. I was a free student last year. Kindly grant me full fee-concession this year also. I shall be thankful to you for this kindness.
Yours obediently
Sham Singh
Roll. No. 25
IX-B
4 March 20_ _.

PSEB 9th Class English Letter Writing

Application For School Leaving Certificate

Suppose you are Anil Kumar. You are a student of IX-E class of A.B.C. High School, Moga. Write an application to the Headmaster of your school to issue your school leaving certificate.
Answer:
The Headmaster
A.B.C. High School
Moga
Sir
I beg to say that I am a student of IX-E of your school. My father has been transferred to Shimla. My parents are leaving for Shimla next week. I cannot stay here alone. I am sorry to leave such a good school, but I can’t help it. My father has signed the application. Kindly issue me my school leaving certificate and oblige.
Yours obediently
Anil Kumar
Roll No. 32
IX-E
15 April 20_ _.

Application For Change Of Section

Suppose your name is Robin. You are a student of IX-B class of Guru Nanak Public School, Ludhiana. Write an application to the Principal of your school, requesting him to change your section.
Answer:
The Principal
Guru Nanak Public School
Ludhiana
Sir
I am a student of IX-B of your school. All my friends are in Section A of class IX. Some boys of IX-A live in our street. They can help me whenever I am unable to attend school. They can help me in other ways also. Kindly shift my name from IX-B to X-A and oblige.
Thanking you
Yours obediently
Robin
IX-B
15 March 20_ _.

PSEB 9th Class English Letter Writing

Permission To Pay The Fees Late :

Suppose you are Charanjit Singh. You are a student of IX-A class of Govt. High School, Khanna. Write an application to the Headmaster of your school requesting him to permit you to pay your fees for the month late by ten days.
Answer:
The Headmaster
Govt. High School
Khanna
Sir
I beg to say that I am a student of IX-A of your school. Tomorrow is the fee day and I am unable to pay it. My father has gone to Delhi. He will come back in ten days. Kindly allow me to pay my fees late by ten days.
Thanking you
Yours obediently
Charanjit Singh
IX-A
9 March 20 – -.

Permission To Go On A Historical Tour

Suppose you are Pardeep Sikka. You are a student of Ix-B class of Govt. Senior Secondary School, Ludhiana. Write an application to your Principal, requesting him to permit your class to go on a historical tour.
Answer:
The Principal
Govt. Senior Secondary School
Ludhiana
Sir
Our school is closing for the summer vacation next week. We, the students of class IX, want to go on a historical tour. We want to see the Taj Mahal. We also want to see Fatehpur Sikri. On our way back, we want to go round Delhi also. The trip will be very useful for us as students of History. It will add to our knowledge. Kindly allow us and also help us to arrange this trip.
Yours obediently
Pardeep Sikka
(Monitor, Class IX-B)
9 March 20_ _.

PSEB 9th Class English Letter Writing

Important Letter:

To Father For Money
Suppose you are Surjit Singh, living in the boarding house of your school. Write a letter to your father, requesting him to send you money to pay the examination fee.
Answer:
24 Boarding House
Arya High School
Nawan Shahar
2 February 20_ _.
47 Deep Nagar
Banga
My dear Father Our annual examination comes off in the month of March. We have filled in our admission forms. I have to deposit the examination fee. The last date is 15th February. I have also to pay the school fee. Please send me two hundred rupees. With love and respect to you and dear mother.
Yours affectionately
Surjit Singh

Invitation To Brother’s Marriage

Suppose you are Manish Kumar. You live at 35, Main Bazaar, Amritsar. Write a letter to your friend, inviting him to your brother’s marriage.
Answer:
35 Main Bazaar
Amritsar
4 March 20_ _.
45 Mall Road
Shimla
My Dear Kundan
You will be glad to know that the marriage of my elder brother comes off on March 19, 20_ _. The marriage party will leave for Delhi early in the morning that day. We shall stay in Delhi for two days. I want you to join the marriage party. You know that Delhi is a historical city. There are many buildings worth seeing. We will see the Red Fort, the Qutub Minar and the Jantar Mantar. Mohan and Sohan are also coming. They will reach here on Sunday. We will have good time together. I hope that you will reach in time.
Yours sincerely
Manish Kumar

PSEB 9th Class English Letter Writing

Explaining The Cause Of Your Failure

Imagine you are Kishore. You live at 21, Model Town, Hoshiarpur. Write a letter to your father, explaining the cause of your failure and promising to do better in the Annual Examination.
Answer:
21 Model Town
Hoshiarpur
17 March 20_ _.
53 Malik Road
Patiala
My dear Father I am very sorry to inform you that I have failed in the last House Examination. I fail in English, Maths and Science. But believe me, father, I am not to blame for it. My failure is not due to any carelessness on my part. I put in hard work. But as ill luck would have it, I fell ill just before the examination. I had high fever. I could not revise my courses. So I was unable to do my papers well. Dear Father, I promise to do better in the Annual Examination. I request you not to mind my failure.
Your loving son
Kishore

To Father About Your Studies

Imagine you are Harinder Singh. You live in the boarding house. Your father wants to know . about your progress at school. Write a letter to him, telling him how you are getting on at school.
Answer:
Boarding House
D.A.V. School
Phagwara
15 March 20_ _.
157 Model Town
Amritsar
My dear Father I am very glad to receive your loving letter. You have asked me about how I am getting on at school. You will be glad to learn that I am quite happy here. I have made some good friends. They are hard-working and gentle. The warden of our hostel is very nice to me. I don’t feel lonely here. As for my studies, I am doing quite well. We are having a test next week. I hope to do very well in English and Mathematics. In other subjects, too, I am doing well. I take interest in games also. I have become a member of the hockey eleven. I attend the playground regularly.
With regards
Yours affectionately
Harinder Singh.

PSEB 9th Class English Letter Writing

Advice To Take Part In Games

Suppose you are Varun. You live at 18, Shakti Nagar, Sangrur. Write a letter to your younger brother, scolding him for not taking part in games.
Answer:
18 Shakti Nagar
Sangrur
19 February 20 – -.
2 Nehru Market
Shimla
My dear Raman
I have just received a letter from Sushma. I am sorry to learn that you are gone very weak in health. You often fall ill also. No doubt, you are doing quite well in studies. But dear brother, this is not good. Overwork will tell upon your health. You must know that games are as useful as studies. They make us active and smart. They keep us healthy. They teach us many good habits. So you must take part in games. I trust you will act upon my advice.
With love
Your loving brother
Varun.

Inviting A Friend To Your Birthday Party

Suppose you are Baljit Singh living at 46, Model Town, Jalandhar City. Invite your friend Manoj to your birthday party.
Answer:
46 Model Town
Jalandhar City
5 March 20 _ _.
14 New Colony
Gurdaspur
My dear Manoj
My birthday is on 12th March. I am inviting all my friends. You must come. We will have a big party. My father is getting a big cake for me. There will be ice cream, biscuits and fruit to eat. Cold drinks will also be served. It will be a nice time to eat, drink and dance together. After the party, we shall go to the rose garden. There we shall play games. We shall also enjoy a ride in the mini-train. Please do come.
With love
Yours sincerely
Baljit Singh.

Invitation To Sister’s Marriage

Imagine you are Harpreet. Write a letter to your friend, inviting him to your sister’s wedding.
Answer:
36 Nehru Nagar
Ludhiana
2 Feb. 20 _ _.
602 Kundan Puri
Dalhousie
My dear Sanjay
You will be glad to know that my elder sister’s marriage comes off on Feb. 16. My sister is very lucky. She has got a very good match. Her in-laws are a very respectable family. They belong to Delhi. The bridegroom is a doctor. As the day of marriage is drawing near, we are becoming more and more busy. The time is short. All preparations are yet to be made. I need your help. You should reach here as soon as possible. I shall be glad to see you here.
With love
Yours sincerely
Harpreet.

PSEB 9th Class English Letter Writing

Congratulating On Recovery From Illness

Suppose you are Parmvir. You live at Kamala Niwas, the Mall, Patiala. Write a letter to your friend, Satish, expressing your sense of relief at his recovery from a long illness.
Answer:
Kamala Niwas
The Mall
Patiala
15 May 20_ _.
102 Ashok Nagar
Ludhiana.
Dear Satish
I am very glad to learn that you have recovered from your illness. I heartily congratulate you on your recovery. I was so unhappy when I heard that you were down with typhoid. Thank God that you have got well. Please take complete rest for some days more. Be very careful about your diet now. Follow the advice of your doctor. Take only milk and fruit for some days. When you pick up strength, do go out for a walk in the mornings. It will do you a lot of good. I shall come to see you on Sunday.
With best wishes
Yours sincerely
Parmvir.

Invitation For Summer Vacation

Suppose you are Sohan. You live at 234, Mohan Pura, Phagwara. Write a letter to your friend, asking him to spend a part of his summer vacation with you.
Answer:
234 Mohan Pura
Phagwara
18 June 20 _ _.
15 Naya Bazaar
Amritsar
My dear Gopal
I am very glad to know that your school also has broken up for the summer vacation. We are going to Shimla. I invite you to spend your vacation with us at Shimla. Shimla is a beautiful hill station. There the air is cool and bracing. We shall go round the various beauty spots there. Hiking among the mountains has a joy of its own. We shall have long walks on the hills. We shall have a good time together. My parents will be glad to have you with us. We will leave for Shimla on 25 June. Kindly write me the time and date of your arrival.
Yours sincerely
Sohan.

Sympathising On Failure

Imagine you are Kamal. You live at 15, New Colony, Jalandhar. Write a letter to your friend who has failed in the examination, asking him not to lose heart but to try again.
Answer:
15 New Colony
Jalandhar
18 March 20 _ _.
370 Nai Basti
Ambala
Dear Ram
I am sad to learn that you have failed in the 8th class examination. In fact, your failure didn’t surprise me much. You did your best. But you fell ill just before your examination. The doctor had advised you complete rest yet you appeared in the examination. Please don’t lose heart. After all you are not to blame. Work hard for the next year. God will bless you with success next time.
Yours sincerely
Kamal.

PSEB 9th Class English Letter Writing

To Landlord For Repairs

Suppose you are Pardeep Kumar. You live at 554, Shivaji Nagar, Ludhiana. Write a letter to your landlord for getting the house repaired.
Answer:
554 Shivaji Nagar
Ludhiana
15 March 20_ _.
102 Shastri Nagar
Ludhiana
Dear Mr. Gupta
I beg to draw your kind attention to the bad condition of your house I am living in. There are big cracks in the walls. The roofs leak during the rains. The whitewash is falling off. Most of the windowpanes are broken. The kitchen door can give way any moment.Last year, many of our household articles were spoiled by rain. I reported the fact to you. You promised to effect the repairs before the next rainy season. Now the rainy season is about to set in. So I request you to effect the necessary repairs.
Yours truly
Pardeep Kumar

Complaint Against The Postman

Imagine you are Ram. You live at 44, Railway Road, Amritsar. Write a letter to the Postmaster, bringing to his notice the irregular delivery of your letters.
Answer:
44 Railway Road
Amritsar
9 March 20 _ _.
The Postmaster
General Post Office
Amritsar
Sir
I am very sorry to report that my letters are not properly delivered to me. Ram Lal, the postman of our area, is very careless. Often he comes very late. He does not do his duty honestly. On the outer wall of my house, I have put up a letter-box. It bears my name. But the postman never puts my letters into this box. He often throws them in at the gate. Sometimes he hands them to the children in the street. Many important letters are thus lost. Kindly look into the matter and take suitable action.
Yours faithfully
Ram

Complaint About Insanitation

Imagine you are Amar Singh. You live at 1035, Model Town, Patiala. Write a letter to the Health Officer of your city, complaining about the insanitary condition of your locality.
Answer:
1035 Model Town
Patiala
16 March 20_ _.
The Health Officer
Nagar Nigam
Patiala
Sir.
I beg to draw your attention to the insanitary condition of our street. Mainly poor people live in this area. Perhaps, that is why, no Sanitary Inspector has ever visited it. There are very few proper drains here. These drains are not cleaned regularly. They are never flushed with water. No dustbins have been provided. People throw all their refuse here and there. Flies and mosquitoes buzz about. All this gives this street a very dirty look. I hope you will surely take suitable action to improve the sanitary condition of our street.
Thanking you
Yours faithfully
Amar Singh.

About Loss Of Bicycle

Imagine you are Onkar Verma. You are living at 70, Adarsh Nagar, Jalandhar. Report to the police about the loss of your bicycle.
Answer:
70 Adarsh Nagar
Jalandhar
25 August 20 _ _.
The Station House Officer Division No. 1 Jalandhar City Sir I want to report the loss of my bicycle. Its make is Atlas. I went to the local D.C.M. store at 4 p.m. yesterday. I came out after half an hour. I found my cycle missing. I asked many persons, but no one could give me any clue. Mine is a new cycle. I purchased it only last month. It is of red colour. Its number is D – 4144207. It has a carrier and a bell. Its chain cover bears my name. Kindly help me to find my cycle.
Yours faithfully
Onkar Verma

PSEB 9th Class English Letter Writing

Ordering Books

Write a letter to a bookseller, ordering books by V.P.P.
Answer:
Baldev Book Shop
Model Town
Sirsa
13 July 20 _ _.
Messrs Malhotra Book Depot Railway Road Jalandhar City Dear Sirs Kindly send us the following books by V.P.P. All the books should be of the latest edition. We need them immediately since they are in great demand. Please send them at your earliest.
1. Modern English Grammar (Class X) 40 copies
2. MBD Physics (Class X) …………… 30 copies
3. MBD Chemistry (Class X) ………… 50 copies
4. MBD Mathematics (Class X) …………….. 40 copies
Yours sincerely
Baldev Krishan
(Partner)