1. Calculation of Standard Deviation for ungrouped data
(i) Direct Method
(ii) Mean method
(iii) Assumed Mean method
(iv) Step deviation method
2. Calculation of Standard deviation for continuous frequency distribution
(i) Mean method
(ii) Assumed Mean method
(iii) Step deviation method
1. Calculation of Standard Deviation for ungrouped data
(i) Direct Method
Note
· While computing standard deviation, arranging data in ascending order is not mandatory.
· If the data values are given directly then to find standard deviation we can use the formula σ =
· If the data values are not given directly but the squares of the deviations from the mean of each observation is given then to find standard deviation we can use the formula σ =
Example 8.4 The number of televisions sold in each day of a week are 13, 8, 4, 9, 7, 12, 10.
Find its standard deviation.
Solution
(ii) Mean method
Another convenient way of finding standard deviation is to use the following formula.
Standard deviation (by mean method) σ =
If di = xi –
Example 8.5 The amount of rainfall in a particular season for 6 days are given as 17.8 cm, 19.2 cm, 16.3 cm, 12.5 cm, 12.8 cm and 11.4 cm. Find its standard deviation.
Solution Arranging the numbers in ascending order we get, 11.4, 12.5, 12.8, 16.3, 17.8, 19.2.
Number of observations n = 6
(iii) Assumed Mean method
When the mean value is not an integer (since calculations are very tedious in decimal form) then it is better to use the assumed mean method to find the standard deviation.
Let x 1 , x2, x 3 , ..., xn be the given data values and let
Let di be the deviation of xi from the assumed mean A, which is usually the middle value or near the middle value of the given data.
di= xi − A gives, xi = di + A ...(1)
Σdi= Σ(xi −A)
= Σxi −(A + A + A + . . . to n times)
Σdi = Σxi – A × n
Example 8.6 The marks scored by 10 students in a class test are 25, 29, 30, 33, 35, 37, 38, 40, 44, 48. Find the standard deviation.
Solution The mean of marks is 35.9 which is not an integer. Hence we take assumed mean, A = 35, n = 10 .
(iv) Step deviation method
Let x 1 , x2, x 3 ,...xn be the given data. Let A be the assumed mean.
Let c be the common divisor of x i - A .
Note
We can use any of the above methods for finding the standard deviation
Example 8.7 The amount that the children have spent for purchasing some eatables in one day trip of a school are 5, 10, 15, 20, 25, 30, 35, 40. Using step deviation method, find the standard deviation of the amount they have spent.
Solution We note that all the observations are divisible by 5. Hence we can use the step deviation method. Let the Assumed mean A = 20, n = 8.
Example 8.8 Find the standard deviation of the following data 7, 4, 8, 10, 11. Add 3 to all the values then find the standard deviation for the new values.
Solution Arranging the values in ascending order we get, 4, 7, 8, 10, 11 and n = 5
When we add 3 to all the values, we get the new values as 7,10,11,13,14.
From the above, we see that the standard deviation will not change when we add some fixed constant to all the values.
Example 8.9 Find the standard deviation of the data 2, 3, 5, 7, 8. Multiply each data by 4. Find the standard deviation of the new values.
Solution Given, n = 5
When we multiply each data by 4, we get the new values as 8, 12, 20, 28, 32.
From the above, we see that when we multiply each data by 4 the standard deviation also get multiplied by 4.
Example 8.10 Find the mean and variance of the first n natural numbers.
Solution
Calculation of Standard deviation for grouped data
(i) Mean method
Example 8.11
48 students were asked to write the total number of hours per week they spent on watching television. With this information find the standard deviation of hours spent for watching television.
Solution
(ii) Assumed Mean Medthod
Let x 1 , x2, x 3 , ...xn be the given data with frequencies f1 , f2, f3 , ... fn respectively. Let x be their mean and A be the assumed mean..
Example 8.12
The marks scored by the students in a slip test are given below.
Find the standard deviation of their marks.
Solution
Let the assumed mean, A = 8
2. Calculation of Standard deviation for continuous frequency distribution
(i) Mean method
Standard deviation
fi = Frequency of the i th class.
(ii) Shortcut method (or) Step deviation method
To make the calculation simple, we provide the following formula. Let A be the assumed mean, xi be the middle value of the ith class and c is the width of the class interval.
Example 8.13
Marks of the students in a particular subject of a class are given below.
Find its standard deviation.
Solution
Let the assumed mean, A = 35, c = 10
Example 8.14
The mean and standard deviation of 15 observations are found to be 10 and 5 respectively. On rechecking it was found that one of the observation with value 8 was incorrect. Calculate the correct mean and standard deviation if the correct observation value was 23?
Solution
Wrong observation value = 8, Correct observation value = 23.
Correct total = 150 − 8 + 23 = 165
Page 2
Exercise 8.1
1. Find the range and coefficient of range of the following data.
(i) 63, 89, 98, 125, 79, 108, 117, 68
(ii) 43.5, 13.6, 18.9, 38.4, 61.4, 29.8
2. If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the largest value.
3. Calculate the range of the following data.
4. A teacher asked the students to complete 60 pages of a record note book. Eight students have completed only 32, 35, 37, 30, 33, 36, 35 and 37 pages. Find the standard deviation of the pages yet to be completed by them.
5. Find the variance and standard deviation of the wages of 9 workers given below: ₹310, ₹290, ₹320, ₹280, ₹300, ₹290, ₹320, ₹310, ₹280.
6. A wall clock strikes the bell once at 1 o’ clock, 2 times at 2 o’ clock, 3 times at 3 o’ clock and so on. How many times will it strike in a particular day. Find the standard deviation of the number of strikes the bell make a day.
7. Find the standard deviation of first 21 natural numbers.
8. If the standard deviation of a data is 4.5 and if each value of the data is decreased by 5, then find the new standard deviation.
9. If the standard deviation of a data is 3.6 and each value of the data is divided by 3, then find the new variance and new standard deviation
10. The rainfall recorded in various places of five districts in a week are given below.
Find its standard deviation.
11. In a study about viral fever, the number of people affected in a town were noted as
Find its standard deviation.
12. The measurements of the diameters (in cms) of the plates prepared in a factory are given below. Find its standard deviation.
13. The time taken by 50 students to complete a 100 meter race are given below. Find its standard deviation.
14. For a group of 100 candidates the mean and standard deviation of their marks were found to be 60 and 15 respectively. Later on it was found that the scores 45 and 72 were wrongly entered as 40 and 27. Find the correct mean and standard deviation.
15. The mean and variance of seven observations are 8 and 16 respectively. If five of these are 2, 4, 10, 12 and 14, then find the remaining two observations.
Answers:
1.(i) 62; 0.33 (ii) 47.8; 0.64
2. 50.2
3. 250
4. 2.34
5. 222.22, 14.91
6. 6.9
7. 6.05
8. 4.5
9. 1.44, 1.2
10. 7.76
11. 14.6
12. 6
13. 1.24
14. 60.5, 14.61
15. 6 and 8
Page 3
Coefficient of Variation
Comparison of two data in terms of measures of central tendencies and dispersions in some cases will not be meaningful, because the variables in the data may not have same units of measurement.
For example consider the two data
Here we cannot compare the standard deviations 1. 5kg and ₹21.60. For comparing two or more data for corresponding changes the relative measure of standard deviation, called “Coefficient of variation” is used.
Coefficient of variation of a data is obtained by dividing the standard deviation by the arithmetic mean. It is usually expressed in terms of percentage. This concept is suggested by one of the most prominent Statistician Karl Pearson.
Thus, coefficient of variation of first data (C.V1) = σ1/x1 ×100%
and coefficient of variation of second data (C.V2) = σ2/ x2 × 100%
The data with lesser coefficient of variation is more consistent or stable than the other data. Consider the two data
If we compare the mean and standard deviation of the two data, we think that the two datas are entirely different. But mean and standard deviation of B are 60% of that of A. Because of the smaller mean the smaller standard deviation led to the misinterpretation.
To compare the dispersion of two data, coefficient of variation = σ/x ×100%
The coefficient of variation of A = 191. 5/700 ×100% = 27. 4%
The coefficient of variation of B = 114. 9/420 ×100% = 27. 4%
Thus the two data have equal coefficient of variation. Since the data have equal coefficient of variation values, we can conclude that one data depends on the other. But the data values of B are exactly 60% of the corresponding data values of A. So they are very much related. Thus, we get a confusing situation.
To get clear picture of the given data, we can find their coefficient of variation. This is why we need coefficient of variation.
Example 8.15
The mean of a data is 25.6 and its coefficient of variation is 18.75. Find the standard deviation.
Solution
Mean
Coefficient of variation, C.V. = σ/
Example 8.16
The following table gives the values of mean and variance of heights and weights of the 10th standard students of a school.
Which is more varying than the other?
Solution
For comparing two data, first we have to find their coefficient of variations
Mean
Therefore standard deviation σ1 = 8. 5
Coefficient of variation
Mean
Standard deviation σ2 = 5. 3kg
Coefficient of variation
= 11. 40% (for weights)
C .V1 = 5.48% and C .V2 = 11.40%
Since C .V2 > C .V1 , the weight of the students is more varying than the height.
Example 8.17
The consumption of number of guava and orange on a particular week by a family are given below.
Which fruit is consistently consumed by the family?
Solution
First we find the coefficient of variation for guavas and oranges separately.
C .V1 = 23.54% , C .V2 = 65.50% Since, C .V1<C .V2 , we can conclude that the consumption of guavas is more consistent than oranges.
Page 4
Exercise 8.2
1. The standard deviation and mean of a data are 6.5 and 12.5 respectively. Find the coefficient of variation.
2. The standard deviation and coefficient of variation of a data are 1.2 and 25.6 respectively. Find the value of mean.
3. If the mean and coefficient of variation of a data are 15 and 48 respectively, then find the value of standard deviation.
4. If n = 5 ,
5. Find the coefficient of variation of 24, 26, 33, 37, 29, 31.
6. The time taken (in minutes) to complete a homework by 8 students in a day are given by 38, 40, 47, 44, 46, 43, 49, 53. Find the coefficient of variation.
7. The total marks scored by two students Sathya and Vidhya in 5 subjects are 460 and 480 with standard deviation 4.6 and 2.4 respectively. Who is more consistent in performance?
8. The mean and standard deviation of marks obtained by 40 students of a class in three subjects Mathematics, Science and Social Science are given below.
Which of the three subjects shows highest variation and which shows lowest variation in marks?
9. The temperature of two cities A and B in a winter season are given below.
Find which city is more consistent in temperature changes?
Answers:
1. 52%
2. 4.69
3. 7.2
4. 180.28%
5. 14.4%
6. 10.07%
7.Vidhya
8. Science, Social
9. City A
Page 5
Probability
Few centuries ago, gambling and gaming were considered to be fashionable and became widely popular among many men. As the games became more complicated, players were interested in knowing the chances of winning or losing a game from a given situation. In 1654, Chevalier de Mere, a French nobleman with a taste of gambling, wrote a letter to one of the prominent mathematician of the time, Blaise Pascal, seeking his advice about how much dividend he would get for a gambling game played by paying money. Pascal worked this problem mathematically but thought of sharing this problem and see how his good friend and mathematician Pierre de Fermat could solve. Their subsequent correspondences on the issue represented the birth of Probability Theory as a new branch of mathematics.
Random Experiment
A random experiment is an experiment in which
(i) The set of all possible outcomes are known (ii) Exact outcome is not known.
Example : 1. Tossing a coin. 2. Rolling a die. 3. Selecting a card from a pack of 52 cards.
Sample space
The set of all possible outcomes in a random experiment is called a sample space. It is generally denoted by S.
Example : When we roll a die, the possible outcomes are the face numbers 1,2,3,4,5,6 of the die. Therefore the sample space is S = {1,2,3,4,5,6}
Sample point
Each element of a sample space is called a sample point.
1. Tree diagram
Tree diagram allow us to see visually all possible outcomes of an random experiment. Each branch in a tree diagram represent a possible outcome.
Illustration
(i) When we throw a die, then from the tree diagram (Fig.8.3), the sample space can be written as S = {1,2,3,4,5,6}
(ii) When we toss two coins, then from the tree diagram (Fig.8.4), the sample space can be written as S={HH,HT,TH,TT}
Example 8.18 Express the sample space for rolling two dice using tree diagram.
Solution When we roll two dice, since each die contain 6 faces marked with 1,2,3,4,5,6 the tree diagram will look like
Hence, the sample space can be written as
S= {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
Event:
In a random experiment, each possible outcome is called an event. Thus, an event will be a subset of the sample space.
Example :
Getting two heads when we toss two coins is an event.
Trial : Performing an experiment once is called a trial.
Example : When we toss a coin thrice, then each toss of a coin is a trial.
Note
Elementary event: If an event E consists of only one outcome then it is called an elementary event.
2. Probability of an Event
In a random experiment, let S be the sample space and E ⊆ S . Then if E is an event, the probability of occurrence of E is defined as
This way of defining the probability is applicable only to finite sample spaces. So in this chapter, we will be dealing problems only with finite sample spaces.
Example 8.19
A bag contains 5 blue balls and 4 green balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is (i) blue (ii) not blue.
Solution
Total number of possible outcomes n(S) = 5 + 4 = 9
(i) Let A be the event of getting a blue ball.
Number of favourable outcomes for the event A. Therefore, n(A) = 5
Probability that the ball drawn is blue. Therefore, P (A) = n(A)/ n(S) = 5/9
(ii)
Example 8.20
Two dice are rolled. Find the probability that the sum of outcomes is
(i) equal to 4
(ii) greater than 10
(iii) less than 13
Solution
When we roll two dice, the sample space is given by
S = { (1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6) }; n (S) = 36
(i) Let A be the event of getting the sum of outcome values equal to 4.
Then A = {(1,3),(2,2),(3,1)}; n (A) = 3 .
Probability of getting the sum of outcomes equal to 4 is P (A) = n(A)/n(S) = 3/36 =1/12
(ii) Let B be the event of getting the sum of outcome values greater than 10.
Then B = {(5,6),(6,5),(6,6)}; n (B) = 3
Probability of getting the sum of outcomes greater than 10 is P (B) = n(B)/n(S) = 3/36 =1/12
(iii) Let C be the event of getting the sum of outcomes less than 13. Here all the outcomes have the sum value less than 13. Hence C = S.
Therefore, n (C ) = n (S) = 36
Probability of getting the total value less than 13 is P (C ) = n(C)/n(S) = 36/36 = 1.
Example 8.21
Two coins are tossed together. What is the probability of getting different faces on the coins?
Solution
When two coins are tossed together, the sample space is
S = { HH, HT, TH, TT } ; n(S) = 4
Let A be the event of getting different faces on the coins.
A = { HT,TH } ; n(A) = 2
Probability of getting different faces on the coins is P(A) =n(A)/n(S) = 2/4 = ½
Example 8.22
From a well shuffled pack of 52 cards, one card is drawn at random. Find the probability of getting
(i) red card
(ii) heart card
(iii) red king
(iv) face card
(v) number card
Solution
n (S) = 52
(i) Let A be the event of getting a red card.
n (A) = 26
Probability of getting a red card is
P (A) = 26/52 = 1/2
(ii) Let B be the event of getting a heart card.
n (B) = 13
Probability of getting a heart card is P
P(B) = n(B)/n(S) = 13/52 = 1/4
(iii) Let C be the event of getting a red king card. A red king card can be either a diamond king or a heart king.
n (C ) = 2
Probability of getting a red king card is
P(C) = n(C)/n(S) = 12/52 = 1/26
(iv) Let D be the event of getting a face card. The face cards are Jack (J), Queen (Q), and King (K).
n(D) = 4 ×3 = 12
Probability of getting a face card is
P (D) = n(D)/n(S) = 12/52 = 3/13
(v) Let E be the event of getting a number card. The number cards are 2, 3, 4, 5, 6, 7, 8, 9 and 10.
n (E) = 4 ×9 = 36
Probability of getting a number card is
P (E) = n(E)/n(S) = 36/52 = 9/13
Example 8.23
What is the probability that a leap year selected at random will contain 53 saturdays. (Hint: 366 = 52 ×7 + 2 )
Solution
A leap year has 366 days. So it has 52 full weeks and 2 days. 52 Saturdays must be in 52 full weeks.
The possible chances for the remaining two days will be the sample space.
S = {(Sun-Mon, Mon-Tue, Tue-Wed, Wed-Thu, Thu-Fri, Fri-Sat, Sat-Sun)}
n (S) = 7
Let A be the event of getting 53rd Saturday.
Then A = {Fri-Sat, Sat-Sun}; n (A) = 2
Probability of getting 53 Saturdays in a leap year is P ( A ) = n (A)/ n (S) = 2/7
Thinking Corner: What will be the probability that a non - leap year will have 53 Saturdays?
Example 8.24 A die is rolled and a coin is tossed simultaneously. Find the probability that the die shows an odd number and the coin shows a head.
Solution
Sample space
S = {1H,1T,2H,2T,3H,3T,4H,4T,5H,5T,6H,6T};
n(S) = 12
Let A be the event of getting an odd number and a head.
A = {1H, 3H, 5H}; n(A) = 3
P (A) = n (A)/ n(S) = 3/12 = 1/4
Example 8.25
A bag contains 6 green balls, some black and red balls. Number of black balls is as twice as the number of red balls. Probability of getting a green ball is thrice the probability of getting a red ball. Find (i) number of black balls (ii) total number of balls.
Solution
Number of green balls is n(G) = 6
Let number of red balls is n(R) = x
Therefore, number of black balls is n(B) = 2x
Total number of balls n(S) = 6 + x + 2x = 6 + 3x
It is given that, P (G) = 3 × P(R)
6/ (6+3x) = 3 × x/(6 + 3x)
3x = 6 gives, x = 2
(i) Number of black balls = 2 × 2 = 4
(ii) Total number of balls = 6 +(3 × 2) = 12
Example 8.26
A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1, 2, 3, …12. What is the probability that it will point to
(i) 7
(ii) a prime number
(iii) a composite number?
Solution
Sample space S = {1,2,3,4,5,6,7,8,9,10,11,12}; n(S) = 12
(i) Let A be the event of resting in 7. n(A)=1
P (A) = n(A)/n(S) = 1/12
(ii) Let B be the event that the arrow will come to rest in a prime number.
B = {2,3,5,7,11}; n (B) = 5
P (B) = n(B)/n(S) = 5/12
(iii) Let C be the event that arrow will come to rest in a composite number.
C = {4,6,8,9,10,12}; n (C ) =6
P (C) = n(C)/n(S) = 6/12 = 1/2
Page 6
1. Write the sample space for tossing three coins using tree diagram.
2. Write the sample space for selecting two balls from a bag containing 6 balls numbered 1 to 6 (using tree diagram).
3. If A is an event of a random experiment such that P(A) : P (
3.B
4. A coin is tossed thrice. What is the probability of getting two consecutive tails?
5. At a fete, cards bearing numbers 1 to 1000, one number on one card are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square number greater than 500, the player wins a prize. What is the probability that (i) the first player wins a prize (ii) the second player wins a prize, if the first has won?
6. A bag contains 12 blue balls and x red balls. If one ball is drawn at random (i) what is the probability that it will be a red ball? (ii) If 8 more red balls are put in the bag, and if the probability of drawing a red ball will be twice that of the probability in (i), then find x.
7. Two unbiased dice are rolled once. Find the probability of getting
(i) a doublet (equal numbers on both dice)
(ii) the product as a prime number
(iii) the sum as a prime number
(iv) the sum as 1
8. Three fair coins are tossed together. Find the probability of getting
(i) all heads
(ii) atleast one tail
(iii) atmost one head
(iv) atmost two tails
9. Two dice are numbered 1,2,3,4,5,6 and 1,1,2,2,3,3 respectively. They are rolled and the sum of the numbers on them is noted. Find the probability of getting each sum from 2 to 9 separately.
10. A bag contains 5 red balls, 6 white balls, 7 green balls, 8 black balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is
(i) White
(ii) black or red
(iii) not white
(iv) neither white nor black
11. In a box there are 20 non-defective and some defective bulbs. If the probability that a bulb selected at random from the box found to be defective is 3/8 then, find the number of defective bulbs.
12. The king and queen of diamonds, queen and jack of hearts, jack and king of spades are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is
(i) a clavor
(ii) a queen of red card
(iii) a king of black card
13. Some boys are playing a game, in which the stone thrown by them landing in a circular region (given in the figure) is considered as win and landing other than the circular region is considered as loss. What is the probability to win the game?
14. Two customers Priya and Amuthan are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another day. What is the probability that both will visit the shop on
(i) the same day
(ii) different days
(iii) consecutive days?
15. In a game, the entry fee is 150. The game consists of tossing a coin 3 times. Dhana bought a ticket for entry. If one or two heads shows she gets her entry fee back. If she throwns 3 heads she receives double the entry fees. Otherwise she will lose. Find the probability that she (i) gets double entry fee (ii) just gets her entry fee (iii) loses the entry fee.
Answers:
Page 7
Algebra of Events
In a random experiment, let S be the sample space. Let A ⊆ S and B ⊆ S be the events in S. We say that
(i) (A Ո B) is an event that occurs only when both A and B occurs.
(ii) (A U B) is an event that occurs when either one of A or B occurs.
(iii)
Note:
· A ∩
· A∪
· If A, B are mutually exclusive events, then P (A ∪ B) = P(A) + P (B)
· P (Union of mutually exclusive events) = ∑( Probability of events)
Thorem 1
If A and B are two events associated with a random experiment, then prove that
(i) P (A Ո
(ii) P (
Proof
(i) By Distributive property of sets,
Therefore, the events A Ո B and A Ո
(ii) By Distributive property of sets,
Therefore, the events A Ո B and
Page 8
Addition Theorem of Probability
(i) If A and B are any two events then
P (A ∪ B ) = P(A) + P(B ) −P(A ∩ B)
(ii) If A,B and C are any three events then
P (A ∪ B ∪ C) = P (A) + P (B) + P (C) − P (A ∩ B ) − P(B ∩C) −P (A ∩C ) + P(A ∩ B ∩C)
Proof
(i) Let A and B be any two events of a random experiment with sample space S.
From the Venn diagram, we have the events only A, A Ո B and only B are mutually exclusive and their union is A U B
Therefore, P (A U B) = P[ (only A) ∪(A ∩ B) ∪ (only B) ]
= P(only A) +P (A ∩ B) + P(only B)
= [P (A) −P (A ∩ B )] + P(A ∩ B) +[P (B ) − P (A ∩ B)]
P (A U B) = P (A) + P (B ) − P (A ∩ B)
(ii) Let A, B, C are any three events of a random experiment with sample space S.
Let D = B ∪C
P (A U B UC) = P (A ∪ D)
= P (A) + P (D ) − P (A ∩ D)
= P (A) + P (B ∪ C ) − P[A ∩ (B ∪C)]
= P (A) + P (B) + P(C ) − P(B ∩C) − P [(A ∩ B ) ∪ (A ∩C)]
= P (A) + P (B) + P (C) − P (B ∩C ) − P(A ∩ B) − P (A ∩C ) + P[(A ∩ B) ∩ (A ∩C)]
P (A U B UC) = P (A) + P (B) + P (C) − P (A ∩ B ) − P(B ∩C) −P (C ∩ A) + P(A ∩ B ∩C)
Example 8.27
If P(A) = 0.37 , P(B) = 0.42 , P (A ∩ B) = 0.09 then find P (A U B) .
Solution
P(A) = 0.37 , P(B) = 0.42 , P (A ∩ B) = 0.09
P (A U B) = P (A) + P (B ) − P (A ∩ B)
P (A U B) = 0.37 + 0.42 − 0.09 = 0. 7
Example 8.28
What is the probability of drawing either a king or a queen in a single draw from a well shuffled pack of 52 cards?
Solution
Total number of cards = 52
Number of king cards = 4
Probability of drawing a king card = 4/52
Number of queen cards = 4
Probability of drawing a queen card= 4/52
Both the events of drawing a king and a queen are mutually exclusive
⇒ P (A ∪ B) = P (A) + P (B)
Therefore, probability of drawing either a king or a queen = 4/52 + 4/52 = 2/13
Example 8.29
Two dice are rolled together. Find the probability of getting a doublet or sum of faces as 4.
Solution
When two dice are rolled together, there will be 6×6 = 36 outcomes. Let S be the sample space. Then n (S) = 36
Let A be the event of getting a doublet and B be the event of getting face sum 4.
Then A = {(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}
B = {(1,3),(2,2),(3,1)}
Therefore, A Ո B = {(2,2)}
Then, n (A) = 6 , n (B) = 3 , n (A ∩ B) = 1.
Therefore, P (getting a doublet or a total of 4) = P (A U B)
P (A U B) = P (A) + P (B ) − P (A ∩ B)
= 6/36 + 3/36 – 1/36 = 8/36 = 2/9
Hence, the required probability is 2/9.
Example 8.30
If A and B are two events such thatP (A) = 1/4 , P (B) = 1/2 and P(A and B)= 1/8, find (i) P (A or B) (ii) P(not A and not B).
Solution
(i) P (A or B) = P (A U B)
= P (A) + P (B ) − P (A ∩ B)
P (A or B) = 1/4 + 1/2 – 1/8 = 5/8
(ii) P (not A and not B) = P (
= P
= 1 − P (A ∪ B)
P(not A and not B) = 1 – 5/8 = 3/8
Example 8.31
A card is drawn from a pack of 52 cards. Find the probability of getting a king or a heart or a red card.
Solution
Total number of cards = 52; n(S) = 52
Let A be the event of getting a king card. n(A) =4
Let B be the event of getting a heart card. n(B) =13
Let C be the event of getting a red card. n(C) =26
P (A Ո B) = P (getting heart king) = 1/52
P (B ՈC) = P (getting red and heart)) = 13/52
P (A ՈC) = P (getting red king) = 2/52
P (A Ո B ՈC) = P (getting heart, king which is red) = 1/52
Therefore, required probability is
P (A U B UC) = P (A) + P (B) + P (C) − P (A ∩ B ) − P(B ∩C) −P (C ∩ A) + P(A ∩ B ∩C)
= 4/52 + 13/52 + 26/52 – 1/52 – 13/52 – 2/52 + 1/52 = 28/52
= 7/13
Example 8.32
In a class of 50 students, 28 opted for NCC, 30 opted for NSS and 18 opted both NCC and NSS. One of the students is selected at random. Find the probability that
(i) The student opted for NCC but not NSS.
(ii) The student opted for NSS but not NCC.
(iii) The student opted for exactly one of them.
Solution
Total number of students n (S) = 50 .
Let A and B be the events of students opted for NCC and NSS respectively.
n (A) = 28 , n (B) = 30 , n (A ∩ B) = 18
(i) Probability of the students opted for NCC but not NSS
P (A Ո
(ii) Probability of the students opted for NSS but not NCC.
P (A Ո
(iii) Probability of the students opted for exactly one of them
(Note that (A Ո
Example 8.33
A and B are two candidates seeking admission to IIT. The probability that A getting selected is 0.5 and the probability that both A and B getting selected is 0.3. Prove that the probability of B being selected is atmost 0.8.
Solution
P (A) = 0.5 , P (A ∩ B) = 0.3
We have P (A U B ) ≤ 1
P (A) + P(B) −P (A ∩ B) ≤ 1
0.5 + P (B) − 0.3 ≤ 1
P (B) ≤ 1 − 0.2
P (B) ≤ 0.8
Therefore, probability of B getting selected is atmost 0.8.
Page 9
Exercise 8.4
1. If P (A) = 2/3 , P (B) = 2/5 , P (A ∪ B) = 1/3 then find P (A Ո B) .
2. A and B are two events such that, P (A) = 0. 42, P (B) = 0.48 , and P (A ∩ B) = 0.16 .
Find
(i) P,(not A)
(ii) P,(not B)
(iii) P,(A or B)
3. If A and B are two mutually exclusive events of a random experiment and P(not A) = 0.45, P (A U B) = 0.65, then find P (B).
4. The probability that atleast one of A and B occur is 0.6. If A and B occur simultaneously with probability 0.2, then find P (
5. The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then find the probability that neither A nor B happen.
6. Two dice are rolled once. Find the probability of getting an even number on the first die or a total of face sum 8.
7. From a well-shuffled pack of 52 cards, a card is drawn at random. Find the probability of it being either a red king or a black queen.
8. A box contains cards numbered 3, 5, 7, 9, … 35, 37. A card is drawn at random from the box. Find the probability that the drawn card have either multiples of 7 or a prime number.
9. Three unbiased coins are tossed once. Find the probability of getting atmost 2 tails or atleast 2 heads.
10. The probability that a person will get an electrification contract is 3/5 and the probability that he will not get plumbing contract is 5/8. The probability of getting atleast one contract is 5/7. What is the probability that he will get both?
11. In a town of 8000 people, 1300 are over 50 years and 3000 are females. It is known that 30% of the females are over 50 years. What is the probability that a chosen individual from the town is either a female or over 50 years?
12. A coin is tossed thrice. Find the probability of getting exactly two heads or atleast one tail or two consecutive heads.
13. If A, B, C are any three events such that probability of B is twice as that of probability of A and probability of C is thrice as that of probability ofA and if P (A ∩ B) = 1/6. P (B ∩ C) = 1/4, P (A ∩ C) = 1/8, P (A ∪ B ∪C) = 9/10, P (A ∩ B ∩C) = 1/15, then find P (A), P (B) and P (C) ?
14. In a class of 35, students are numbered from 1 to 35. The ratio of boys to girls is 4:3. The roll numbers of students begin with boys and end with girls. Find the probability that a student selected is either a boy with prime roll number or a girl with composite roll number or an even roll number.
Answers:
1. 11/15
2. (i) 0.58 (ii) 0.52 (iii) 0.74
3. 0.1
4. 1.2
5. 0.2
6. 5/9
7. 1/13
8. 13/18
9. 73/280
10. 17/40
11. 1
12. 11/48, 11/24, 11/16
Page 10
Multiple choice questions
1. Which of the following is not a measure of dispersion?
(1) Range
(2) Standard deviation
(3) Arithmetic mean
(4) Variance
2. The range of the data 8, 8, 8, 8, 8 . . . 8 is
(1) 0
(2) 1
(3) 8
(4) 3
Solution
Range = L - S = 8 - 8 = 0
3. The sum of all deviations of the data from its mean is
(1) Always positive
(2) always negative
(3) zero
(4) non-zero integer
4. The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all deviations is
(1) 40000
(2) 160900
(3) 160000
(4) 30000
5. Variance of first 20 natural numbers is
(1) 32.25
(2) 44.25
(3) 33.25
(4) 30
6. The standard deviation of a data is 3. If each value is multiplied by 5 then the new variance is
(1) 3
(2) 15
(3) 5
(4) 225
7. If the standard deviation of x, y, z is p then the standard deviation of 3x + 5 , 3y + 5 , 3z + 5 is
(1) 3p + 5
(2) 3p
(3) p + 5
(4) 9p + 15
8. If the mean and coefficient of variation of a data are 4 and 87.5% then the standard deviation is
(1) 3.5
(2) 3
(3) 4.5
(4) 2.5
9. Which of the following is incorrect?
(1) P (A) > 1
(2) 0 ≤ P (A) ≤ 1
(3) P(ɸ) = 0
(4) P (A) + P (
10. The probability a red marble selected at random from a jar containing p red, q blue and r green marbles is
Ans: (2)
11. A page is selected at random from a book. The probability that the digit at units place of the page number chosen is less than 7 is
(1) 3/10
(2) 7/10
(3) 3/9
(4) 7/9
12. The probability of getting a job for a person is x/3 . If the probability of not getting the job is 2/3 then the value of x is
(1) 2
(2) 1
(3) 3
(4) 1.5
13. Kamalam went to play a lucky draw contest. 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is 1/9 , then the number of tickets bought by Kamalam is
(1) 5
(2) 10
(3) 15
(4) 20
14. If a letter is chosen at random from the English alphabets {a,b,...,z}, then the probability that the letter chosen precedes x
(1) 12/13
(2) 1/13
(3) 23/26
(4) 3/26
15. A purse contains 10 notes of ₹2000, 15 notes of ₹500, and 25 notes of ₹200. One note is drawn at random. What is the probability that the note is either a ₹500 note or ₹200 note?
(1) 1/5
(2) 3/10
(3) 2/3
(4) 4/5
Page 11
1. The mean of the following frequency distribution is 62.8 and the sum of all frequencies is 50. Compute the missing frequencies f1 and f2.
2. The diameter of circles (in mm) drawn in a design are given below.
Calculate the standard deviation.
3. The frequency distribution is given below.
4. The standard deviation of some temperature data in degree celsius (oC) is 5. If the data were converted into degree Farenheit (oF) then what is the variance?
5. If for a distribution, ∑ (x − 5) = 3, ∑(x − 5)2 = 43, and total number of observations is 18, find the mean and standard deviation.
6. Prices of peanut packets in various places of two cities are given below. In which city, prices were more stable?
7. If the range and coefficient of range of the data are 20 and 0.2 respectively, then find the largest and smallest values of the data.
8. If two dice are rolled, then find the probability of getting the product of face value 6 or the difference of face values 5.
9. In a two children family, find the probability that there is at least one girl in a family.
10. A bag contains 5 white and some black balls. If the probability of drawing a black ball from the bag is twice the probability of drawing a white ball then find the number of black balls.
11. The probability that a student will pass the final examination in both English and Tamil is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing the Tamil examination?
12. The King, Queen and Jack of the suit spade are removed from a deck of 52 cards. One card is selected from the remaining cards. Find the probability of getting (i) a diamond (ii) a queen (iii) a spade (iv) a heart card bearing the number 5.
Answers:
1. 8,12
2. 5.55
3. 7
4. 81
5. 5.17, 1.53
6. City A
7. 60, 40
8. 1/9
9. 3/4
10. 10
11. 13/20
12. (i) 13/20 (ii) 3/49 (iii) 1/49
Page 12
Points to Remember
· Range = L–S (L - Largest value, S - Smallest value)
· Coefficient of range =
· Standard deviation
· Standard deviation (ungrouped data)
· Standard deviation of first n natural numbers
· Standard deviation (grouped data)
· Coefficient of variation C.V =
· If the C.V. value is less, then the observations of corresponding data are consistent.
If the C.V. value is more then the observations of corresponding are inconsistent.
· In a random experiment, the set of all outcomes are known but exact outcome is not known.
· The set of all possible outcomes is called sample space.
· A, B are said to be mutually exclusive events if A ∩ B = ɸ
· Probability of event E is P (E) = n(E)/n(S)
(i) The probability of sure event is 1 and the probability of impossible event is 0.
(ii) 0 ≤ P (E) ≤ 1 ;(iii) P (
· If A and B are mutually exclusive events then P (A ∪ B ) = P(A) + P(B) .
(i) P (A ∩
(ii) P (A ∩
· P (A U B) = P (A) + P (B) – P (A ∩ B) , for any two events A, B.
· For any three events A, B, C
P (A U B UC) = P (A) + P (B) + P (C) − P (A ∩ B ) − P(B ∩C) −P (C ∩ A) + P(A ∩ B ∩C)
Page 13
Prose
His First Flight
Liam O’Flaherty
The young seagull was alone on his ledge. His two brothers and his sister had already flown away the day before. He had been afraid to fly with them. Somehow, when he had taken a little run forward to the brink of the ledge and attempted to flap his wings, he became afraid. The great expanse of sea stretched down beneath, and it was such a long way down – miles down. He felt certain that his wings would never support him; so he bent his head and ran away back to the little hole under the ledge where he slept at night.
Even when each of his brothers and his little sister, whose wings were far shorter than his own, ran to the brink, flapped their wings, and flew away, he failed to muster up courage to take that plunge which appeared to him so desperate. His father and mother had come around calling to him shrilly, scolding him, threatening to let him starve on his ledge, unless he flew away. But for the life of him, he could not move.
a. Why did the seagull fail to fly?
b. What did the parents do, when the young seagull failed to fly?
That was twenty-four hours ago. Since then, nobody had come near him. The day before, all day long, he had watched his parents flying about with his brothers and sister, perfecting them in the art of flight, teaching them how to skim the waves and how to dive for fish. He had, in fact, seen his older brother catch his first herring and devour it, standing on a rock, while his parents circled around raising a proud cackle. And all the morning, the whole family had walked about on the big plateau midway down the opposite cliff, laughing at his cowardice.
The sun was now ascending the sky, blazing warmly on his ledge that faced the south. He felt the heat because he had not eaten since the previous nightfall. Then, he had found a dried piece of mackerel’s tail at the far end of his ledge. Now, there was not a single scrap of food left. He had searched every inch, rooting among the rough, dirt-caked straw nest where he and his brothers and sister had been hatched. He even gnawed at the dried pieces of eggshell. It was like eating a part of himself.
c. What was the first catch of the young seagull’s older brother?
d. What did the young seagull manage to find in his search for food on the ledge?
He then trotted back and forth from one end of the ledge to the other, his long gray legs stepping daintily, trying to find some means of reaching his parents without having to fly. But on each side of him, the ledge ended in a sheer fall of precipice, with the sea beneath. And between him and his parents, there was a deep, wide crack.
Surely he could reach them without flying if he could only move northwards along the cliff face? But then, on what could he walk? There was no ledge, and he was not a fly. And above him, he could see nothing. The precipice was sheer, and the top of it was, perhaps, farther away than the sea beneath him.
He stepped slowly out to the brink of the ledge, and, standing on one leg with the other leg hidden under his wing, he closed one eye, then the other, and pretended to be falling asleep. Still, they took no notice of him. He saw his two brothers and his sister lying on the plateau dozing, with their heads sunk into their necks. His father was preening the feathers on his white back. Only his mother was looking at him.
She was standing on a little high hump on the plateau, her white breast thrust forward. Now and again, she tore at a piece of fish that lay at her feet, and then scraped each side of her beak on the rock. The sight of the food maddened him. How he loved to tear food that way, scraping his beak now and again to whet it! He uttered a low cackle. His mother cackled too, and looked at him.
e. What did the young bird do to seek the attention of his parents?
f. What made the young seagull go mad?
‘Ga, ga, ga,’ he cried, begging her to bring him over some food. ‘Gawl- ool-ah,’ she screamed back mockingly. But he kept calling plaintively, and after a minute or so, he uttered a joyful scream. His mother had picked up a piece of fish and was flying across to him with it. He leaned out eagerly, tapping the rock with his feet, trying to get nearer to her as she flew across. But when she was just opposite to him, abreast of the ledge, she halted, her legs hanging limp, her wings motionless, the piece of fish in her beak almost within reach of his beak.
He waited a moment in surprise, wondering why she did not come nearer, and then maddened by hunger, he dived at the fish. With a loud scream, he fell outwards and downwards into space. His mother had swooped upwards. As he passed beneath her, he heard the swish of her wings.
g. Why did the young bird utter a joyful scream?
h. Did the mother bird offer any food to the young bird?
Then a monstrous terror seized him and his heart stood still. He could hear nothing. But it only lasted a moment. The next moment, he felt his wings spread outwards. The wind rushed against his breast feathers, then under his stomach and against his wings. He could feel the tips of his wings cutting through the air.
He was not falling headlong now. He was soaring gradually, downwards and outwards. He was no longer afraid. He just felt a bit dizzy. Then, he flapped his wings once and he soared upwards.
He uttered a joyous scream and flapped them again. He soared higher. He raised his breast and banked against the wind. ‘Ga, ga, ga. Ga, ga, ga.’ ‘Gawlool-ah.’ His mother swooped past him, her wings making a loud noise. He answered her with another scream. Then, his father flew over him screaming. Then, he saw his two brothers and sister flying around him, soaring and diving.
Then, he completely forgot that he had not always been able to fly, and commenced to dive and soar, shrieking shrilly.
i. How did the bird feel when it started flying for the first time?
j. What did the young bird’s family do when he started flying?
He was near the sea now, flying straight over it, facing out over the ocean. He saw a vast green sea beneath him, with little ridges moving over it; he turned his beak sideways and crowed amusedly. His parents and his brothers and sister had landed on this green floor in front of him. They were beckoning to him, calling shrilly. He dropped his legs to stand on the green sea. His legs sank into it. He screamed with fright and attempted to rise again, flapping his wings. But he was tired and weak with hunger and he could not rise exhausted by the strange exercise. His feet sank into the green sea, and then his belly touched it and he sank no farther.
He was floating on it. And around him, his family was screaming, praising him, and their beaks were offering him scraps of dog-fish.
He had made his first flight.
About the author
Liam O'Flaherty (1896–1984) was an Irish novelist and short story writer and a major figure in the Irish literary renaissance. He was a founding member of the Communist Party of Ireland. A native Irish-speaker from the Gaeltacht, O'Flaherty wrote almost exclusively in English, except for a small number of short stories in the Irish language. He spent most of his time in travelling and lived comfortably and quietly outside the spotlight.
Page 14
Glossary
ledge (n)- a narrow shelf that juts out from a vertical surface
shrilly (adv.)- producing a high-pitched and piercing voice or sound
herring (n)- a long silver fish that swims in large groups in the sea
devour (v)- to eat something eagerly and in large amounts, so that nothing is left
cackle (n)- a sharp, broken noise or cry of a hen, goose or seagull
mackerel (n)- a sea fish with a strong taste, often used as food
gnaw (v)- to bite or chew something repeatedly
trot (v)- to run at a moderate pace with short steps
precipice (n)- a very steep side of a cliff or a mountain
whet (v)- to sharpen
preening (v)- cleaning feathers with beak
plaintively (adv.)- sadly, calling in a sad way
swoop (v)- to move very quickly and easily through the air
beckoning (v) - making a gesture with the hand or head to encourage someone to approach or follow.
Page 15
WHILE READING QUESTIONS:
a. Why did the seagull fail to fly?
The seagull failed to fly, because he was afraid to fly.
b. What did the parents do, when the young seagull failed to fly?
When the young seagull failed to fly, his parents scolded him, and threatened to let him starve on the ledge.
c. What was the first catch of the young seagull’s older brother?
Herring was the first catch of the young seagull’s older brother.
d. What did the young seagull manage to find in his search for food on the ledge?
The young seagull managed to find the dried pieces of Mackerel’s tail in the previous night. The next morning, he found the dried pieces of eggshell to eat.
e. What did the young bird do to seek the attention of his parents?
At first, the young bird pretended to be fall asleep. Later it uttered a low cackle and kept calling sadly to seek the attention of his parents.
f. What made the young seagull go mad?
The young seagull was very hungry and her mother did not come nearer to feed him.
It made the young seagull go mad.
g. Why did the young bird utter a joyful scream?
The young bird saw his mother picking up a piece of fish towards him. So he uttered a joyful scream. Later when he began to fly, he uttered a joyful scream.
h. Did the mother bird offer any food to the young bird?
No, the mother did not offer any food to the young bird.
i. How did the bird feel, when it started flying for the first time?
When the seagull started flying for the first time, a monsterous terror seized him for a moment, but then he uttered a joyful scream.
j. What did the young birds’ family do when he started flying?
The young birds’ family was very happy. His mother swooped past him, his father flew over him, and his brothers and sister were flying around him, high and low out of joy.
1. How was the young seagull’s first attempt to fly? (or) Why did the seagull fail to fly?
The young seagull’s first attempt to fly was a failure, because he was afraid to fly. He failed to muster up courage to fly. Instead of flapping his wings and flying away, he ran back to the little hole.
2. How did the parents support and encourage the young seagull’s brothers and sister?
The parents supported and encouraged the young seagull’s brothers and sister, by perfecting them in the art of flight, teaching them how to skim and surf the waves and how to dive for fish.
3. Give an instance that shows the pathetic condition of the young bird.
The young seagull failed to muster up courage to fly. So he had to stay in his nest. He had no food. He could not find anything but the dried pieces of eggshell to eat.
4. How did the bird try to reach its parents without having to fly?
The bird walked back and forth from one end of the ledge to the other. Without trying to fly and stepping daintily, he tried to find some means of reaching his parents.There was a deep wide crack between him and his parents.
5. Do you think that the young seagull’s parents were harsh to him? Why?
No. I don’t think that the parents were harsh to him. Here the young seagull’s parents trained him to fly. The mother seagull showed a piece of fish to the hungry young seagull. Maddened by hunger, he dived at the fish and began to fly.
6. What prompted the young seagull to fly finally?
The mother seagull showed a piece of fish to the hungry young seagull. But he couldn’t reach the food as it was out of reach. Maddened by hunger, he dived at the fish. Thus the parental care, its natural bird instinct to fly and its urge for survival prompted the young seagull to fly, finally.
7. What happened to the young seagull when it landed on the green sea?
The young seagull landed on the green sea and sank into it. His belly touched the water and he sank no farther. He was floating on it.
B. Answer each of the following questions in a paragraph of about 100-150 words.
1. Describe the struggles underwent by the young seagull to overcome its fear of flying.
Lesson : HIS FIRST FLIGHT
Author : Liam O’Flaherty
Theme : Parenting
Characters : The young seagull and its family
Outlook : The young seagull’s fear – hungry – mother seagull’s training – his first flight
The young seagull was alone on his ledge. Unlike his brothers and sister, he was afraid to fly. He failed to muster up courage to fly. His parents had come around calling to him shrilly, scolding him, threatening to let him starve on his ledge. He had no food. He could not find anything but the dried pieces of eggshell to eat. His parents wanted to teach him fly. So the mother seagull showed a piece of fish to the hungry young seagull. But he couldn’t reach the food as it was out of reach. Maddened by hunger, he dived at the fish. In order to grab it, he had no other choice other than to flap his wings and fly towards his meal. He landed on the green sea and sank into it. He was floating on the water. The young birds’ family was very happy and they offered him scraps of dog-fish for his first flight. Thus the parental care, his natural bird instinct to fly and his urge for survival prompted him to fly, finally.
2. Your parents sometimes behave like the young bird’s parents. They may seem cruel and unrelenting. Does it mean that they do not care for you? Explain your views about it with reference from the story.
• Parents are our first teachers. Guiding their ward/children at every stage is their primary responsibility. If they fail to do this, the children cannot attain perfection.
• It is said that children start learning and responding even when they are in the womb of the mother. A child which grows, without the guidance of the parents, lack in the art of speech, walking, holding things, eating and even doing their everyday basic activity. They even need toilet training.
• Some children can learn easily. But few hesitate or struggle while learning new things. To them, the parents have to be harsh for the betterment of their life as we see the young seagull in this lesson. As the old proverb says “bend the twig bend the tree”. They may seem cruel and unrelenting but it is for the good of their children. It is the duty of every parent to educate and teach their young ones the art of life.
ESSAY
Introduction
The young seagull
The reaction of the parents
The young one’s first flight
Landing on the water
The reaction of the family
Conclusion
Introduction:
Liam O’Flaherty was a famous Irish novelist and short story writer. One of his great work is ‘His First Flight’. A story that proves the saying ‘To master any art, one should overcome fear.’
The young seagull:
The young seagull was one among the four offsprings of the father and the mother seagulls. He was very timid. He was alone on the ledge. Unlike his two brothers and sister, he was afraid to fly. He failed to muster up courage to fly. Instead of flapping his wings and flying away, he ran back to the little hole.
The reaction of the parents:
His parents had come around calling him shrilly, scolding him, threatening to let him starve on the ledge. He had no food. He could find nothing but the dried pieces of eggshell to eat. His parents wanted to teach him to fly.
The young one’s first flight:
So the mother seagull showed a piece of fish to the hungry young seagull. But he couldn’t reach the food as it was out of reach. Maddened by hunger, he dived at the fish. In order to grab it, he had no choice other than to flap his wings and fly towards his meal.
Landing on the water:
He landed on the green sea and sank into it. His belly touched the water and he sank no farther. He was floating on the water.
The reaction of the family:
The young birds’ family was very happy. His mother swooped past him, his father flew over him, and his brothers and sister were flying around him, high and low out of joy. They offered him scraps of dog-fish for the success of his first flight. Thus, his natural bird instinct and his urge for survival prompted him to fly finally.
Conclusion:
These are the struggles underwent by the young seagull to overcome its fear of flying.
Moral: Necessity is the mother of action.
Page 16
Vocabulary
Read the following sentences.
Set 1
1. The young seagull uttered a joyful scream. (adjective)
2. The young seagull screamed with joy. (noun)
3. The young seagull screamed joyfully. (adverb)
Set 2
1. The young bird pretended to be falling asleep. (verb)
2. The young bird made a pretension of falling asleep. (noun)
3. The young bird made a pretentious posture of falling asleep. (adjective)
Note that in the Set 1, the adjective ‘joyful’ is changed to its noun form ‘joy’ and to its adverb form ‘joyfully’.
In the Set 2, the verb ‘pretend’ has been transformed to its noun form ‘pretension’ and to its adjective form ‘pretentious’.
We can transform a sentence by interchanging parts of speech without changing its meaning.
C. Change the parts of speech of the given words in the chart.
D. Read the following sentences and change the form of the underlined words as directed.
1. His family was screaming and offering him food. (to adjective)
To Adjective: She is a screaming beast.
2. The young seagull gave out a loud call. (to adverb)
To Adverb:The young seagull called out loudly
3. The bird cackled amusedly while flying. (to noun)
To Noun:The bird cackled with amusement.
4. The depth of the sea from the ledge scared the seagull. (to adjective)
Adjective: The seagull was scared of the deep sea.
5. The successful flight of the bird was a proud moment for the seagull’s family. (to verb)
To Verb: The bird flew successfully.
E. Use the following words to construct meaningful sentences on your own.
1. coward - Tom is a coward.
2. gradual - The economic growth is gradual.
3. praise - Always praise the good deeds of others.
4. courageous - Gandhiji was very courageous.
5. starvation - My health is spoiled because of starvation.
Page 17
Listening
F. *Here is a travelogue by the students of Government Girls Higher Secondary School, Pattukkottai after their trip to Darjeeling. Listen to the travelogue and answer the following questions.
i) Fill in the blanks with suitable words.
1. The students visited _Darjeeling_ city.
2. Kanchenjunga is the third highest mountain in the world.
3. Tiger hill is 13 km away from Darjeeling.
4. The drinking water is supplied by Senchal lake to the city.
5. After Senchal lake, they visited Batasia loop
ii) Do you think they had a memorable and enjoyable school trip?
Yes. They had a memorable and enjoyable school trip.
iii) Name a few places that you wish to visit with your classmates as a school trip.
Thekkady, Kochi, Munnar, and Trivandrum
iv) State whether the following statements are True or False.
1. As the sky was cloudy, they could get the glimpse of the Mount Everest. - False
2. The toy train covers 14 km in three hours. - True
3. Tiger hill has earned international fame for the best sunset view. - True
Page 18
Speaking
Your family has planned for a two-day trip to a tourist spot nearby in a reserved forest. Your father has no idea about what safety measures and precautions to be taken before you start. Enact a role-play on the above situation.
Student 1: As a son / daughter
Student 2: As a father
These would help you.
Important places to be visited
Food and accommodation
Mode of transport
Necessary clothes for two days
First-aid kit and medicines required if any etc.
Son/Daughter : Dad, Shall we go for a picnic?
Father : Sure. Have you chosen any spot?
Son/Daughter : Yes, Dad. Puliyancholai forest.
Father : Nice place. Ask your mother to prepare food for two days.
Son/Daughter : Ok, Dad. Shall we go by car?
Father : Mmm. Go and pack your dresses for two days.
Son/Daughter : Is there anything else to pack, Dad?
Father : Yes, Pack the things like first-aid kit and medicines.
Son/Daughter : Sure, Dad.
Father : I will make our car ready for our trip. Bye.
Son/Daughter : Bye, Dad.
G. Here is a dialogue between a father and his daughter. Continue the dialogue with at least five utterances and use all the clues given above.
Father: Hi Mary, it has been a very long time since we went on a trip. Let’s plan one.
Mary: Yes, dad. I am also longing to go. Why don’t we plan one for this weekend?
Father: Sure. Tell me, where shall we go?
Mary: Some place nearby but for at least two days.
Father: Hmm… I think we should go to the reserved forest nearby.
Mary: Yeah. I’ve never been to a forest. I have seen a forest only on the TV and movies. The forest is a good choice!
Father: OK. If we are going to the forest, we must list out what we should carry with us for two days.
Mary: I think we should carry suitable clothes like daily wear for 2 days.
Father: What about the food? Do you have any idea, Mary?
Mary: Yeah. For food, I suggest Rotis, chappathis, bread, butter and jam.
Father:. Don’t you think we need First-aid kit and medicines required?
Mary: Yes, of course. We must also arrange proper transport and safe accommodation.
Page 19
Reading
H. Read the following passage and answer the questions that follow.
BUNGEE-JUMPING
Bungee jumping is an activity that involves jumping from a tall structure while connected to a long elastic cord. The tall structure is usually a fixed object, such as a building, bridge or crane; but it is also possible to jump from a movable object, such as a hot-air-balloon or helicopter, that has the ability to hover above the ground. The thrill comes from the free-falling and the rebound. When the person jumps, the cord stretches and the jumper flies upwards again as the cord recoils, and continues to oscillate up and down until all the kinetic energy is dissipated.
Jumping Heights, located in Mohan Chatti village, in Rishikesh has been rated as one of the most preferred bungee jumping destinations in India at a height of 83 meters. It is the only place in India where bungee jumping can be done from a fixed platform. This is also India’s only fixed platform Bungee- performed from a professional cantilever, to separate it from entertainment parks, and create instead, an extreme adventure zone. The Bungee has been designed by David Allardice of New Zealand.
The Cantilever platform is built over a rocky cliff over-looking the river Hall, tributary of River Ganges. Bungee-ing amidst the vastness of nature lends the experience an absolutely breathtaking quality. Jumping heights is well known for its safety measures and experienced staff. It costs around Rs 2500 per jump, a bit expensive, but totally worth the experience. The Bungee jumping experience has been set amidst the astoundingly stunning landscape of Rishikesh. To Bungee jump, one must be at least 12 years and should weigh between 40-110 kg.
Questions
1. What is Bungee Jumping?
Bungee jumping is an activity that involves jumping from a tall structure while connected to a long elastic cord.
2. Can Bungee be performed from a movable object? How?
Yes. It is also possible to perform Bungee from a movable object. With the help of a hot-air balloon or helicopter, that has the ability to hover above the ground.
3. When do you think Bungee becomes thrilling?
Bungee becomes thrilling from the free falling and the rebound. When the person jumps, the cord stretches and the jumper flies upwards again as the cord recoils, and continues to oscillate up and down until all the kinetic energy is dissipated.
4. What is the experience when one falls off the platform?
When one falls off the platform, he or she gets excitement and thrill very much.
5. Where is the Bungee jumping point located in India?
The Bungee jumping experience has been set amidst the astoundingly stunning landscape of Rishikesh.
6. What is the minimum age to Bungee jump?
The minimum age to Bungee Jump is 12 years.
Page 20
Writing
Advertisement
An advertisement is an audio or visual form of marketing communication to promote or sell a product, service or idea.
An advertisement should include the following to make it attractive.
1. Name of the product / brand / outlet.
2. Address with contact information and websites.
3. Appealing Images (visuals) of the Product / Service / Idea to be advertised.
4. Target demographics / audience / customers.
5. Feel-Good discounts and offers.
6. Colourful Background.
7. Colourful and readable text.
8. Brief and catchy descriptions and benefits about the product.
9. Use borders and lines to organize.
Now look at the model advertisement given below
I. Prepare attractive advertisements using the hints given below.
1. Home appliances – Aadi Sale – 20-50% - Special Combo Offers – Muthusamy & Co., Raja Street, Gingee.
2. Mobile Galaxy – Smart phones – accessories – SIM cards – Recharge – Free Power banks on Mobile purchase – No.1, Toll gate, Trichy
Report Writing
A report is designed to lead people through the information in a structured way, and also to enable them to find the information that they want quickly and easily. It is a short, sharp, concise document which is written for a particular purpose and audience.
Format of a report.
Title of the report
❖ Report Writer’s name
❖ What…? (name of the event)
❖ When…? (day and time of the event)
❖ Where…? (venue of the event)
❖ Why…? (the purpose of the event)
❖ Who…? (Chief guest,)
❖ How…? (the details of the event like Program, its impact etc.)
❖ Use simple sentences in the Past Tense.
❖ Be brief.
❖ Do not exaggerate the event.
Here is a sample report on the Annual Sports Day of a school. Observe the format and the language used.
Annual Sports Day
By Charan, X - C
Government Higher Secondary School, Hosur, organized the Annual Sports Day on August 29, 2018. The event was to inculcate the spirit of sportsmanship and fondness for sports in children. Approximately 1,000 students participated in the track and field events. The program began with a prayer rendered by the school choir. Following this, the Headmaster delivered the welcome speech. The Sports Day was inaugurated by the Chief Guest, followed by march past, led by the school captain with a placard bearing the School’s name and motto. Then the much awaited track and field events began. As the events went by, the school campus reverberated with enthusiastic cheers from the spectators. Many new school level records were made in 50 metres, 100 metres, and 200 metres races. The merit and participation certificates were given away by the Chief Guest and Guests of Honour. In his speech, the Chief Guest praised the endeavours of the school. Then, the Headmaster proposed the vote of thanks. The event ended with the National Anthem.
J. Write a report of the following events in about 100-120 words.
1. ‘Educational Development Day’ was organized in your school on 15th July. The District Collector was the Chief Guest of the event. As part of the event, many competitions were held and the prizes were distributed to the winners and participants. It was a grand and successful event. Now, as the member of the organizing committee, write a report on the event in about 120 words.
Educational Development Day
Sathish
15th July 2019
Government Higher Sec. School, Ponmalai organized the Educational Development Day on 15th July. The event was organized to stress the value of Education. Nearly 1500 students participated. The Programme consisted of many interesting events. The District Collector was the chief Guest of the event. He was welcomed by our Head Master. Many students participated in the competitions and proved their mettle. The District Collector delivered chief guest address to the students. Prizes were also distributed to the winners and participants. It was a grand success. Vote of thanks was proposed by the school pupil leader. Finally the programme ended with the National Anthem.
2. You are the School Pupil Leader. You have been asked to write a report on the Inaugural Ceremony of English Literary Association of your school which was held recently. Write a report on the same in not more than 120 words.
Inaugural Ceremony of English Literary Association
Mahendra Varman R
16th June 2019
Government Higher Sec. School, Aarani organized Inaugural Ceremony of English Literary Association on 15th June. It was held under the presidentship of Prof.R.Karuna. Members of the Association were elected. Students displayed their histrionic talents at the meeting. All the spectators enjoyed the events a lot. The teachers of the English Department and the Headmistress guided the students to conduct the events properly. At last the programme came to an end with the vote of thanks and the National Anthem.
3. You are the Coordinator of the Science Forum of your school. An event had been organized on account of National Science Day for the members of the forum. Now, write a report on the observation of “National Science Day” at your school.
National Science Day
MAHENDRAN
28th Feb. 2020
National Science Day was organised by the Science Forum of Government Higher Secondary School, Nanguneri. The Head of the Department of Physics Mr.Ezilarasan was the chief guest. All the members of the forum participated with full vigour. Lot of exhibits were displayed by the students of all classes. Not only students but also the parents provided their full support and participated in the programme. It was really an occasion to bring out the hidden talents of the students.
Our Headmistress delivered welcome speech .Our chief guest was much impressed by the performance of our students and conveyed his appreciation. He also guided the students for further course of action in his enlightening speech. Atlast the vote of thanks was delivered by me as the coordinator of the Science Forum.The programme came to a halt with the National Anthem.
Page 21
Grammar
Modals
We have already learnt about Modals in Class IX. Now, let us revise.
A modal verb is used to indicate modality (that expresses a speaker’s general intention) i.e. likelihood, ability, permission, request, capacity, suggestions, order, obligation, advice etc.
We use modals to show if we believe something is certain, probable or possible. Modals are,
can, could, may, might, will, would, shall, should, must, ought to, need, used to & dare to.
A. Complete these sentences using appropriate modals. The clues in the brackets will help you.
1. When I was a child, I used to climb trees easily but now I can’t. (ability in the past)
2. I will win this singing contest. (determination)
3. You can / may buy this book. It is worth buying. (advice or suggestion)
4. Poongothai can speak several languages. (ability in the present)
5. I swear I will not / shall not tell lies again. (promise)
6. My father used to play badminton in the evenings when he was at college. (past habit)
7. You must / ought to / should do as I say! (command)
8. May I have another glass of water? (request)
9. Sibi has not practised hard but he might win the race. (possibility)
10. We should / ought to preserve our natural resources. (duty)
B. Rewrite the following sentences by rectifying the errors in the use of modals.
1. Would I have your autograph?
May / Can I have your autograph?
2. I can be fifteen next April.
I will be fifteen next April.
3. Take an umbrella. It should rain later.
Take an umbrella. It may rain later.
4. The magistrate ordered that he might pay the fine.
The magistrate ordered that he should pay the fine.
5. Make me a cup of tea, shall you?
Make me a cup of tea, will you?
6. You may speak politely to the elders.
must speak politely to the elders.
7. You will get your teeth cleaned at least once a year.
You must get your teeth cleaned at least once a year.
8. We could grow vegetables in our kitchen garden but we don’t do it now.
We can grow vegetables in our kitchen garden but we cannot do it now.
9. Must I get your jacket? The weather is cold.
May / Can I get your jacket? The weather is cold.
10. Could the train be on time?
Will the train be on time?
C. Read the dialogue and fill in the blanks with suitable modals.
Dad: Shall we go out for dinner tonight?
Charan: Yes, Dad. We shall go to a restaurant where I will have some ice cream.
Dad: OK. Then, I will be home by 7 p.m. Mom and you must / should be ready by then.
Charan: Sure. We will. My friend told me that there is a magic show nearby. Would you please take us there?
Dad: We may not have time to go for the magic show, I suppose. If we have enough time left, we would / will plan.
Charan: By the way, need we inform our gate keeper about our outing?
Dad: Yes, we need so that he will be aware we aren’t at home.
Charan: Shall / Need I call up Mom and tell her about our plan today?
Dad: You need to. Otherwise, we might be in trouble when she returns home.
Charan: Hmm… by the time you come home in the evening, we will be waiting for you. Hope you will not / won’t be late. Bye.
D. Read the following dialogues and supply appropriate modals.
Student : Can we leave our bags in the class during the break?
Teacher: Yes, you can but arrange them neatly.
Passenger: My child is 6 years old. Do I have to buy him a ticket?
Conductor: Yes, you should. It costs half of the price of an adult ticket.
Vani: Can we go for coffee after the meeting?
Yoga: No, I can’t. I have to go home.
Salesman: When will I receive my order?
Customer: I cannot assure you sir, the order will be delivered tomorrow.
Neela: Do you think I should write about my educational background in the resume?
Preethi: Yes, you should . You would get a better job.
Imagine you have been to Thanjavur recently. Based on your experience and the data given below about Thanjavur, suggest and guide your friend who wishes to visit Thanjavur and places nearby, using modals in your sentences.
Answer:
1. You can also go to Thiruvaiyaru which is famous for classical music.
2. I would suggest you to go to Kallanai Dam.
3. You would be happy to visit Poondi Basilica noted for its scenic beauty around.
E. Here are a few sentences already done for you. The clues given would be helpful to make more sentences on your own.
1. I would suggest that you take the Uzhavan Express to Thanjavur from Chennai.
2. You will be more comfortable if you could book 3 tier A/C.
3. You could enjoy Brihadeeswarar Temple (Big temple) ..
4. You should visit Saraswathi Mahal (Library) at the palace.
5. You mustn’t miss miss the museum.
6. You can buy art plates and paintings there.
7. You could enjoy the palace there..
8. You can also go to Thiruvaiyaru which is famous for classical music..
9. I would suggest you to go to Kallanai Dam..
10. You would be happy to visit Poondi Basilica noted for its scenic beauty around..
Active and Passive
In Class IX, we have already learnt about Active and Passive Voices. Now, we shall learn some more forms of the voice.
F. Change the following sentences to the other voice.
1. The manager appointed many office assistants.
Many office assistants were appointed by the manager.
2. You are making a cake now.
A cake is being made by you now.
3. That portrait was painted by my grandmother.
My grandmother painted that portrait.
4. Malini had bought a colourful hat for her daughter.
A colourful hat had been bought by Malini for her daughter.
5. They have asked me to pay the fine.
I was asked to pay the fine by them.
6. The militants were being taken to prison by the police.
The police was taking the militants to prison.
7. His behaviour vexes me.
I am vexed by his behavior.
8. Rosy will solve the problem.
The problem will be solved by Rosy.
9. Our army has defeated the enemy.
The enemy has been defeated by our army.
10. The salesman answered all the questions patiently.
All the questions were answered patiently by the salesman.
Passive Voice – Request
In Active Voice, a request begins with 'Please'. When we change a request from Active to Passive Voice, we should begin the sentence with ‘You are requested to’ in place of 'Please'. If the request is in negative form, the request in passive voice should begin with ‘You are requested not to’.
(e.g.) 1. Please assemble in the ground. (Active)
You are requested to assemble in the ground. (Passive
2. Please do not use mobile phones here. (Active)
You are requested not to use mobile phones here. (Passive)
Passive Voice – Advice
When we change an advice from active to passive voice, we should begin the sentence with ‘You are advised to’. If the advice is in negative form, it should begin with ‘You are advised not to’.
(e.g.) 1. Work hard (Active)
You are advised to work hard. (Passive)
Do not eat junk food. (Active)
You are advised not to eat junk food. (Passive)
Similarly, you can also use the following for other imperatives.
You are instructed to …
You are instructed not to …
You are ordered to …
You are ordered not to …
Passive Voice – Omitting the agent
In the sentences beginning with someone/no one, omit the ‘agent’ (subject) in the passive voice.
(e.g.) 1. Somebody has taken away my book. (Active)
My book has been taken away. (Passive)
2. No one has bought the tickets. (Active)
The tickets have not been bought. (Passive)
(Add ‘not’ to the verb for nobody, none, no one)
Passive Voice – Interrogatives
When sentences are changed to Passive, they begin with a verb (in ‘Yes/ No’ questions) or with a question word followed by the verb (in ‘Wh’ questions).
a. Questions beginning with Auxiliary verbs
(e.g.) 1. Did he write a letter? (Active)
Was a letter written by him? (Passive)
2. Is he watching us? (Active)
Are we being watched by him? (Passive)
b. Questions beginning with ‘wh’ words
(e.g.) 1. Who will accept this? (Active)
By whom will this be accepted? (Passive)
2. Who has arranged this meeting? (Active)
By whom has this meeting been arranged? (Passive)
3. When will you finish the building? (Active)
When will the building be finished by you? (Passive)
(the agent ‘by you’ is optional)
4. How did they do this? (Active)
How was this done by them? (Passive)
(the agent ‘by them’ is optional)
G. Change the following into Passive voice.
1. Please call him at once.
Let him be called at once. (or) You are requested to call him at once.
2. How did you cross the river?
How was the river crossed by you?
3. No one is borrowing the novels from the library.
The novels are being borrowed by no one from the library.
4. Will you help me?
Will I be helped by you?
5. Go for a jog early in the morning.
You are instructed to go for a jog early in the morning.
6. Why have you left your brother at home?
Why has your brother been left at home by you?
7. Nobody should violate the rules.
The rules should be violated.
8. Someone has to initiate it immediately.
It has to be initiated immediately.
9. Have you invited Raman to the party?
Has Raman been invited by you to the party?
10. Please do not walk on the grass.
You are requested not to walk on the grass.
11. Cross the busy roads carefully.
You are advised to cross the busy roads carefully. (you can also use instructed)
12. When will you book the tickets to Bengaluru?
When will the tickets to Bengaluru be booked by you?
Note: We need not mention Indefinite subjects in passive voice
Some Indefinite Subjects are…….
anyone : no one
any body : no body
every one : some one
every one : some body
H. In the following sentences the verbs have two objects namely Direct and Indirect objects. Change each of the following sentences into two passives using direct object as the subject in one and indirect in the other.
1. John gave a bar of chocolate to Jill.
a: Jill was given a bar of chocolate by John.
b: A bar of chocolate was given to Jill by John.
2. Pragathi lent a pencil to Keerthana.
a. Keerthana was lent a pencil by Pragathi.
b. A pencil was lent to Keerthana by Pragathi.
3. Sudha told the truth to her friend.
a. Sudha’s friend was told the truth by Sudha.
b. The truth was told by Sudha to her friend.
4. They offered the job to Venkat.
a. Venkat was offered the job by them.
b. The job was offered by them to Venkat.
5. The boss showed the new computer to Kaviya.
a. Kaviya was showed the new computer by the boss.
b. The new computer was showed to Kaviya by the boss.
I. Rewrite the following passage in Passive Voice.
A few days ago, someone stole Ambrose’s motorbike. Ambrose had left it outside his house. He reported the theft to the police. The police told him that they would try to find his motorbike. This morning, they found his motorbike. The police called Ambrose to the police station. The thieves had painted it and then sold it to someone else. The new owner had parked the motorbike outside a mall when the police found it. After an enquiry, the police arrested the thieves.
Answer
A few days ago, Ambrose’s motor bike was stolen. It had been left by Ambrose outside his house. The theft was reported by him to the police. He was told by the police that (the matter of) finding his motorbike would be tried by them. This morning his motorbike was found by them. Ambrose was called by the police, to the police station. It had been painted by the thieves, and it was sold. The motorbike had been parked by the new owner, outside a mall when its was found by the police. After an enquiry, the thieves were arrested by the police.
J. Write a recipe of your favourite dish in passive voice. Remember to list out the ingredients of the dish you have chosen and their quantity. Use Simple Present tense to write your recipe.
Carrot Kheer
Ingredients
¼ Kg of the carrot taken.
200 gms of sugar taken.
100 gms of cashew nuts
2 no elaichi (cardamom)
50 gms of ghee
Carrots are scrapped and cooked for 3 minutes. The boiled carrots are mashed nicely. The mashed carrots are taken in a pan. Simmer over low flame, 200 gms of sugar and 250ml of milk is added and stirred well. The cashew nuts and elaichi are roasted and added to the mix. The mixture is stirred again well still sugar gets dissolved properly. Now the ghee is added and stirred. Finally the carrot kheer is ready to be served.
K. Write a report of an event held at your school using Passive voice. Use Simple Past Tense to narrate the event.
National Science Day
Mahendra Varman R
28th Feb, 2020
The National Science Day was celebrated in our school. It was presided over by the Principal of Government college, Chennai. The welcome speech was delivered by our Head master. A debate about the cause for the global warming was conducted. Many exhibits were displayed. The vote of thanks was delivered by the school pupil leader. Finally National Anthem was sung and the programme was concluded.
Page 22
Poem
Life
Henry Van Dyke
Let me but live my life from year to year,
With forward face and unreluctant soul;
Not hurrying to, nor turning from the goal;
Not mourning for the things that disappear
In the dim past, nor holding back in fear
From what the future veils; but with a whole
And happy heart, that pays its toll
To Youth and Age, and travels on with cheer.
So let the way wind up the hill or down,
O'er rough or smooth, the journey will be joy:
Still seeking what I sought when but a boy,
New friendship, high adventure, and a crown,
My heart will keep the courage of the quest,
And hope the road's last turn will be the best.
About the Poet
Henry Van Dyke (1852 – 1933) was an American author, poet, educator, and clergyman. He served as a professor of English literature at Princeton University between 1899 and 1923. He was elected to the American Academy of Arts and Letters and received many other honours.
Page 23
Glossary
mourning (v) - feeling or expressing great sadness
veils (v) - to hide or cover something so that you cannot see it clearly or understand it
crown (n) - a prize or position offered for being the best
quest (n) - a long search for something that is difficult to find
unreluctant* (adj.) - willing to do something (*This form is generally not used but the poet has coined it for emphasis)
Sonnet : The word sonnet is derived from the Italian word “sonetto,” which means a ‘little song’ or ‘small lyric’. In poetry, a sonnet has 14 lines, and is written in 'iambic pentameter' (A line with ten syllables, accented on every second beat). The first eight lines of a sonnet is known as “octave” and the last six lines is known as “sestet”. Sonnets can be categorized on the basis of their rhyme scheme.
Page 24
1. Let me but live my life from year to year,
With forward face and unreluctant soul;
a. Whom does the word ‘me’ refer to?
The word ‘me’ refers to the poet.
b. What kind of life does the poet want to lead?
The poet wants to lead joyful life with forward face and unreluctant soul.
c. What does the phrase ‘unreluctant soul’ mean here?
Here, the phrase ‘unreluctant soul’ means the person who is willing to do something.
d. Identify the rhyming words of the given lines.
year, disappear soul, goal
2. Not hurrying to, nor turning from the goal;
Not mourning for the things that disappear
a. Why do you think the poet is not in a hurry?
The poet does not want to move away from his goal. So I think he is not in a hurry.
b. What should one not mourn for?
One should not mourn for the things, he has lost.
3. In the dim past, nor holding back in fear
From what the future veils; but with a whole
And happy heart, that pays its toll
To Youth and Age, and travels on with cheer.
a. What does the poet mean by the phrase ‘in the dim past’?
‘In the dim past’ refers to unhappy or unpleasant past experiences.
b. Is the poet afraid of future?
No, the poet is not afraid of future.
c. How can one travel on with cheer?
One can travel on with cheer by thinking of the experiences of youth and old age.
d. Who pays the toll to whom?
The poet’s happy heart pays its toll to his youth and old age.
fe What does the poet not want to do in fear?
The poet does not want to hold back his journey of life in fear.
f. Whose Youth and Age is referred to here?
The poet’s ‘youth and age’ is referred to here.
g. Identify the rhyme scheme of the given lines.
abba
4. So let the way wind up the hill or down,
O'er rough or smooth, the journey will be joy:
Still seeking what I sought when but a boy,
New friendship, high adventure, and a crown,
a. How is the way of life?
The way of life is full of twists, turns,and ups and downs. It is sometimes rough and sometimes smooth.
b. How should be the journey of life?
The journey of life should be joyful and looking ahead.
c. What did the poet seek as a boy?
As a boy, the poet sought new friendship, high adventure and a crown.
d. Is the poet a boy?
No. The poet is not a boy.
e. Identify the rhyme scheme of the given lines.
abba
f. Identify the rhyming words of the given lines.
down, crown joy, boy '
5. My heart will keep the courage of the quest,
And hope the road's last turn will be the best.
a. What kind of quest does the poet seek here?
The poet seeks for the courage of the heart.
b. What is the poet’s hope?
The poet hopes that every turn in his life's journey will be the best. He is optimistic.
c. Identify the rhyming words of the given lines.
quest, best
6. In the dim past, nor holding back in fear
From what the future veils; but with a whole
And happy heart, that pays its toll
To Youth and Age, and travels on with cheer.
a. Identify the rhyming words of the given lines.
fear, cheer - whole, toll
7. Let me but live my life from year to year,
With forward face and unreluctant soul;
Not hurrying to, nor turning from the goal;
Not mourning for the things that disappear
a. Identify the rhyme scheme of the given lines.
a,b,b,a
B. Answer the following question in about 80 – 100 words
1. Describe the journey of life as depicted in the poem by Henry Van Dyke.
Poem : LIFE
Poet : Henry Van Dyke.
Theme : Live joyfully
Poem outline : Journey of life - joyful - not mourn - not hold back - hopes - every turn will be the best
Henry Van Dyke was an American author, poet, educator and clergyman. In this poem ‘Life’ he beautifully depicts his attitude towards life. The poet wants to live a joyful and fearless life. He neither wants to hurry nor moves away from his goal. He does not want to mourn the things that he has lost. He does not hold back for fear of the future. He wants to live his life with a whole and happy heart which cheerfully travels with him from the youth to old age. Therefore, it does not matter to him whether the path goes up or down the hill, rough or smooth, the journey will be looking ahead. He will continue to seek what he wanted as a boy - new friendship, high adventure and a crown (fame). His heart will remain courageous and pursue his desires. He hopes that every turn in his life's journey will be the best.
Life is a game, play it. Life is a challenge, face it.
ESSAY
· Introduction
· The poet’s wish
· The poet’s journey
· The poet’s hope
· Conclusion
Introduction
Henry Van Dyke was an American author, poet, educator and clergyman. The poem ‘Life’ is the poet's own reflection on his life and tells his point of view on the more important things in life.
The poet’s wish
The poet wants to lead a joyful life with forward face and unreluctant soul. He wants neither to hurry to his goal nor move away from his goal. He does not want to mourn the things that he has lost. He does not hold back for fear of the future. The poet wants to live his life with a whole and happy heart which cheerfully travels with him from youth to old age.
The poet’s journey
Therefore, it does not matter to him whether the path goes up or down the hill or rough or smooth. The poet will continue to seek what he wanted as a boy - new friendship, high adventure and a crown (fame).
The poet’s hope
His heart will remain courageous in order to pursue his desires. He hopes that every turn in his life's journey will be the best.
Conclusion
This poem shows the poet’s optimistic view of life through his personal experiences.
Life is a game, Play it.
Life is a challenge, Face it.
C. Based on your understanding of the poem, complete the following passage by the using the phrases given in the box.
The poet wants to live his life joyful, willing to do something. He neither wants to hurry nor move away from his goal. He does not want to mourn the things he has lost, not hold back for fear of the future. He instead prefers to live his life with a whole and happy heart which cheerfully travels from youth to old age. Therefore, it does not matter to him whether the path goes up or down the hill, rough or smooth, the journey will be looking ahead. He will continue to seek what he wanted as a boy - new friendship, high adventure and a crown (prize). His heart will remain courageous and pursue his desires. He hopes that every turn in his life's journey will be the best.
Read and Enjoy
Sea Fever
John Masefield
I must go down to the seas again, to the lonely sea and the sky,
And all I ask is a tall ship and a star to steer her by;
And the wheel’s kick and the wind’s song and the white sail’s shaking,
And a grey mist on the sea’s face, and a grey dawn breaking.
I must go down to the seas again, for the call of the running tide
Is a wild call and a clear call that may not be denied;
And all I ask is a windy day with the white clouds flying,
And the flung spray and the blown spume, and the sea-gulls crying.
I must go down to the seas again, to the vagrant gypsy life,
To the gull’s way and the whale’s way where the wind’s like a whetted knife;
And all I ask is a merry yarn from a laughing fellow-rover,
And quiet sleep and a sweet dream when the long trick’s over.
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Supplementary
The Tempest
An Extract from Charles Lamb's - Tales From Shakespeare
There was an island in the sea, the only inhabitants of which were an old man, named Prospero, and his daughter Miranda, a very beautiful young lady. She came to this island so young, that she had no memory of having seen any other human face than her father’s.
They lived in a cave made out of a rock; it was divided into several apartments, one of which Prospero called his study; there he kept his books, which chiefly treated of magic. By virtue of his art, he had released many good spirits from a witch called Sycorax who had them imprisoned in the bodies of large trees. These gentle spirits were ever after obedient to the will of Prospero. Of these Ariel was the chief.
Ariel took rather too much pleasure in tormenting an ugly monster called Caliban, because he was the son of his old enemy Sycorax. Caliban was employed like a slave, to fetch wood, and do the most laborious offices; and Ariel had the charge of compelling him to these services.
With the help of these spirits, Prospero could command the winds, and the waves of the sea. By his orders they raised a violent storm, in the midst of which, he showed his daughter a fine large ship, which he told her was full of living beings like themselves. “Oh my dear father,” said she, “if by your art you have raised this dreadful storm, have pity on their sad distress. See! the vessel will be dashed to pieces. Poor souls! they will all perish.”
“Be not so amazed, daughter Miranda,” said Prospero; “there is no harm done. I have so ordered it, that no person in the ship shall receive any hurt. What I have done has been in care of you, my dear child. You are ignorant. Can you remember a time before you came to this cell? I think you cannot, for you were not then three years of age.”
“Twelve years ago, Miranda,” continued Prospero, “I was Duke of Milan, and you were a princess, and my only heir. I had a younger brother, whose name was Antonio, to whom I trusted everything; My brother Antonio being thus in possession of my power, began to think himself the duke indeed. The opportunity I gave him of making himself popular among my subjects awakened in his bad nature a proud ambition to deprive me of my dukedom: this he soon effected with the aid of the King of Naples, a powerful prince, who was my enemy.”
“Wherefore,” said Miranda, “did they not that hour destroy us?”
“My child,” answered her father, “they dared not, so dear was the love that my people bore me. Antonio carried us on board a ship, and when we were some leagues out at sea, he forced us into a small boat, without either tackle, sail, or mast: there he left us, as he thought, to perish. But a kind lord of my court, one Gonzalo, who loved me, had privately placed in the boat, water, provisions, apparel, and some books which I prize above my dukedom.”
“O my father,” said Miranda, “what a trouble must I have been to you then!”
“No, my love,” said Prospero, “you were a little angel that did preserve me. Your innocent smiles made me bear up against my misfortunes. Our food lasted till we landed on this desert island, since when my chief delight has been in teaching you, Miranda, and well have you profited by my instructions.”
“Heaven thank you, my dear father,” said Miranda. “Now tell me, sir, your reason for raising this sea-storm?”
“Know then,” said her father, “that by means of this storm, my enemies, the King of Naples, and my cruel brother, are cast ashore upon this island.”
Having so said, Prospero gently touched his daughter with his magic wand, and she fell fast asleep; for the spirit Ariel just then presented himself before his master, to give an account of the tempest, and how he had disposed of the ship’s company, and though the spirits were always invisible to Miranda, Prospero did not choose she should hear him holding conversation (as would seem to her) with the empty air.
“Well, my brave spirit,” said Prospero to Ariel, “how have you performed your task?”
Ariel gave a lively description of the storm, and of the terrors of the mariners; and how the king’s son, Ferdinand, was the first who leaped into the sea; and his father thought he saw his dear son swallowed up by the waves and lost. “But he is safe,” said Ariel, “in a corner of the isle, sadly lamenting the loss of the king, his father.
“That’s my delicate Ariel,” said Prospero. “Bring him here: my daughter must see this young prince. Where is the king, and my brother?”
“I left them,” answered Ariel, “searching for Ferdinand, whom they have little hopes of finding, thinking they saw him perish. Of the ship’s crew not one is missing; though each one thinks himself the only one saved: and the ship, though invisible to them, is safe in the harbour.”
Ariel then went to fetch Ferdinand.
“O my young gentleman,” said Ariel, when he saw him, “I will soon move you. You must be brought, I find, for the Lady Miranda to have a sight of your pretty person. Come, sir, follow me.”
He followed in amazement the sound of Ariel’s voice, till it led him to Prospero and Miranda, who were sitting under the shade of a large tree. Now Miranda had never seen a man before, except her own father.
“Miranda,” said Prospero, “tell me what you are looking at yonder.”
“O father,” said Miranda, in a strange surprise, “surely that is a spirit. Lord! How it looks about! Believe me, it is a beautiful creature. Is it not a spirit?”
“No, girl,” answered her father; “it eats, and sleeps, and has senses such as we have. This young man you see was in the ship. He is somewhat altered by grief, or you might call him a handsome person. He has lost his companions, and is wandering about to find them.”
Miranda, who thought all men had grave faces and grey beards like her father, was delighted with the appearance of this beautiful young prince; and Ferdinand, seeing such a lovely lady in this desert place, and from the strange sounds he had heard, expecting nothing but wonders, thought he was upon an enchanted island, and that Miranda was the goddess of the place, and as such he began to address her.
She timidly answered, she was no goddess, but a simple maid, and was going to give him an account of herself, when Prospero interrupted her. He was well pleased to find they admired each other, but to try Ferdinand’s constancy, he resolved to throw some difficulties in their way: therefore advancing forward, he addressed the prince with a stern air, telling him, he came to the island as a spy, to take it from him who was the lord of it. “Follow me,” said he, “I will tie your neck and feet together. You shall drink sea-water; shell -fish, withered roots, and husks of acorns shall be your food.” “No,” said Ferdinand, “I will resist this” and drew his sword; but Prospero, waving his magic wand, fixed him to the spot where he stood, so that he had no power to move.
Miranda hung upon her father, saying, “Why are you so ungentle? Have pity, sir; I will be his surety. This is the second man I ever saw, and to me he seems a true one.”
“Silence,” said the father: “one word more will make me chide you, girl! What! An advocate for an impostor! You think there are no more such fine men, having seen only him and Caliban.” This he said to prove his daughter’s constancy; and she replied, “My affections are most humble. I have no wish to see a goodlier man.”
“Come on, young man,” said Prospero to the Prince; “you have no power to disobey me.”
Prospero had commanded Ferdinand to pile up some heavy logs of wood. Kings’ sons not being much used to laborious work, Miranda soon after found him almost dying with fatigue. “Alas!” said she, “do not work so hard; my father is at his studies, he is safe for these three hours; pray rest yourself.”
“O my dear lady,” said Ferdinand, “I dare not. I must finish my task before I take my rest.”
“If you will sit down,” said Miranda, “I will carry your logs the while.” But this Ferdinand would by no means agree to.
Prospero, who had enjoined Ferdinand this task merely as a trial of his love, was not at his books, as his daughter supposed, but was standing by them invisible, to overhear what they said.
Ferdinand inquired her name, which she told, saying it was against her father’s express command she did so.
And then Ferdinand, in a fine long speech, told the innocent Miranda he was heir to the crown of Naples, and that she should be his queen.
Prospero then appeared before them.
“Fear nothing, my child,” said he; “I have overheard, and approve of all you have said. And, Ferdinand, if I have too severely used you, I will make you rich amends, by giving you my daughter. All your vexations were but trials of your love, and you have nobly stood the test. Then as my gift, take my daughter.”
When Prospero left them, he called his spirit Ariel, who quickly appeared before him, eager to relate what he had done with Prospero’s brother and the King of Naples. Ariel said he had left them almost out of their senses with fear, at the strange things he had caused them to see and hear. When fatigued with wandering about, and famished for want of food, he had suddenly set before them a delicious banquet, and then, just as they were going to eat, he appeared visible before them in the shape of a harpy, a voracious monster with wings, and the feast vanished away. Then, to their utter amazement, this seeming harpy spoke to them, reminding them of their cruelty in driving Prospero from his dukedom, and leaving him and his infant daughter to perish in the sea; saying, that for this cause these terrors were suffered to afflict them.
The King of Naples, and Antonio the false brother, repented the injustice they had done to Prospero.
“Then bring them here, Ariel,” said Prospero.
Ariel soon returned with the king, Antonio, and old Gonzalo. This Gonzalo was the same who had so kindly provided Prospero formerly with books and provisions, when his wicked brother left him, as he thought, to perish in an open boat in the sea.
Grief and terror had so stupefied their senses, that they did not know Prospero. He first discovered himself to the good old Gonzalo, calling him the preserver of his life; and then his brother and the king knew that he was the injured Prospero.
Antonio with tears, and sad words of sorrow and true repentance, implored his brother’s forgiveness and Prospero forgave them; and, upon their engaging to restore his dukedom, he said to the King of Naples, “I have a gift in store for you too;” and opening a door, showed him his son Ferdinand playing chess with Miranda.
Nothing could exceed the joy of the father and the son at this unexpected meeting, for they each thought the other drowned in the storm.
The King of Naples was almost as much astonished at the beauty and excellent graces of the young Miranda, as his son had been. “Who is this maid?” said he; “She is the daughter to this Prospero, who is the famous Duke of Milan, of whose renown I have heard so much, but never saw him till now: of him I have received a new life: he has made himself to me a second father, giving me this dear lady,” said Ferdinand
“No more of that,” said Prospero: “let us not remember our troubles past, since they so happily have ended.” And then Prospero embraced his brother, and again assured him of his forgiveness.
Prospero now told them that their ship was safe in the harbour, and the sailors all on board her, and that he and his daughter would accompany them home the next morning.
Before Prospero left the island, he dismissed Ariel from his service, to the great joy of that lively little spirit.
About the author
William Shakespeare (1564–1616) was born in Stratford-upon-Avon, England. He was an English poet, playwright and actor. Widely regarded as both the greatest writer in the English language and the world's pre-eminent dramatist. His surviving body of work includes 37 plays, 154 sonnets and two narrative poems, the majority of which he penned between 1589 and 1613.
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Glossary
tormenting (v) – making someone suffer or worry a lot
dreadful (adj.) - extremely bad or unpleasant
duke (n) - a man of very high social rank in some European countries; a king
deprive (v) - to take something important or necessary away from someone
resistance (n) - the act of fighting against something
fatigue (n) - extreme tiredness
vexation (n) - worry or anger
famished (adj.) - extremely hungry
voracious (adj.) - very eager for something