CBSE Class 12 Mathematics Value Based Questions Set A
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VALUE BASED QUESTIONS |
NOTE: Model answers are being given to the value based questions. These are only suggestive answers. The students can answer these questions according to their own thinking.
CHAPTER 1
Q.1. Determine whether each of the following relations in the set A of students in a school at a particular time are symmetric and transitive :
(i) R = {(x, y) : x and yare honest.}
(ii) R = {(x, y) : x and yare obedient.}
(iii) R = {(x, y) : x and yare hardworking}
What are the advantages of students being honest, obedient and hardworking?
ANSWERS
1. Relations in (i), (ii) and (iii) are all symmetric and transitive. If the students are honest, obedient and hardworking, they will surely rise in life and will become ideal citizens of the country. Values promoted are honesty, obedience and hard working.
Q.2. Two SChools A and B decided to award prizes to their students for three values' \ honesty (x), punctuality (y) and obedience (z). School A decided to award a total of ₹11000 for the three values to 5, 4 and 3 students respectively while school B 'decided to award ₹10700 for the three values to 4, 3 and 5 students respectively. I If all the three prizes together amount to ₹2700, then
(i) Represent the above situation by a matrix equation and form Linear equations using matrix multiplication. '
(ii) Is it possible to solve the system of equations so obtained using matrices?
(iii) Which value you prefer to be awarded most and why? (CBSE Sample Paper)
Q.3. Two schools decided to award prizes to their teachers for three qualities \knowledge (x), guidance(y) and motivation (z), School A decided to award a total of ₹ 8700 for three values 4, 5 and,2 teachers respectively while school B ' decided to award a total of ₹ 8500 for three values 3, 4 and 5 teachers respectively, If all the three prizes together amount to ₹2200, then
(i) Represent the, above situation by a matrix equation and form linear equations using matrix multiplication. \ (ii) Is it possible to solve the system the equations so obtained using matriees?
(iii) Which quality you prefer to be rewarded most and why?
Q.4. In a parliament election, a political party hired a public relations firm to promote its candidate In three ways: telephone, house calls and letters. The cost per contact (in paise) is given in matrix A as
The number of contacts of each type made in two cities X and Y is given in the matrix B as
Find the total amount spent by the party in two cities. What should one consider before casting his/her vote 'party's promotional activities or their social activities?
Ans.4. CityX ₹ 3400, city Y ₹ 7200 \
One should look on the social activities of the party and at the same time know about the qualification of the candidate. Candidate must have integrity of character with indication towards welfare of the society. Values promoted are integrity of character and welfare of society.
Q.5. The co-operative store of a particular society has 10 dozens Mathematics books, 8 dozen biology books and 5 dozen English books. Their selling prices are ₹83, ₹f 34.50 and ₹ 45 each respectively. Find the total amount the store will receive from selling all the books using matrix method.
Why should we encourage co-operative stores?
5.₹15972; we should encouratge co-operative stores as they remove the middle men and result in lower prices. Value promoted is the availability of books at reasonable prices.
Q.6. Three shopkeepers A, Band C go to a store to buy stationary. A purchases 12 dozen notebooks, 5 dozen books. B purchases 10 dozen notebooks, 6 dozen books and C purchase 11 dozen notebooks, 13 dozen books. A notebook costs ₹ 40 and a book costs ₹ 50. Calculate each individual's bill using matrices.
'Use of paper should be minimised'. Comment.
Ans.6. A -₹ 78760, B -₹ 8400and C-₹ 13080. In process of making paper, we have to cut many trees which would lead to increase in pollution, ecological imbalance and soil erosion. Value promoted is saving out trees and environment.
Q.7. A firm produces three types of paper A, Band C which it sells in two markets. Annual sales in units are given below :
Market Units sold
I 8000 4000 16000
II 7000 18000 8000
If the sale prices per unit of A, B, C are ₹ 2, ₹ 3, ₹1.50 and cost prices per unit are ₹ 1.70, f 2.50 and ₹ 0.80 respectively, find total profit in each market by using matrix algebra. Why should we reduce the use of paper and encourage recycling the same?
What values are being promoted?
Ans.7. Market I - ₹ 15600, Market II -₹16700. Use of paper should be reduced as it leads to cutting of trees. Given the current level of pollution, carbon dioxide and emissions, cutting of trees is just equivalent of committing a crime. Therefore, to save our trees we should recycle paper.
Q.8. In a certain city there are 50 colleges and 400 schools. Each school and college have 18 peons,S clerks and 1 cashier. Each college in addition has one section officer and one librarian. The monthly salary of each of them is as follows.
peon: ₹1200,clerk :₹ 2000,cashier: ₹2400;section officer: ₹ 2800 and librarian ! I ₹ 3600. Using matrix algebra, find
(i) total number of posts of each type in schools and colleges l
ii) the total monthly salary bill of all schools and colleges together.
What is the importance of education in life?
Ans.8. (i) Number of posts: peons -8100, clerks -2650, cashiers -450, section officers -50, librarians -50
(ii) ₹ 1,64,20,000 Education is important for overall development of an individual. In today's world, elementary education is must for day to day work. Value promoted is education.
CHAPTER 6
Q.9. Find the interval on which the function {defined by f (r) =2,x3 -15x2 + 36x + 6 is
(i) increasing (ii) decreasing
We know that crime is increasing day by day. What remedies do you suggest to decrease crime? What values are being promoted?
Ans.9. (i) (-∞,2] u [3,∞] (ii) [2, 3]
Lack of education, inequitable distribution of income, unemployment and poverty etc. are the main cause of crime. Government should work on programs for providing employment, education for masses and hence eradication of poverty. Values promoted are education, eradication of poverty and good behaviour of citizens.
Q.10. Show that the function f (x) = tan-1 (cos x + sin x) is strictly increasing in the interval (O, Π/4). Which are the latest scams uncovered in India? What steps do you think would be essential in decreasing corruption?
Ans.10. Some latest scams uncovered in India are Common Wealth Games scam, 2G scam and COALGATE scam etc. To decrease corruption, Government must make strong rules/laws against corruption, stop roll of money power in elections etc. People should induce self discipline and commitment to our day to day life. The values promoted are disciplined life and no bribes.
Q.11. In a slogan writing competition in a school, Ashma wrote the slogan 'Truth pays, never betrays' on a trapezium shaped card board. If the lengths of three sides of a trapezium other than the base are 40 em each, find the area of the trapezium when it is maximum. What are the advantages of speaking truth?
11. Maximum area of trapezium = 1200√3 cm2 you always speak truth, then
(i) people will believe you
(ii) people will have faith in you
(iii) you will have good social recognition
(iv) there is no stress on you.
Q.12. Show that the surface area of a closed cuboid with square base and given volume is minimum when it is a cube? How can we minimise the use of electricity consumption? What value is being promoted?
12. To save electricity, we should use natural resources such as solar energy. Also, infrastructure should be designed in such a manner so that we may use . maximum day light. The values promoted are saving energy and environment.
Q.13. A light house is located at A 2 km off-shore from the nearest point 0 on a straight beach and a shop is located at B of the beach at a distance of 4 km from O. If the housekeeper can row with motor boat at the speed of 6 km/hr and can walk at the rate of 4 km/hr, where should he plan to reach the shore so as to cover the distance to the shop in the least possible time?
Keeping the safety and petrol prices in mind justify the values to be promoted for the minimum distance to be covered with motor boat. What is your opinion if housekeeper swims instead of using motor boat?
Ans.13. He should reach theshore at the point whose distance from the point 0 = √3.2 km. Values promoted are safety of life and minimum use of energy (petrol). If the housekeeper swims instead of using motor boat it is very good for health and use of petrol!diesel is totally saved.
Q.14. When travelling at x km/hr, a truck burns diesel at the rate of 1/300 (1800/x + x) litre per km. If the diesel costs ₹40 per litre and driver is paid ₹30 per hour, find the steady speed that will minimise lhe Lutal cost uf trip of 500 km, Keeping the safety and diesel prices in mind justify the values to be promoted for the distance of 500 km to be covered in minimum cost.
Q.15. The cost of fuel for running a train is promoted to the square of the speed generated in kmz'hr, It costs ₹ 49 per hour when the train is moving at the speed of 16 km/hr. What is the most economical speed if the fixed charges are ~ 300 per hour, over and above the running cost? Keeping the safety and fuel prices in mind justify the values to be promoted for the most economical speed.
15. Most economical speed = 40 km/hr.
The values promoted are.safety of life, minimum use of fuel (diesel, electricity.or coal) so that the cost of journey is. minimum..Saving energy.
Q.16. A square piece of tin of side 18 em is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. What should.be the side of the square to be cut off so that the volume of the box is maximum? Also find the maximum volume. Justify the values to be promoted to avoid the wastage of the tin.
16. Side of the square to be cut off is 3 em and the maximum volume of the box is 432 cm3.
Values promoted are maximum utility with minimum wastage.
Q.17. A furniture dealer deals in only two items chairs and tables. He has ₹50000 to invest and a space to store atmost 60 pieces. A table costs ₹2500 and a chair ₹ 500. He estimates that from the sale of one table, he can make a profit of ₹250 and from the sale of one chair, a profit of ₹75. He wants to know that how many tables and chairs he should buy form the available money so as to maximise his total profit, assuming that he car. sell all items that he buys. Make it as a linear programming problem and solve it graphically. What values are being promoted?
17. 10 tables and 50 chairs; maximum profit ₹ 6250. Values promoted are the maximum utility of money and space of storage.
Q.18. A firm manufactures two types of products A and B and sells them at a profit of ₹ 5 per unit of type A and ₹ 3 per unit of type B. Each product is processed on two machines M, and M2. One unit of type A requires one minute of processing time on M, and two minutes of processing time on M2 whereas one unit of type B requires one minute of processing time on M, and one minute of processing time on M2 Machines M, and M2 are respectively available for atmost 5 hours and 6 hours in a day. Find out how many units of each type of product should the firm produce per day in order to maximize the profit. Also find the maximum profit. What should be the qualities of a good machine?
18. 60 units of type A and 240 units of type Brmaximum profite ₹1020. A good machine should have the following qualities : '.
(i) consumes less energy (electricity/pertool)
(ii) produces quality products
(iii) easily operated
(iv) does work in short time.
Q.19. A manufacturer manufactures two types of plastic bags using two machines A and B. To manufacture a bag of first type, machine A is operated for 2 minutes and machine B for 3 minutes; to manufacture a bag of second type machine A is operated for 1 minute and machine B is operated for 4 minutes. Each machine can be operated for atmost 8 hours per day. A bag of first type is sold at a profit of ₹ 0.25 and a bag of second type is sold at a profit of ₹ 0.50. How many bags of each type should be manufactured and sold per day so as to maximise his profit. Make it as an L.P.P. and solve it graphically;
Why plastic bags should not be used? What values are being promoted?
19. 96 bags of each type; maximum profit = ₹ 72. Plastic bags are non-biodegradable and harmful for environment. These spoil the productivity of soil and block drainage system. Values promoted are saving environment and productivity of soil.
Q.20. If a young man rides his motorcycle at 25 km per hour, he has to spend ₹2 per kilometre on petrol; if he rides it at a faster speed of 40 km per hour, the petrol cost increases to ₹ 5 per kilometre. He has ₹100 to spend on petrol and wishes to find the maximum distance he can travel within one hour. Express this as L.P.P. and solve it graphically.
"Speed thrills but kills." comment. What values are being promoted?
20. Total distance covered is 30 km; 50/3 km at 25 km/hr and 40/3 km at 40 km/hr. Number of road accidents and death tolls on account of more speed has risen alarmingly. Most of accidents occur due to over speeding. Speeding often gives the persons behind the wheels the impression that he/she is in control of the vehicle. Whereas opposite is true i.e. with the extreme speed the vehicles is no longer in control of the driver. The values promoted are the safety of life and saving petrol (energy).
Q.21. A small scale factory makes two types of dolls. One doll of type I takes 1.5 hours of electronic machine and 3 hours of hand operated machine; one doll of type II takesS hours of electronic machine and 1 hour of hand operated machine. In a . day, the factory has the ability of not more than 42 hours ofelectronic machines and 24 hours of hand operated machines. If the profit on one doll of type I is ₹ 20 and on one dollof type II is ₹40, then find the number of dolls of each type that the factory should manufacture to earn maximum profit. Make it as an L.P.P. .and solve it graphically.
Why are small scale industries important in India? What values are being. promoted by establishing small scale industry?
21. Dolls of type I = 4 and dolls of type II = 12; maximum profit = ~ 200. Small scale industry generates more employment with low investment. Hence resulting into equatable distribution of money and the progress of the country. Values promoted are generating employment, equatable distribution of money and helping in removing poverty.
Q.22. A dealer in rural area wishes to purchase a number of sewing machines. Hel~as only ₹ 5760 to invest and has space for atmost 20 items. A electronic sewing machine costs him ₹360 and a manually operated sewing machinef 240. He can sell an electronic Sewing Machine at a profit of ₹ 22 and a manually operated sewing machine at a profit of ₹18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize his profit. Make it as a linear programming problem and solve it graphically. Keeping the rural background in mind justify the 'values' to be promoted for the selection of the manually operated machine. (CBSE Sample Paper).
22. The dealer should buy 8 electronic machines and 12 hand operated machines. Keeping the 'save environment' and 'conservation of exhaustible resources' in mind the manually operated machine should be promoted so that energy could . be saved. The dealer uses his/her wisdom to create employment opportunities .. by usinghand operated machines.
Q.23. A retired person wants to invest ₹ 30000 in fixed income securities. His broker recomends investing in two bonds, bond A yielding 7% per annum and bond B yielding 10% per annum. He decides to invest atmost ₹12000 in bond Band atleast ₹ 6000 in bond A. He also wants that the amount invested in bond A should be more than the amount invested in bond B. What should the broker recornend if the investor wants to maximize his return on investment? Why investment is important for future life?
23..₹ 18000in bond A and ₹12000 in bond B; maximum return =₹2460, Investment is.important for future life because it assures the person that he/she has enough money tor further to meet the daily requirements and enough money for any unseen events.
Q.24. A house wife wishes to mix together two kinds of foods FI and F2 in such a way that the mixture contains atleast 10 units of vitamins, 12 units of minerals and 8 units of proteins. The nutrient contents of one kg of foods FI and F2 are as given below:
Vitamins Minerals Proteins
Food FI 1 2 3
Food F2 2 2 1
One kg of food FI cost ₹16 and one kg of food F2 costs ₹ 20. Formulate the above problem as an L.P.P. and solve it graphically to find the least cost of the mixture which will produce the diet. What type of food should a student consume?
24. 2kg of food FI and 4 kg of food F2 should be mixed; minimum cost of this food is ₹ 112. A student should consume -such a food that contains all the .neutrients in appropriate quantity required for the healthy body.
Q.25. Suppose every gram of wheat provides 0.1 g of proteins and 0.25 g carbohydrate, and the corresponding values for rice are 0.05 g and 0.5 g respectively. Wheat costs ₹ 20 and rice ₹30 per kg. The minimum daily requirement of an average man for proteins and carbohydrates is 50 g and 200 g respectively. In what quantities should wheat and rice be mixed in the daily diet to provide the minimum daily requirements of proteins and carbohydrates at minimum cost? What is the minimum cost? What is balanced diet and what is the importance of balanced diet in daily life? What value is being promoted?
25. 400 g wheat and 200 g rice; minimum cost is ₹ 14. A diet which contains allthe nutrients in the correct quantityis called a balanced diet. Balanced diet protects . us against many diseases, so it is important to have all nutrients in our daily food to keep the body healthy. The value promoted is "keeping healthy body".
Q.26. There are two types of fertilisers FI and F2. FI consists of 10% nitrogen and 6% phosphoric acid and F2 consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that he needs atleast 14 kg of nitrogen and 14 kg of phosphoric acid for his crop. If FI costs ₹ 6 per kg and F2 costs f 5per kg, determine how much of each types of fertiliser should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost? I What do you understand by organic forming and why this is important? What values are being promoted?
26. 100kg of FI and 80 kg of F2; minimum cost =₹1000. Organic forming is a form of agriculture which uses natural and green organic manure, strictly excludes the use of chemical and synthetic fertiliser and it lies on techniques such as crop rotation logical pest control etc. Organic forming keeps the fertility of the soil, vegetables and fruits free from chemicals which are good for health, environment clean and more friendly. Values promoted are keeping productivity of the soil, environment clean and .free from pollution, vegetables and fruits free from chemicals.
Q.27. A company has two factories located at villages P and Q and has three depots situated at A, B and Co The daily requirements of depots A, B andC is .respectively 7, 6 and 4 units, while the production capacity of the factories at P and Q are respectively 9 and 8 units. The cost (in ₹) of transportation per unit ₹ is given below
How many units should be transported from each factory to each depot in order that the transportation cost is minimum? Form an L.P.P. and solve it graphically?
What steps should a State Government take to promote private industry in i backward and rural areas? What values are being promoted?
27. Factory P should supply 0, 6, 3 units to depots A, B, C respectively and factory Q should supply 7, 0, 1 units to depots A, B, C· respectively; minimum transportation cost is ₹ 185.
To promote private industry in backward and rural areas, the State Government should take the following steps :
1.Provide land on concessional rates.
2. Provide tax rebate.
3. Supply electricity at concessional rates.
4. Develop basic infrastructure like roads etc.
The values promoted are :
1. Development of villages and generating employment
2. Equatable distribution of wealth.
3. To help the poor people.
Q.28. Thereare two factories located at place P and the other at place Q. From these I .factories, a certain product is to be delivered to each of the depots situated at A, B. and C. The daily requirements of the depots are respectively 60, 50 and 40 units of.the product while the production capacity of the factories at P and Q are respectively 100 and 50 units. The cost of transportation per unit is given below:
How many units of the product should be transported from each factory to each depot in order that the transportation cost is minimum? What will be the minimum cost of transportation? What should be the feactures of the best location of a factory?
28. 10, 50, 40 units of product from factory P and 50, 0, 0 units of product from factory Q to depots A, Band C respectively; minimum transportation cost = ₹ 510
Location of a factory should have the following features :
(i) enough natural resources (raw material)
(ii) enough supply of electricity (energy)
(iii) enough labour
(iv) enough transport facility
Q.29. Out of 100 students, 60 students read Hindi newspaper, 40 read Tamil newspaper and 20 students read both Hindi and Tamil newspaper. Find the probability that a student selected at random reads
(i) neither Hindi nor Tamil newspaper.
(ii) Tamil newspaper given that he has already read Hindi newspaper.
(iii) Hindi newspaper given that he has already read Tamil newspaper. What values are being promoted in this question?
29 (i) 1/5 (ii) 1/3 (iii) 1/2
Values promoted are: unity and diversity; mutual respect for different cultures.
Q.30. The probability that a teacher will give an unannounced test during any class meeting is 1/5 k. If a student is absent twice, then find the probability that the student will miss atleast one test.
By remaining absent from the class, what values are being violated by the student?
30. 9/25 .The student is violating:
(i) Regularity (ii) Honesty
If a student is irregular then he/she can not be disciplined and this effects overall growth. The student is not honest towards studies and career.
Q.31. A speaks truth in 60% cases and B speaks truth in 90% cases. Determine the' percentage of cases in which they are likely to contradict each other in stating the same fact. What values are being violated by speaking lie?
31.42%. When a person speaks lie, he/she will be violating the value of integrity and truthfulness. The habit of speaking lie will not let him/her develop the integrity of character, trust and faithfulness.
Q.32. The probability of student A passing an examination is 3/5 and of student B passing is 4/5 Find the probability of passing the examination by
(i) both students A and B.
(ii) atleast one of the students A and B.
What ideal conditions a student should keep in mind while appearing in an examination?
32 (i) 12/25 (ii) 23/25
When appearing in an examination, a student should have no intention of copying or cheating. Copying or cheating may help in passing the exam but inculcates habit of dishonesty which leads to corruption and many other ills.
Q.33. Kamal and Monika appear for an interview for two vacancies. The probability of Kamal's selection is 1/3 and that of Monika's selection is 1/5 Find the probability that only one of them is selected. Should the selection of candidates be based on merit, recommendation, bribe or reservation? What values are being promoted?
33. 2/5 The selection should be based on merit. Values promoted are intelligence and honesty.
Q.34. A problem in Mathematics is given to three students whose chances of solving it are 1/3 . 1/5 and 1/6 What is the probability that atleast one of them solves the problem? Which ideal condition will you keep in your mind while solving the problem?
34. 5/9 Independent work, no copying
Q.35. A and B throw a pair of dice turn by turn. The first to throw 9 is awarded a prize. If A starts the game, what are their respective chances of winning? Is gambling a good way of earning money?
35. A's chance of winning = 9/17 B's chance of winning = 8/17
Gambling is not a good way of earning money because(
i) it is against the law (in India)
(ii) a person becomes habitual and in the long run he/she loses every thing
Q.36. In a game, 3 fair coins are tossed. A person is paid ₹ 5 if he gets all heads or all tails and he pays ₹ 3 if he gets one head or two heads. What can be expect to win on an average per game? Is gambling allowed in India? If no, why gambling is banned?
36. On an average, loss of ₹1 per game.
Gambling is not allowed in India. It is banned as itis a wager event not leading to any constructive economic activity. It reinforces poverty as the gambler takes greater risk in the hope of a big win.
Q.37. The probability of an AIDs patient escaping the death is 1/10 Out of 3 persons suffering from AIDs, find the probability that atleast one person will escape the death. What steps should be taken to prevent AIDs? What values are being promoted?
37. 271 / 1000. Proper sex education should be imparted in schools. Must use new syrings for every injection. The values promoted are safety from AIDs and healthy life.
Q.38. In an engineering college, 5% of students suffer from tagging. From a sample of 3 students taken at random, find the probability that
(i) none is suffering from ragging.
(ii) exactly two of them are suffering from ragging.
(iii) atleast one of them is suffering from ragging.
Why did Indian Government banned ragging in India? What values are being promoted?
Q.39. Suppose 5 men out of 100 and 25 women out of 1000 are good orators. A good orator is chosen at random. Find the probability that a male person is selected, Assume that there are equal numer of men and women. Should women be given equal rights? What values are being promoted?
39. 2/3 Yes, women must be give equal rights.
The values promoted are :
(i) equal opportunity of work, equal social status
(ii) women empowerment
(iii) no genender discrimination.
Q.40. A person has undertaken a construction job. The probabilities are 0.65 that there will be strike, 0.80 that the construction job will be completed on time if there is no strike and 0.32 that the construction job will be completed on time if there is a strike. Determine the probability thatthe construction work will be completed qon time. How construction is affected in case of strikes and riots? What values are promoted?
40. 0.438. In case of strikes, there is wastage of man hours and there are no productive activities. In case of riots, unnecessary tension between people of different communities. The values promoted are dedication towards work and religious harmony.
Q.41. An insurance company insured 2000 scooter drivers and 3000 motorbike divers, The probability of an accident involving a scooter driver is 0.01 and that of motorbike driver is 0.02. One of the insured person met with an accident. Find the probability that he/she was a motorbike driver. Why should one take at insurance cover? What factors does the company takes into account before deciding insurance premium? What values are being promoted?
41. 3/4 One must take insurance cover (policy) to protecthirnself/herself from the unseen events which are less likely to occur but once occurred cause substantial damage. Insurance companies decide on the premium by calculating the probability of the occurrence of the unforeseen events. Values promoted are protect~g against risk to life and financial help in case of physical injuries.
Q.42. Suppose a girl throws a fair die. If she gets 1 or 6, she tosses a coin 3 times and notes the number of heads. If she gets 2, 3, 4 or 5, she tosses a coin once and notes whether a head or a tail is obtained. If she obtained exactly one head, what is the probability that she threw 2, 3, 4 or 5 with the die. Should we differentiate between a girl child anda boy child? What values are being promoted?
42. 8/11No. the values promoted are :
(i) a girl child is equally important as a boy child
(ii) if the number of girls is less, then there would be imbalance in the society which will lead to crimes
(iii) discrimination between a girl and a boy is against the law.
Q.43. Assume that the chance for a patient having a heart attack is 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choice anyone of the two options with equal probabilities. It is given that after going through the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga. Which option would you suggest to the patient and why?
43. 14/29A course of mediation and yoga because it has· no side effects.
Q.44. A candidate has to reach the examination centre in time. Probability of his going by bus or by scooter or by bicycle are 3/10, 1/10 and 3/5 respectively. The probability that he will be late is 1/4 and 1/3 respectively if he travels by bus or by scooter. But he reaches in time it he uses bicycle. He reached the centre late. Find the probability that he travelled by bus. Which mode of transport he should use and why?
44. 9/13Bicycle because it is good for health and then is no use of diesel/petrol.
Q.45. A speaks truth 8 times out 10 times. A die is rolled. He reports that it was 5. What is the probability that it was actually 5? What can you say about the truthfulness of a person?
45. 4/9 If a person speaks truth them integrity of character develops and he / she rises in life.
Q.46. In answering a question on MCQ test with 4 choices per question, a student knows the answer, guesses or copies the answer. Let i1/2 e the probability that he knows the answer, 1/4 be the probability that he guesses and i that he copies it. Assuming that a student, who copies the answer, will be correct with the probability 3/4, what is the probability that the student knows the answer, given that he answered it correctly?
Arjun does not know the answer to one of the questions in. the test. The .evaluation process has negative marking. Which value would Arjun violate if he resorts to unfair means? How would an act like the above hamper his character development in the corning years? (CBSESample Paper)
46. 2/3 If Arjun copies the answer, he will be violating the value of honesty in his character. He should not guess the answer as well as that may fetch him negative marking for a wrong guess. He should accept the question the way it is and leave it unanswered as cheating may get him marks in this exam but this habit may not let him develop an integrity of character in the long run
Q.47. An insurance company insured 2000 cyclists, 4000 scooter drivers and 6000 motorbike drivers. The probability of an accident involving a cyclist, scooter driver and a motorbike driver are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver? Which mode of transport would you suggest to a student and why?
47. 9/26 Suggestion : Cycle should be promoted as it is good for
(i) Health (ii) No pollution (iii) Save energy (no petrol)
Q.48. A doctor is to visit a patient. From the past experience, it is known that the probability that he will come by public transport, taxi, scooter or car are respectively 1/10 ,1/5, 3/10 and 2/5The probabilities that he will be late are 1/4 , 1/3 and 1/12 if he comes by public transport, taxi or scooter respectively, but if he comes by car, he will not be late. When he arrives, he is late. What is the probability that he came by taxi?
Why should we use public transport? What values are being promoted?
48. 4/7 We should use public transport because it is safe, less expensive and helps in . saving fuel (energy). Values promoted are safety of life and saving energy.
Q.49. There is a group of 50 people who are patriotic out of which 20 believe in non violence. Two persons are selected at random out of them, write the probability distribution for the selected persons who are non violent. Also find the mean of the distribution. Explain the importance of Non violence in partiotism.
(CBSE Sample Paper)
Q.50. There are three bags. The first bag contains 1 white, 2 suffron and 3 green balls, the second bag contains 2 white, 3 saffron and 1 green ball and the thrid bag. contains 3 whi~~TC-l"saffron and 2 green balls. A bag is chosen at random and from it two balls are drawn at random. If oneballis whiteand theotherballissaffron, what is the probability that the second bag was chosen? Which are the three colour in our national flag? What values are being promoted?
50. 6/11 In our national flag, the three colouds in order are :
Saffron, white and green.
Saffron shows sacrifice,
White shows peace and
Green shows prosperity.
The values promoted are-sacrifice, peace and prosperity.
Q.51. Let X denote the number of hours you study on a holiday. Also it is known that
where k is a constant.
(i) Find the value of k.
(ii) What is the probability that you study atleast two hours? Exactly two hours? Atmost two hours?
Which time is considered the best time' for self study?
What value is being promoted?
51. (i) 0.15
(ii) P(atleast 2 hours) = 0.75, P(exactly 2 hours) = 0.3 and " Ptatmost 2 hours) = 055 Morning time is considered the best timefor self study because in the morning you are fresh (after a good sleep), there is no external disturbance and can concentrate better on studies. Value promoted is the importance of self study.
Q.52. Four defective organes are accidentally mixed with sixteen good ones. Three oranges are drawn from the mixed lot. Find the probability distribution of X;the number of defective oranges. What will happen if 4 bad persons are mixed with 16 good ones?
Q.53. There is a group of 20 persons who are rich out of which 5 are helpful to poor people. Three persons are selected at random out of them, writethe probability distribution for the selected persons who are helpful to poor people. Also find the mean of the distribution. Explain the value promoted in the question.
Q.54. A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find probability distribution of number of tails. Which value is being violated by using a biased coin?
Q.55. A die is loaded in such a way that getting an even number is 4 times as getting an odd number. If the die is rolled thrice, find the probability distribution of getting an odd number. Which value is being violated while using a biased die?
[Hint. Let p be the probability of getting an odd number in a single throw of a die, then probability of getting an odd number =4p. We have, P(l) + P(2) + P(3) + P(4) + P(S) + P(6) =1
=> P + 4p + P + 4p + P + 4p =1 => lSp = 1 => P = 15·
Probability of getting an odd number in a single throw of a die
p(1) + p(3) + p(5) = p +p +p =3p =3*1/15=1/5
Probability of getting an odd number in a single throw of a die is 1/5
and probabilities of getting an even number = 4/5 .
As the die is rolled thrice, the events are independent, so it is a case of binomial distribution. The random variable X takes values 0, 1, 2 and 3.]
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