2037977530maths Value Based Question Bank for Class Xii 2013-14

8/13/2019 2037977530maths Value Based Question Bank for Class Xii 2013-14

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Prepared by: M. S. KumarSwamy, TGT(Maths) Page - A -

MATHEMATICS

VALUE BASED QUESTIONS

QUESTION BANK

for

CLASS XII

2013 14

CHAPTER WISE COVERGAE OF EXPECTED

VALUE BASED QUESTIONS

Prepared by

M. S. KUMARSWAMY , TGT(MATHS)M. Sc. Gold Medallist (Elect.), B. Ed.

Ken dr iya Vidya l ay a do n imal ai


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Prepared by: M. S. KumarSwamy, TGT(Maths) Page - B -

PREFACE

It gives me great pleasure in presenting the Question Bank for Value Based

Questions for Class XII Mathematics for March 2014 Board Examination. It is in strictly

according to the latest guidelines issued by CBSE.

The CBSE has introduced the concept of value based questions in question

papers of all main subject from the session 2012-13. Total 3-5 marks questions will be

value based from this year onward in CBSE question papers. These questions are based

on values & key messages brought out on the basis of prescribed text. Students have the

liberty to go beyond the set text.

I avail this opportunity to convey my sincere thanks to respected sir Shri

Isampal, Deputy Commissioner, KVS RO Bangalore, respected sir Shri P. V. Sairanga

Rao, Deputy Commissioner, KVS RO Varanasi, respected sir Shri P. Deva Kumar,

Deputy Commissioner, KVS RO Ahmedabad, respected sir Shri. K. L. Nagaraju,

Assistant Commissioner, KVS RO Bangalore and respected sir Shri.Gangadharaiah,

Assistant Commissioner, KVS RO Bangalore for their blessings, motivation and

encouragement in bringing out this notes in such an excellent form.

I also extend my special thanks to respected madam Smt. Nirmala Kumari M.,

Principal, KV Donimalai and respected Shri. M. Vishwanatham, Principal, KV Raichur

for their kind suggestions and motivation while preparing this notes.

I would like to place on record my thanks to respected sir Shri. P. K. Chandran,

Principal, presently working in KV Bambolim. I have started my career in KVS under his

guidance, suggestions and motivation.

Inspite of my best efforts to make this notes error free, some errors might have

gone unnoticed. I shall be grateful to the students and teacher if the same are brought to

my notice. You may send your valuable suggestions, feedback or queries through email

to [email protected] that would be verified by me and the corrections would be

incorporated in the next year Question Bank.

M. S. KUMARSWAMY
mailto:[email protected]:[email protected]


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Prepared by: M. S. KumarSwamy, TGT(Maths) Page - C -

DEDICATED

TO

MY FATHER

LATE SHRI. M. S. MALLAYYA


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Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1 -

RELATIONS AND FUNCTIONS

1. Let L be the set of all the people in a locality. Let relation R in set L isdefined by (x, y) R x and y are like minded. Do you think R is anequivalence relation ? There are equivalence classes under the head

Honest, Punctual, Care for environment, Late comers. For whichequivalence class you would like to be its member ?

2. Let A be the set of all human beings in a town at a particular time. Therelation R is given by (x, y) R x and y are associated with SAVE THERARE SPECIES campaign. Find whether the relation R is reflexive,symmetric and transitive ? Do you want to campaign for the abovementioned cause ?

3. Let A be the set of 50 students (numbered 1 to 50) who like riding a

bicycle and make environment pollution free. Let f : A

N, N the set ofnatural number defined by f (x) = number of student x. Show that f is one-one but not onto. If we restrict N from 1 to 60, in what way we can make fonto ? Do you want to be a part in making function onto ?

4. Let set A be the set of people of different age groups associated withCLEANLINESS drive, Let * be a binary operation of setA defined by a * b= older of (a, b), a, b A. Is * commutative, associative inA ? Are you alsoa part of setA ?

5. Let L be the set of all the lines in a plane and R be the relation in L defined

as R = {(l1, l2) : l1 is parallel to l2}. Show that R is an equivalence relation.Find all the lines related to y = 3x 5. Let us relate parallel lines to parallelthinking. Let L be the set of people with same thinking BE HONEST.Would you like to be member of this equivalence relation ? Give yourviews in two lines.

6. Show that the relation R defined in the set A of all polygons as R = {(P1,P2) : P1 and P2 have same number of sides}, is an equivalence relation.What is the set of all elements in A related to the right-angled triangle Twith sides 3, 4 and 5 ? Do you think persons having the same ideology

form an equivalence relation ?

7. Let T be the set of all triangles in a plane and relation R on T be defined byx R y x is similar to y, i.e., R = {(x, y) : x is similar to y}. Show that R isan equivalence relation on T. Consider three right triangles x with sides 3,4, 5; y with sides 5, 12, 13 and z with sides 6, 8, 10. Which trianglesamong x, y, z are related ? Are the campaign for SAVE ENVIRONMENT,SAVE NATURAL RESOURCES, SAVE WILD LIFE inter related ?

8. Let R be a relation defined as R = { (x,y) : x and y study in the same class}.Show that R is an equivalence relation. If x is a brilliant student and y is a

slow learner and x helps y in his studies, what quality does x possess?


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18.Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2),(3,3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive. Howdifferent relations play a major role in our life?

19.Show that the relation R = { (a,b) : 2 divides ( a b)} in the set Z ofintegers is an equivalence relation. Also give two examples of social

relations which are equivalence relations.

20.Let A = Set of boys of XII Class in some school. Let a R b, if and only if aand b use unfair means in the exam, a,b A(i) Is R a transitive relation?(ii) Should a student use such means? If not why

21.Prove that f : RR is a bijection given by f (x) = x2+3. Find f 1 (x). Doesthe truthfulness and honesty may have any relation?

22.Set A = {a1, a2, a3, a4, a5} and B = {b1, b2, b3, b4} where ai s and bi s areschool going students. Define a relation from a set A to set B by xRy iff y isa true friend of x. If R = {(a1, b1), (a2, b1), (a3, b3), (a4, b2), (a5, b2)}. Is R abijective function? Do you think that true friendship is important in life?How?

23. If h denotes the number of honest people and p denotes the number ofpunctual people and a relation between honest people and punctualpeople is given as h = p + 5. If P denotes the number of people whoprogress in life and a relation between number of people who progressand honest people is given as P = (h/8) + 5. Find the relation between

number of people who progress in life and punctual people. How does thepunctuality important in the progress of life?

24.Let A be the set of all students of class XII in a school and R be therelation having the same sex (i.e., male or female) on set A, then provethat R is an equivalence relation. Do you think, co-education may behelpful in child development and why?

25.Everyone wants to be a perfect ideal human being. Let us assume thatdishonesty is one of the factors that affects our perfectness andperfectness has an inverse square relationship with dishonesty. For any

value x of level of dishonesty, we have a unique value y of perfection.(i) Write down the equation that relates y with x.(ii) Does this relationship from (0, )x X to (0, )y , form a function?

(iii) For what level of dishonesty one can achieve1

4

th

level of perfection?

(iv) What will be the change in level of perfection when the level ofdishonesty changes from 4 to 2?


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MATRICES

1. Two schools A and B decided to award prizes to their students for threevalues Honesty (x), Punctuality(y) and Obedience (z). SchoolA decided toaward a total of Rs. 15,000 for the three values to 4, 3 and 2 students

respectively, while school B decided to award Rs. 19,000 for the threevalues to 5, 4 and 3 students respectively. If all the three prizes togetheramount to Rs. 5,000, then

(i) Represent the above situation by a matrix equation and form linearequation using matrix multiplication.(ii) Which value you prefer to be rewarded most and why ?

2. A store in a mall has three dozen shirts with SAVE ENVIRONMENTprinted, two dozen shirts SAVE TIGER printed and five dozen shirts withGROW PLANTS printed. The cost of each shirt is Rs. 595, Rs. 610 and

Rs. 795 respectively. All these items were sold in a day. Find totalcollection of the store using matrix method.Which shirt you would like to buy and why ?

3. In section A of class XII of a particular school students were asked tograde each student under values Empathy, Honest, Respectful. Gradesare to be given as A, B, C. The following information was received.

Empathy Honest RespectfulA 26 20 30B 12 10 10

C 7 15 5

The same activity was carried out in section B of class XII of the sameschool and the following information was received.

Empathy Honest RespectfulA 30 16 38B 10 20 7C 8 12 3

Represent the above information in the matrix form and use matrices tofind how many students got A grade in the three values ?Which value according to you is most important to acquire ?

4. Three shopkeepers A, B, C are using polythene, handmade bags(prepared by prisoners), and newspaper s envelope as carry bags. It isfound that the shopkeepers A, B, C are using (20,30,40), (30,40,20,),(40,20,30) polythene, handmade bags and newspapers envelopesrespectively. The shopkeepers A, B, C spent Rs.250, Rs.270 & Rs.200 onthese carry bags respectively. Find the cost of each carry bags using

matrices. Keeping in mind the social & environmental conditions, whichshopkeeper is better? Why?


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5. In a Legislative assembly election, a political party hired a public relationfirm to promote its candidate in three ways: telephone, house calls andletters. The numbers of contacts of each type in three cities A, B & C are(500, 1000, 5000), (3000, 1000, 10000) and (2000, 1500, 4000),respectively. The party paid Rs.3700, Rs.7200, and Rs.4300 in cities A, B& C respectively. Find the costs per contact using matrix method.Keeping in mind the economic condition of the country, which way of

promotion is better in your view?

6. A trust fund has Rs.30,000 is to be invested in two different types ofbonds. The first bond pays 5% interest per annum which will be given toorphanage and second bond pays 7% interest per annum which will begiven to an N.G.O. cancer aid society. Using matrix multiplication,determine how to divide Rs.30,000 among two types of Bonds if the trustfund obtains an annual total interest of Rs.1800. What are the valuesreflected in this question?

7. Using matrix method, solve the following system of equations: x + 2y + z =

7, x y + z = 4, x + 3y +2z = 10. Suppose x represents the number ofpersons who take food at home, y represents the number of persons whotake junk food in market and z represent the number of persons who takefood at hotel. Which way of taking food you prefer and why?

8. A school has to reward the students participating in co-curricular activities(Category I), with 100% attendance (Category II) and brave students(Category III) in a function. The sum of the numbers of all the threecategory students is 6. If we multiply the number of students of category IIIby 2 and add to the number of students of category I to the result, we get

7. By adding II and III category students to three times the I categorystudents, we get 12. Form the matrix equation and, hence solve it.

9. For keeping fit, X people believe in morning walk, Y people believe in yogaand Z people join gym. Total no. of people are 70. Further 20%, 30% and40% people are suffering from any diseases who believe in morning walk,yoga and gym respectively. Total no. of such people is 21. If morning walkcosts Rs. 0, yoga costs Rs.500/month and gym costs Rs. 400/month andtotal expenditure is Rs. 23000.(i) Formulate a matrix problem.(ii) Calculate the no. of each type of people.

(iii) Why exercise is important for health?

10.An amount of Rs.600 crores is spent by the government in three schemes.Scheme A is for saving girl child from the cruel parents who don t wantgirl child and get the abortion before her birth. Scheme B is for saving ofnewlywed girls from death due to dowry. Scheme C is planning for goodhealth for senior citizen. Now twice the amount spent on Scheme Ctogether with amount spent on Scheme A is Rs. 700 crores. And threetimes the amount spent on Scheme A together with amount spent onScheme B and Scheme C is Rs.1200 crores. Find the amount spent oneach schemes using matrices. What is the importance of saving girl child

from the cruel parents who don t want girl child and get the abortionbefore her birth?


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11.There are three families. First family consists of 2 male members, 4 femalemembers and 3 children. Second family consists of 3 male members, 3female members and 2 children. Third family consists of 2 male members,2 female members and 5 children. Male member earns Rs. 500 per dayand spends Rs.300 per day. Female member earns Rs.400 per day andspends Rs. 250 per day, child member spends Rs.40 per day. Find the

money each family saves per day using matrices? What is the necessity ofsaving in the family?

12.Two schools A and B decided to award prizes to their students for threevalues honesty (x), punctuality (y) and obedience (z). School A decided toaward a total of Rs.11000 for the three values to 5, 4 and 3 studentsrespectively while school B decided to award Rs.10700 for the threevalues to 4, 3 and 5 students respectively. If all the three prizes togetheramount to Rs.2700, then:i. Represent the above situation by a matrix equation and form linearequations using matrix multiplication.

ii. Is it possible to solve the system of equations so obtained usingmatrices?iii. Which value you prefer to be rewarded most and why?

13.Three friends A, B and C visited a Super Market for purchasing fresh fruits.A purchased 1kg apples, 3kg grapes and 4kg oranges and paid Rs.800. Bpurchased 2kg apples, 1kg grapes and 2kg oranges and paid Rs. 500.While C paid Rs.700 for 5kg apples, 1kg grapes and 1kg oranges. Find thecost of each fruit per kg by using matrix method. Why are the fruits goodfor health?

14.Mr. Manoj has invested a part of his income in 10% (bond A) and anotherpart of his income in 15% (bond B). His interest during a certain period isRs.4000. Had he invested 20% more in bond A and 10% more in bond B,his interest would have been increased by Rs.500 for the same period.Then: (i) Represent the above situation by a matrix equation and formlinear equations using matrix multiplication. (ii) Is it possible to solve thesystem of equations so obtained by matrices? If yes, solve it too.

15. In XII class examination, 25 students from school A and 35 students fromschool B appeared. Only 20 students from each school could get through

the examination. Out of them, 15 students from school A and 10 studentsfrom school B secured full marks. Write down this information in matrixfrom.

16.A trust fund has `30,000 that is to be invested in two different types ofbonds. The first bond pays 5% p.a. interest which will be given toorphanage and second bond pays 7% interest p.a. which will be used forthe financial benefits of the trust. Using matrix multiplication, determinehow to divide Rs.30,000 among two types of bonds if the trust fund obtainsan Rs. annual total interest of Rs.1800.(i) What are the values reflected in the question?

(ii) Why is it required to help orphan children?


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17. In a survey of 20 richest person of three cities A, B and C it is found that incity A, 5 believe in honesty, 10 in hardwork, 5 in unfair means while in cityB, 5 believe in honesty, 8 in hardwork, 7 in unfair means and in city C, 6believe in honesty, 8 in hardwork, 6 in unfair means. If the per day incomeof these richest persons of cities A, B and C are Rs. 32.5K, Rs.30.5K andRs.31K respectively, then find the per day income of each type of personby matrix method.

(i) Which type of persons have more per day income?(ii) According to you, which type of person is better for country?

18.The cost of 4 chocolates, 3 samosas and 2 apples is Rs.60 and that of 2chocolates, 4 samosas, and 6 apples is Rs.90. The cost of 6 chocolates, 2samosas, 3 apples is Rs.70. Find the cost of each item by matrix method.What do you think is the healthiest diet?Suggest an item that could replace chocolates and samosas to make thediet healthier?

19.There are 3 families. Family A consists of 2 men, 3 women and 1 child.Family B has 2 men 1 woman and 3 children. Family C has 4 men, 2women and 6 Children. Daily expenses of men, women and children are200,155 and 200 respectively. Only men and women earn and children donot. Using matrix multiplication calculate the daily expenses of each family.What impact does having more children in the family create on thesociety? Comment.

20.Gaurav donates 3 pens, 2 bags and 1 instrument box worth Rs.41,Dheeraj donates 2 pens, 1 bag and 2 instrument boxes worth Rs29, whileAnkur donates 2 pens, 2 bags and instrument boxes to a rural school.

Translate the problem into a system of linear equations. Solve & find thecost of each item.By the act of these three people what values do you learn?

21.There are 2 families A & B. There are 4 men, 6 women and 2 children infamily A, 2 men, 2 women and 4 children in family B. The recommendeddaily allowance for calories is 2400 for men, 1900 for women, 1800 forchildren and 45gms of proteins for men, 55gms for women and 33gms forchildren. Represent the above information using matrices. Using matrixmultiplication, calculate the total requirement of calories and proteins foreach of the 2 families.What awareness can you create among people about the balanced diet?

22.Last year 1 packet of tea and 3 packets of sugar together cost Rs.96.Thisyear, the rate of tea increased by 15% and that of sugar by 10%. So, thesame amounts of tea and sugar now cost Rs.108.60. Find the rates ofsugar and tea per packet last year and this year using matrix method.What do you think is the impact of inflation on family expenses?

23.A part of the monthly expenses of a family is constant while the remainingvaries with the price of rice, fuel etc., When the price of rice is Rs 25/Kg

the monthly expenses of the family is Rs.1000. when it is Rs 24/Kg themonthly expenses is Rs 980. Find the total monthly expenses of the family


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when the cost of rice is Rs 35/Kg. Is this family below poverty line? Givesome suggestions to improve their standard of living.

24.A dietician to mix two types of food,Food1 and Food2 in such a way that

the vitamin content of the mixture contains 8 units of vitamin A and 10

units of vitamin C. Food 1 contains 2units/kg of vitamin A and 1 units/kg of

vitamin C. While Food2 contains 1 unit/kg of vitamin A and 2 units/kg ofvitamin C. How many kg of Food1 and Food2 to mixed for getting her

requirement? Formulate this problem as matrix form and solve by matrix

method. What is the importance of vitamin content food in our diet than

junk food

25.Three shopkeepers A, B, C go to a store to buy stationary. A purchases 12dozen notebooks, 5 dozen pens and 6 dozen pencils. B purchases 10dozen notebooks, 6 dozen pens and 7 dozen pencils.C purchases 11dozen notebooks, 13 dozen pens and 8 dozen pencils. A note book costs40 paise, a pen costs Rs. 1.25 and a pencil cost 35 paise. Use matrixmultiplication to calculate each individuals bill. What values should notcome across the shopkeeper's mind to compete?

26.Consider the following information regarding the number of men and

women workers in three factories I, II and III

Factories Men workers Women workersI 30 25II 32 20III 29 23

Represent the above information in the form 3x2 matrix.What does the entry in the third row and second column represent?Is it necessary to equalize the number of men and women workers? Whatis your opinion? Explain the importance of gender equality in employment.

27. In his saving of Rs 200000, father divides the amount between his two

children and a servant. He gives 45% each to his son and daughter and

the remaining to his servant. Write this in matrix form and calculate how

much does the servant get and what is the value point in this question.

28. In a legislative assembly election, a political group hired a public relationsfirm to promote its candidates in three ways: telephone, house calls andletters. The cost per contact (in Paisa ) is given in matrix A as

40 Telephone

100 House call

50 Letter

A

. The number of contacts of each type made in two

cities X and Y is given in matrix B as

Telephone House call Letter

1000 500 5000

3000 1000 10000

XB

Y

Find the total amount spent by the group in the two cities.What is your opinion to reduce the cost of election?


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29.There are two families P and Q . There are 3 men, 3 women and 12children in family P and 2men, 2 women and 4 children in family Q. Therecommended daily allowance for calories is : Man : 2400, woman : 2000,child : 1400 and man : 60g for proteins is : woman : 40g and child : 35g.

(i) Represent the above information by matrices. Using matrixmultiplication, calculate the total requirement of calories and proteins of

each of the two families.

(ii) Which family is an ideal family and why ?

30.Represent the following problem by a system of linear equations : Rs154500 is the Cost of 3 cycles, 2 motorbikes and one car, the cost of onecycle, one motorbike and 2 cars is Rs 226500. The cost of 4 cycles and 3motorbikes is Rs 81000. Use matrix to Find the cost of each . Whichmode of conveyance preferred the most and why?

31.Two firms P and Q decided to award prizes to their employees for three

values Punctuality (x), Honesty (y) and obedience (z). Firm P decided toaward a total of Rs 22000 for the three values to 10,8 and 6 employeesrespectively, while firm Q decided to award Rs 21400 for the three valuesto 8,6 and 10 employees respectively. If all the three prizes togetheramount to Rs 2700, then

(i) Represent the above situation by a matrix equation and form linearequations using matrix multiplication.

(ii) Is it possible to solve the system of linear equations so obtained usingmatrices?

(iii) Which value you prefer to be rewarded most and why?

32.Two schools A and B decided to award prizes to their students for thethree values Truth (x), patriotism (y) and Non - violence (z). School Adecided to award a total of Rs 11000. For the three values to 5,4 and 3students respectively. While school B decided to award Rs 10700 for thethree values to 4,3 and 5 students respectively . If all the three prizestogether amount to Rs 2700, then

(i) Represent the above situation by a matrix equation and form linearequations using matrix multiplication.

(ii) Is it possible to solve the system of equations so obtained usingmatrices?

(iii) Which value you prefer to be awarded most and why?

33.A sum of saving amount of Rs 10000 is put into three investments at therate of 10%,12% and 15% p.a. The combined income of first and secondinvestment is Rs 190 less of the income of third investment. If thecombined income is Rs 1310, then find the Investment in each usingmatrices. Keeping nations growth in mind, justify the value of saving in

individual life.


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34.(a) A trust fund has Rs. 30000 that must be invested in two different typesof bonds. The first bond pays 5% interest per year & the second bondpays 7% interest per year. Using matrix multiplication , determine how todivide Rs.30000 among the two types of bonds if the trust fund mustobtain an annual total interest of Rs.2000.

(b)If the same interest is obtained by investing in social welfare measures,

which type of investment you would prefer & why.

35.Two institutions P and Q decided to award prizes for academic, sports and

all-round achievements awarded rupees 12000 to 3,1,1 students while Q

awarded rupees 7000 1o 1 , 0, 2 students in the above category. All the

three prizes together amount to rupees 6000.Find the matrix

representation of the above representation. Solve the system of equations

using matrices. Do you agree that prizes should be given for honesty and

good character also? Give reasons.

36.The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost of 2 kgonion, 4 kg wheat and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kgwheat and 3 kg rice is Rs 70. Find cost of each item per kg by matrixmethod. What do you think is the impact of inflation on family expenses?


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APPLICATIONS OF DERIVATIVES

1. The total cost C(x) of planting x plants in a garden is given by C(x) =0.005x3 0.02x2+ 30x + 6000. Find the marginal cost when 200 trees areplanted. Do you think plantation helps in saving the environment ?

2. The total revenue received from the sale of x souvenirs in connection withPEACE DAY is given by R(x) = 3x2+ 40x + 10. Find the marginal revenuewhen 100 souvenirs were sold. What is the importance of celebratingPeace Day in our life ?

3. A rectangular plot is to be developed for a meeting to be organised onSAVE WILD LIFE. It is given that the plot must have a fixed perimeter.Find the area of the plot so that maximum persons can attend the meet.

Would you also like to attend the meet ? What are your views on SAVEWILD LIFE?

4. Two sign boards, one circular and one square are to be made using a wireof length 40 m and cutting it into two pieces. The sign boards are to depictBE HONEST and BE PUNCTUAL and these are to be displayed nearthe main gate of the school. What should be the lengths of the two pieces,so that the combined area of the square and the circle is minimum ? Doyou think these values are important in life ?

5. A cylindrical box is to be made, which is open at the top and has a given

surface area. Souvenirs of different life values are to be stored in the box,so we would like to have maximum volume of the box. What should be thedimensions of the cylindrical box ? Name some of the values which areimportant to each person.

6. An organisation wants to inculcate awareness among people about SAVEENERGY. For this it wants to display a big balloon in the air. A balloonwhich always remains spherical is being inflated by pumping in gas at therate of 900 cm3/sec. Find the rate at which the radius of the balloon isincreasing when the radius of the balloon is 15 cm. Do you think we shouldbe a part of SAVE ENERGY campaign ?

7. The performance of a student in x months in governed by the relation f (x)= 2x3 15x2+ 36x + 17 in [0, 4]. Find during which month his performanceis increasing or decreasing. What steps a student should take to improvethe performance.

8. Rectangular boards of different areas are to be made for use as displayboards. On these boards life skills are to be displayed. The area ofexpanding rectangle is increasing at the rate of 48 cm2/sec. The length ofrectangle is always equal to square of breadth. At what rate the length isincreasing when breadth is 4.5 cm ? Name two life skills which you wouldlike to acquire.


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9. Verify Lagranges Mean Value theorem for the function f(x) = (x 3) (x 6)(x 9) in the interval [3, 5]. On the graphical representation for the abovefunction, two moral values are engraved, one on the line segment joining(3, 0) and (5, 8) and the other at C. Suggest two moral values to beengraved.

10.A rectangular piece of tin of sides 45 cm and 24 cm is to be made into abox without top by cutting a square piece from each corner and folding theflaps. What should be the side of the square to be cut off so that thevolume of the box is maximum ? On four sides of this box write four lifeskills.

11.Define absolute value function | x |. Let f be a function defined as :

5 | |, 0

( ), 0

6

x xwhen x

f x xwhen x

Show that f is discontinuous at x = 0. What are your views aboutLEARNING. Is learning a continuous process.

12.Find the equation of the tangent to the curve y = x sinxcosx at2

x .

Along the tangent write two like skills / moral values which one shouldacquire.

13.A cone is 10 cm in diameter and 10 cm deep. Water is poured into it at therate of 4 cubic cm/minute. At what rate is the water level rising at the

instance when depth is 6 cm ? Water is a natural resource. What is theimportance of water in our daily life?

14.A window is in the shape of a rectangle surmounted by a semicircle. If itsperimeter is 30 m, then find the dimensions of the window so that it mayadmit maximum light. Do you think that by getting maximum light we cansave electricity ? Do you agree that we should save electricity ?

15.Show that semi-vertical angle of a right circular cone, of given total surface

area and maximum volume, is 11

sin3

. On the surface is written Respect

for beliefs and cultures of various religions. Do you believe in mutualrespect ?

16.Show that the semi-vertical angle of a cone of maximum volume and given

slant height is 1tan 2 . This statement will help us in making a conical tentfor a gathering on CLEANLINESS. What are your views about theCLEANLINESS ?

17.The volume of a spherical balloon is increasing at the rate of 20 cm3/sec.Find the rate of change of its surface area at the instant when its radius is8 cm. On the balloon Make India Polio Free is printed. Do you think thatwe should work seriously towards Polio eradication ?


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18.Water is leaking from a conical funnel at the rate of 5cm3/sec. If the radiusof the base of the funnel is 5 cm and its altitude is 10 cm, find the rate atwhich the water level is dropping, when it is 2.5 cm from the top. Is leakingof water leads to wastage of water ? Do you think we can afford to wasteour natural resources ?

19.Show that the curves 2x = y2 and 2xy = k, cut at right angles if k2 = 8.

Suggest one moral value to be written at the point of intersection ofcurves.

20.Show that the altitude of the right circular cone of maximum volume that

can be inscribed in a sphere of radius r is4

3

r. This statement will help us

in making a conical cup for serving WATER to the people. What are yourviews about the serving water to the people?

21.Show that height of the cylinder of greatest volume which can be inscribed

in a right circular cone of heighth

and semi vertical angle a is one-thirdthat of the cone and the greatest volume of cylinder is 3 2

4tan

27h . This

statement will help us in making a cylindrical glass for serving WATER tothe people during summer season. What are your views about the servingwater to the people?

22.Show that the height of the cylinder of maximum volume that can be

inscribed in a sphere of radius R is2

3

R. Also find the maximum volume.

This statement will help us in making a cylindrical glass for servingWATER to the people during summer season. What are your views aboutthe serving water to the people?

23.A tank with rectangular base and rectangular sides, open at the top is tobe constructed so that its depth is 2 m and volume is 8 m3. If building oftank costs Rs 70 per sq metres for the base and Rs 45 per square metrefor sides. What is the cost of least expensive tank? On the top of tank iswritten Respect for beliefs and cultures of various religions. Do youbelieve in mutual respect ?

24.An open topped box is to be constructed by removing equal squares fromeach corner of a 3 metre by 8 metre rectangular sheet of aluminium andfolding up the sides. Find the volume of the largest such box. On the top ofthe box Make India Polio Free is printed. Do you think that we shouldwork seriously towards Polio eradication ?

25.A water tank has the shape of an inverted right circular cone with its axis

vertical and vertex lowermost. Its semi-vertical angle is 1tan 0.5 . Water ispoured into it at a constant rate of 5 cubic metre per hour. Find the rate atwhich the level of the water is rising at the instant when the depth of waterin the tank is 4 m. On the top of tank is written GO GREEN INDIA. Give

some of values about green India?


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26.Show that the right circular cone of least curved surface and given volume

has an altitude equal to 2 time the radius of the base. This statement willhelp us in making a cylindrical glass for serving WATER to the peopleduring summer season. What are your views about the serving water tothe people?

27.The radius of a spherical diamond is measured as 7 cm with an error of

0.04 cm. Find the approximate error in calculating its volume .if the cost of1 cm diamond is rupees 1000,what is the loss to the buyer of thediamond? What lesson do you get?

28.Let x be the number of years a person is engaged in the share market. Hisincome is given by f(x) = x4 - 8 x3 + 22 x2 + 10 , 0< x 10. Find theintervals in which his income is increasing and decreasing. Do you thinkthat dealing in share market is a risky affair? Give reasons

29.A window is in the form of rectangle surmounted by a semicircular

opening. The total perimeter of the window is 10m. Find the dimensions ofthe window to admit maximum sunlight through the whole opening. Explainthe importance of sunlight.

30.An Apache helicopter of enemy is flying along the curve given by y = x2+7. A soldier, placed at (3,7) wants to shoot down the helicopter when it isnearest to him. Find the nearest distance. What is the main quality neededfor the soldier? What steps can be taken to ensure peace betweencountries?

31.A window is in the form of rectangle surmounted by a semicircular

opening. The total perimeter of the window is 20m. Find the dimensions ofthe window to admit maximum light through the whole opening. What isthe benefit of using maximum area for the window?

32.Show that the percentage error in calculating the volume of a cubical box ifan error of 1% is made in measuring the length of edges of the cube is3%. What is the value you learn from that?

33.The total area of a page is 150cm2. The combined width of the margin atthe top and bottom is 3cm and the side 2cm. What must be thedimensions of the page in order to get the maximum area of printed

matter?

34.A stone is dropped into a quiet lake and waves move in circles at a speedof 4cm per second. At the instant, when the radius of the circular wave is10 cm, how fast is the enclosed area increasing? What steps can you taketo maintain a clean lake?

35. If the radius of a sphere is measured as 7 m with an error of 0.02 m, thenfind the approximate error in calculating its volume. What will you do if youget an incorrect value in your practical exam?


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36.Find local maximum and local minimum values of the function f given byf (x) = 3x4+ 4x3 12x2+ 12. What can you do to maximize your efforts toget maximum marks in exam?

37.A car starts from a point P at time t = 0 seconds and stops at point Q. The

distance x, in metres, covered by it, in t seconds is given by2 2

3

tx t

.

Find the time taken by it to reach Q and also find distance between P andQ. What steps should you take for safe driving?

38.The edge of a cubical gold is measured as 8 cm with an error of 0.03 cm.Find the approximate error in its volume. What is the loss to the buyer ofthe gold if the cost of 1 cubic cm of gold is Rs. 3000. What lesson do youget?

39.The bottom of a rectangular fish tank is 30 cm X 15 cm. Water is pumped

into the tank either by man-made pump at the rate of 50 cubic cm/minuteor by motor pump at the rate of 75 cubic cm/minute. Find the rate at whichthe level of the water in the tank is rising when water is pumped by motorpump. Which pump would you prefer and why?

40.A jet of an enemy is flying along the curve 2 7y x . A solider is placed at

the point (3,7). Find the nearest distance between the solider and the jet.The soldier is refused to fire the jet when it is nearest to him? Is this act ofthe solider justifiable. Discuss.

41.Find the volume of the largest cylinder that can be scooped out from agiven wooden solid cone. Give a valued method of using the left out woodand justify?

42.A car driver is driving a car on the dangerous path given by

1, 1

( ) ,1, 1

1

mx

xf x m Nx

xm

Find the dangerous point (point of discontinuity) on the path. Whether thedriver should pass that point or not? Justify your answers.

43.A car parking company has 500 subscribers and collects fixed charges ofRs.300 per subscriber per month. The company proposes to increase themonthly subscription and it is believed that for every increase of Re.1, onesubscriber will discontinue the service. What increase will bring maximumincome of the company? What values are driven by this problem?

44.A farmer wants to construct a circular well and a square garden in his field.He wants to keep sum of their perimeters fixed. Then prove that the sumof their areas is least when the side of square garden is double the radius

of the circular well. Do you think good planning can save energy, time andmoney?


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45. In a competition a brave child tries to inflate a huge spherical balloonbearing slogans against child labour at the rate of 900 cubic centimeters ofgas per second. Find the rate at which the radius of the balloon is

increasing when its radius is 15cm. Also write any three values/life skillreflected in this question.

46. In a kite festival, a kite is at a height of 120m and 130m string is out. If thekite is moving horizontally at the rate of 5.2m/sec, find the rate at which thestring is being pulled out at that instant. How a festival enhance nationalintegration.

47.An expensive square piece of golden color board of side 24 centimeters. isto be made into a box without top by cutting a square from each cornerand folding the flaps to form a box. What should be the side of the square

piece to be cut from each corner of the board to hold maximum volumeand minimize the wastage? What is the importance of minimizing thewastage in utilizing the resources?

48.A student is given card board of area 27 square centimeters. He wishes toform a box with square base to have maximum capacity and no wastageof the board. What are the dimensions of the box so formed? Do youagree that students dont utilize the resources properly? Justify.

49.Check whether the function100( ) sin 1f x x x is strictly increasing or

strictly decreasing or none of both on (1, 1) . Should the nature of a manbe like this function? Justify your answers.

50. If

34

3

xy x , when x denotes the number of hours worked and y

denotes the amount (in Rupees) earned. Then find the value of x (ininterval) for which the income remains increasing? Explain the importanceof earning in life?


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APPLICATIONS OF THE INTEGRALS

1. A sign board in the shape of a parabola y2= 16x is to be made such that

area is bounded by the parabola y2

= 16x and the line x = 4. On the signboard life values such as OBEDIENT OBSERVANT EMPATHY,SINCERE etc., are to be written. What is the area of the sign board?What do you think about acquiring value EMPATHY ?

2. Three hoardings are displayed at the pointsA, B and C displayingA (DONOT LITTER), B (KEEP YOUR PLACE CLEAN) and C (GO GREEN). Ifthese three points form a triangle ABC. Find the area of ABC, usingmethod of integration, if points A, B and C are (0, 2), (4, 8) and (8, 4)respectively. Give your views in two lines about GO GREEN.

3. A field is in the form of parabola x2= 4y. A farmer has planted trees in theexterior to the region bounded by the parabola and y = |x| and theremaining part for playing games for children. Find the area of the groundwhere the students are playing games. What is the importance of gamesin students life

4. Evaluate

2

2 1

xdx

x . State any one reason to have integrity in real life

5. The area between x = y2and x=4 is divided into equal parts by the line x =

a, find the value of a. A man constructed a house in one of the area andplanted trees in the other area. Find the area where he constructedhouse? What is the importance of plantation of trees?

6. Evaluate/ 4

0log(1 tan )x dx

.What can be the possible limits of integrityin real life according to you?

7. A farmer has a plot in the shape of a circle x2+ y2 = 4. He divides hisproperty among his son and his daughter in such a way that for son hegives the area interior to the parabola y2= x and for daughter the area

interior to the parabola y2= -x. How much area the son got? Have both ofthem got equal share? What is the value for life behind this?

8. Find the integration of cos2xcos4xcos6x. What is the importance ofintegration of different religions for our country peace?

9. Using the method of integration find the area bounded by the curve |x| + |y|= 1 . What is the value of truthfulness in our life?

10.Find the integration of exsin x dx. Write any famous proverb for unity.

11. Integrate sin (ax + b) cos (ax + b). Write any two characteristics ofMahatma Gandhi which you adore the most?


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12.Find the area lying above x-axis and included between the circle x2+ y2=8x and the parabola y2= 4x. What is the importance of non-violence in ourlife?

13.A farmer has a piece of land. He wishes to divide equally in his two sons to

maintain peace and harmony in the family. If his land is denoted by areabounded by curve y2 = 4x and x = 4 and to divide the area equally hedraws a linewhat is the value of a? What is the importance of equalityamong the people?

14.A circular Olympic gold medal has a radius 2cm and taking the centre atthe origin, Find its area by method of integration. What is the importance ofOlympic Games for a sportsman and why? Olympic game is a supremeplatform for a sportsman. In Olympic Games all countries of the worldparticipate and try their best and make their country proud.

15.A poor deceased farmer has agriculture land bounded by the curve y=cosx, between x = 0 and x=2 . He has two sons. Now they want todistribute this land in three parts (As already partitioned). Find the area ofeach part. Which parts should be given to the farmer & why? Justify youranswer.

16. If a triangular field is bounded by the lines x+2y = 2, y-x = 1 and 2x+y =7Using integration compute the area of the field (i)If in each square unitarea 4 trees may be planted. Find the number of trees can be planted Inthe field.(ii)Why plantation of trees is necessary?

17.A parking lot in an IT company as an area bounded by the curve y = 4 x2and the lines y = 0 and y = 3. The line y = 3 divides the area into two partsout of which the greater area is allotted for car owners who practice carpooling. Find this area using integration. Write any two benefits ofcarpooling.

18. Integrity is an integral part of a students life. Elucidate. Similarly find the

value of the integral2 2 7

dx

x x

19.A construction company is constructing a gated community in a plot of 10grounds. When he decides to allocate sufficient space for a park and gym

in an area given by

3 4

3a

a

xd x

. Find a using/ 2

3

0 0

2 sina

xdx a xdx

.Highlight the values reflected by the gesture of the company.

20.Evaluate using limit as a sum :3

2

1(2 5 1)x x dx

Mention two suitable situations in your everyday life


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21.Using integration find the area of the bounded region y = 1 + | x + 1 | ; Therequired area is divided into two regions and the students are asked to puta posters on Child Labour and Education for all in those two. Whichtheme according to you deserves a bigger space? Justify.

22. Integrate exsin2x with respect to x. What values are integrated and instilledin children with the singing of the National Anthem?

23.Find the area of the region enclosed by the curve y = x2 lines x = 0, y = 1and y = 4. A farmer plans to construct an electrical fence around thisbounded region to protect his crop. But his son rejects this idea and wantsa wooden fence to be erected. Who would you favour? Mention two valuesdemonstrated by the son.

24.Draw the graph and evaluate the integral3

1| 3 |x dx . What geometric

property does the shaded region exhibit about the line x = 3. Write any twovalues you in real life that you can correlate with this property.

25.Evaluate as the limit of a sum :3 2

1(2 3 1)x x dx . Mr. X. crossed the

limit while speaking at a public function by using abusive language. Whatvalues should one possess while speaking in a public forum. Mention anytwo.


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VECTOR, THREE-DIMENSIONAL GEOMETRY

1. Two groups of students representing SAVE MOTHER EARTH and GO

GREEN are standing on two planes represented by the equation .( 2 ) 5r i j k

and .(2 ) 8r i j k

. What is the angle between the two

planes ? Name few activities which should be taken up to Save MotherEarth.

2. Find the coordinates of the foot of the perpendicular drawn from the pointA(1,8,4) to the line joining the points B(0,-1,3) and C(2,-3,1). Representfoot of the perpendicular with one life skill.

3. Find the image of the point (1,2,3) in the plane x+2y+4z=38. Represent theimage of the point with one life skill.

4. Three hoardings are displayed at the points A,B and C displaying A(Do notlitter), B(Keep your place clean) and C(Go green). If these 3 points form atriangle ABC, find the area of the triangle ABC using method of vectors ifpoints A,B and C are (0,2,1),(4,8,2) and (8,4,3) respectively. Give yourviews in two lines about GO GREEN.

5. If , ,a b c

are position vectors of vertices A,B,C of a triangle ABC, show that

the area of the triangle is 1

2a b b c c a . A student takes honesty,

truthfulness and complacency as the three sides of the triangle. Whichside of the triangle do we prefer to take? Give your suggestion.

6. Let A and B be two points whose position vectors are 3 4 8i j k and

4 7 4i j k respectively. Find AB

and BA

. If point A represents a person

who is regular and systematic and B represents a lazy person, which

vector AB

or BA

would you choose for your success?

7. In metropolitan city a bypass road to be constructed passing through the

point (1,1,1) and parallel to the road whose equation given by .( 2 3 ) 5r i j k . Find the equation of the bypass road. State one benefit

that people get from this?

8. Find the reflection of the point (1,2,-1) in the plane 3x 5y + 4z = 5. Whatis the value of fixing mirrors on T roads?

9. Find the foot of the perpendicular from the point (2,3,4) to the line4 1

2 6 3

x y z . Also find the perpendicular distance from a given point to

a line. If you want to construct a road joining point and the line which wayyou prefer to make and why?


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10.Find the coordinates of the point where the line through (5, 1, 6) and (3,4,1) crosses the YZ-plane. What should we have in mind while crossing aroad?

11.Find the equation of the plane through the line of intersection of the planesx + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x y+ z = 0. Which value will you choose if you have to choose between good

and truth?

12.Find | ab|, if a = 2 3i j k and b = 3 5 2i j k . We should be firm and

determined about __________________ in life.(Hint: some value as youperceive is a possible answer). Why?

13.Find the area of a triangle having the points A(1, 1, 1), B(1, 2, 3) and C(2,3, 1) as its vertices. What is the difference between finding its area and atriangle in which all points are in a single plane?

14.Find the coordinates of the point where the line through the points A (3, 4,1) and B(5, 1, 6) crosses the XY-plane. Name any two values which weget from our friends.

15.Considering the earth as a plane having equation 5x + 9y 10z + 138 = 0,

a monument is standing vertically such that its peak is at the point (1, 2,3). Find the height of the monument. How can we save our monument?

16.Let the point P(5, 9, 3) lies on the top of Qutub Minar, Delhi. Find the

image of the point on the line:1 2 3

2 3 4

x y z . Do you think that the

conservation of monuments is important? Why?

17.Two bikers are running at the speed more than allowed speed on the road

along the lines (3 )r i j k i j

and 4 (2 3 )r i k i k

. Using

Shortest distance formula check whether they meet to an accident or not?While driving, the driver should maintain the speed limit as allowed.Comment.

18.Two airships are moving in space along the following lines3 5 7

1 2 1

x y z and

1 1 1

7 6 1

x y z

. An astronaut wants to move

from one ship to another ship when two airships are closest. What is theleast distance between the ships that he has to travel?

19.Find the area of a hoarding board with logo GO GREEN in the form oftriangle having the points A(1, 1, 1), B(1, 2, 3) and C(2, 3, 1) as itsvertices. Give your views in two lines about GO GREEN.


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20.Find the vector equation of the line passing through (1, 2, 3) and parallel to

the roads .( 2 ) 5r i j k

and .(3 ) 6r i j k

. What should we have in

mind while crossing a road?

21.A bird is located at the point A(3, 2, 8) in space. It wants to move to theplane whose equation is given by 3x + 2y + 6z + 16 = 0 in the shortesttime. Find the distance she covered.

22.From the point A(2, 3, 8) in space, a shooter aims to hit the target at P(6,

5, 11). If the line of fire is2 3 8

4 2 3

x y z , what do you think about the

success of the shooter?

23.A bird at A(7, 14, 5) in space wants to reach a point P on the plane 2x + 4y z = 2 when AP is least. Find the position of P and also the distance APtravelled by the bird.

24.Show that a powerful bomb shot along the line of fire 1 2 32 3 4

x y z

will never hit a helicopter flying in the plane 2x + 4y 4z + 11 = 0.

25.A gunner who is hiding himself from the enemy is at the point G(2, 1, 3)and observes an enemy bomber flying along the plane 3x + 6y + 2z +10 =0. What is the least distance of G from the plane?

26.Find the area of a hoarding board with logo GO GREEN in the form of

parallelogram whose adjacent sides are given by the vectors 3 4a i j k

and

b i j k

. Give your views in two lines about GO GREEN.

27.Find the coordinates of the point where the line through (5, 1, 6) and (3,4,1) crosses the ZX-plane. What should we have in mind while crossing aroad?

28. If the lines1 2 3 1 1 6

3 2 2 3 1 5

x y z x y zand

k k

are perpendicular,

find the value of k. If you want to construct a road joining point and the linewhich way you prefer to make and why?

29.Find the distance of the point ( 1, 5, 10) from the point of intersection

of the two roads 2 2 (3 4 2 )r i j k i j k

and .( ) 5.r i j k

What

should we have in mind while crossing a road?

30. If the coordinates of the hoarding showing display SAVE WATER whichis in the quadrilateral with A, B, C, D be (1, 2, 3), (4, 5, 7), ( 4, 3, 6) and(2, 9, 2) respectively, then find the angle between the lines AB and CD.Give your views in two lines about SAVE WATER.


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DIFFERENTIAL EQUATIONS

1. Form the differential equation of the family of circles touching y axis at

origin. What are the values conveyed by the family of circles formed?

2. The temperature T of a cooling object drops at a rate which is proportionalto the difference T S, where S is the constant temperature of the

surrounding medium. Thus ( )dT

k T Sdt

, where k > o is a constant and t

is the time. Solve the differential equation if it is given that T(0) =150. Whatare the demerits of global warming?

3. Form the differential equation of the family of parabolas having vertex atthe origin and axis along positive y-axis. Mosquito bite is the origin for

`Dengue . Suggest two methods to curb the breeding of mosquitoes.

4. Show that the given differential equation is homogeneous and solve it.x2 dy + y (x+y) dx = 0. Which is advantageous to life homogeneity orhetrogenity ? Justify your answer.

5. Solve the differential equation: x(x2 1 )dy

dx=1 ; y =0 when x = 2. If `y is

distance and x is the time.dy

dxis velocity. Ravi rides a vehicle beyond the

limit in a highway.What suggestions would you give him to help him understand the risks ofoverspeeding?

6. In a college hostel accommodating 1000 students, one of the hostellerscame in carrying a flu virus, and the hostel was isolated. If the rate atwhich the virus spreads is assumed to be proportional to the product of thenumber N of infected students and the number of non-infected students,and if infected students are 50 after 4 days then show that more than 95%of the hostellers will be infected after 10 days.If Shyam was the first student to be infected what precautions he should

have initiated to avoid this situation.

7. The population of a city increases at a rate proportional to the number ofinhabitants present at any time t. If the population of the city was 200000in 1990 and 250000 in 2000, what will be the population in 2010? What isthe main awareness to be given among the people to control population?

8. If the interest is compounded continuously at 6% per annum, how muchworth Rs 1000 will be after 10 years? How long will it take to double Rs1000? (Given e0.6= 1.822 ). What is the importance of savings among thestudents?


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9. Form the differential equation of the family of parabolas having vertex atorigin and axis along positive y-axis. Suggest one method to enhance thegender equity in our country?

10.Show that the differential equation (x y)dy

dx= x + 2y is homogeneous

and solve it. State one step to eliminate the racial discrimination?

11.Find the equation of a curve passing through the point (0, 1). If the slope ofthe tangent to the curve at any point (x, y) is equal to the sum of the xcoordinate (abscissa) and the product of the x coordinate and y coordinate(ordinate) of that point. In what way the coordination among people willbring harmony in society?

12.Solve the differential equation

(xdy y dx) y sin(y

x) = (y dx + x dy) x cos(

y

x)

In what way human conscience overcomes the human mind?

13.The population of a village increases continuously at the rate proportionalto the number of its inhabitants present at any time. If the population of thevillage was 20, 000 in 1999 and 25000 in the year 2004, what will be thepopulation of the village in 2009? What are the values coming in your mindconsidering village life?

14.Solve the differential equation2( 2 )

dyx y y

dx . Given that when x=2,

y=1.If x denotes the people who are Polite and y denotes the % of peoplewho are intelligent. Find when. A polite child is always liked by all insociety. Do you agree? Justify.

15. 0dy y

dx x , where x denotes the percentage population living in a city & y

denotes the area for living a healthy life of population. Find the particularSolution when Is higher density of population is harmful? Justify yoursanswer.

16.The velocity v and mass m of a rocket at time t are given by the equation:

0dv dm

m Vdt dt

, where V is the constant velocity of emission. If the rocket

starts from rest when t = 0 with mass m0 , then prove that:

0log m

v Vm

. Should we encourage the rocket technology? Comment.

17.The male-female ratio of a village increases continuously at the rateproportional to the rate at any time. If the ratio of male-female of the villagewas 1000:980 in 1999 and 1000:950 in 2009, what will be the ratio in

2019?(i) Why is the gender equality value-able for the society?


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LINEAR PROGRAMMING

1. Suppose every gram of wheat produces 0.1 g of protein and 0.25 g ofcarbohydrates and corresponding values for rice are 0.05 g and 0.5 g

respectively. Wheat cost Rs. 25 and rice Rs. 100 per kilogram. Theminimum daily requirements of proteins and carbohydrates for an averageman are 50 g and 200 g respectively. In what quantities should wheat andrice be mixed in a daily diet to provide minimum daily requirements ofproteins and carbohydrates at minimum cost, assuming that both wheatand rice are to be taken in a diet ? What is your opinion about healthy dietname few ingredients necessary for a healthy diet ?

2. A retired person has Rs. 70,000 to invest in two types of bonds. First typeof bond yields an annual income of 8% on the amount invested and thesecond type of bond yields 10% per annum. As per norms he has to invest

minimum of Rs. 10,000 in first type and not more than Rs. 30,000 insecond type. How should he plan his investment so as to get maximumreturn after one year of investment ? Do you think that a person shouldstart saving at an early age for his retirement ? Can you name someavenues ?

3. A company manufactures two types of stickers A : SAVEENVIRONMENT and B : BE COURTEOUS. Type A requires 5 minuteseach for cutting and 10 minutes each for assembling. Type B requires 8minutes each for cutting and 8 minutes each for assembling. There are 3hours and 20 minutes available for cutting and 4 hours available for

assembling in a day. He earns a profit of Rs. 50 on each type A and Rs.60 on each type B. How many stickers of each type should the companymanufacture in a day to maximize profit ? Give your views about SAVEENVIRONMENT and BE COURTEOUS.

4. A farmer decides to plant up to 10 hectares with cabbages and potatoes.He decides to grow at least 2, but not more than 8 hectares of cabbageand at least 1 but not more than 6 hectares of potatoes. If he can make aprofit of Rs. 1,500 per hectare on cabbage and Rs. 2,000 per hectare onpotatoes, how should he plan his farming so as to get the maximum profit,assuming the total yield that he gets is sold. What is your opinion aboutfarmer getting maximum profit ? Do you think we should help the farmersin every way to maximise the production ?

5. Asha wants to invest atmost Rs. 20,000 in VIII series National SavingBonds and Kisan Vikas Patra. According to rules she has to invest at leastRs. 5,000 in Saving Bonds and atmost Rs. 8,000 in Kisan Vikas Patra. Ifthe rate of interest on Saving Bonds is 10% p.a. and rate on Kisan VikasPatra is 15% p.a., how much money should she invest in each to earnmaximum yearly income. Also, find the maximum yearly income. Do youthink our investment in National Saving Bonds and Kissan Vikas Patra

help in the well being of the nation ?


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6. A factory owner purchases two types of machinesA and B for his factoryto produce Eco-friendly vehicles. The requirements and limitations for themachines are as follows :

Area occupiedby

machine

(in sq. m)

Labour force foreach machine

(man)

Daily Outputin units

Machine A 1000 12 60Machine B 1200 8 40

He has an area of 9,000 sq. m available and 72 skilled men who canoperate the machines. How many machines of each type should he buy tomaximise the daily output ? Do you agree we should use Eco-friendlyvehicle for transportation ?

7. Two godowns,A and B have a grain storage capacity of 100 quintals and50 quintals respectively. They supply to three ration shops, D, E and Fwhose requirements are 60, 50 and 40 quintals respectively. The cost oftransportation per quintal from the godowns to the shops are given as

Transportation cost per quintal (in Rs.)FromTo

A B

D 6 4E 3 2F 2 3

How should the supplies be transported so that the transportation cost isminimum ? What are other positive effects of minimum cost ?

8. If a person drives his car at 25 km/hr, he has to spend Rs. 2/km on petrol.If he drives it at a faster speed of 40 km/hr, the petrol cost increases to Rs.5/km. He has Rs. 100 to spend on petrol and wishes to find what is themaximum distance he can travel within one hour. Express this as a L.P.P.and solve it. Which is a better option as a fuel, petrol or CNG ?

9. A producer has 30 units and 17 units of labour and capital respectively,which he can use to produce two types of goods X and Y. To produce one

unit of X, 2 units of labour and 3 units of capital are required. Similarly 3units of labour and 1 unit of capital are required to produce one unit of Y. IfX and Y are priced at Rs. 100 and Rs. 120 per unit respectively, howshould the producer use his resources to maximise the total revenue.Solve the problem graphically. Which life skills produces is supposed todevelop.

10.A company produces two types of hoardings A and B representing lifeskills. Profits on each types of hoarding are Rs. 2 and Rs. 1.5 respectively.A hoarding of type A requires twice as much time as of hoarding B. Thecompany can produce at the most 1000 hoardings of type B per day.Material for only 800 hoardings per day is available. At the most 400buckles for hoardings of type A and 700 of type B are available per day.


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How many hoardings of each type should the company produce so as tomaximise the profit ? Which two life skills would you like to be written on Aand B ?

11.A company produces two types of goods A and B that require gold andsilver. Each unit of type A requires 1 gram of silver and 2 grams of gold.Each unit of type B requires 2 grams of silver and 1 gram of gold. The

company has only 100 grams of silver and 80 grams of gold. Each unit oftypeA brings a profit of Rs. 500 and each unit of type B brings a profit ofRs 400. Find the number of units of each type the company shouldproduce to maximise the profit. These goods A and B are to be used assouviners during debate on SAVE WILD LIFE. What do you mean bySAVE WILD LIFE ?

12.A small manufacturing firm produces two types of gadgetsA and B whichare first processed in the foundary shop, then sent to another machineshop for finishing. The number of man hours of labour required in eachshop for the production of each unit of A and B and the number of man

hours for the firm available per week are as follows :

Foundaryshop

Machineshop

GadgetA 10 5Gadget B 6 4Firm capacity perweek(in hours)

1000 600

The profit on sale of A is Rs. 30 per unit and on B is Rs. 50 per unit.Formulate the linear programming model for determining how many unitsof each gadgets should be produced per week to maximise the firmsprofit. The firm keeps its workers happy and cares for them. Do you thinkcompany is in good shape and progress well ? Which life skill companyacquires ?

13.A carpenter has 20 and 15 square metres of plywood and sunmicarespectively. He produces products A and B. Product A requires 2 and 1square metres and product B requires 1 and 3 square metres of plywoodand sunmica respectively. If the profit on one piece of product A is Rs. 30

and on one piece of product B is Rs. 20, how many pieces of product Aand B should he make to maximise his profit ? These products are to beused as sign boards for a procession regarding awareness among peopletowards their environment. Suggest two slogans for productA and productB, one each.

14.A hospital dietician wishes to find the cheapest combination of two foodsAand B, that contains at least 0.5 mg of thiamine and at least 600 calories.Each unit of food A contains 0.12 mg of thiamine and 100 calories, whileeach unit of food B contains 0.01 mg of thiamine and 150 calories. If eachfood costs Rs. 10 per unit, how many units of each should be combined for

minimum cost ? Is balanced food necessary for us to remain active ? Whatare your views about Junk food ?


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15.A dealer wishes to purchase a number of fans and sewing machines. Hehas only Rs. 57,600 to invest and has space for atmost 20 items. A fancosts him Rs. 3,600 and a sewing machine Rs. 2,400. Profit on selling afan and a sewing machine are Rs. 220 and Rs. 180 respectively.Assuming that he can sell all the items that he can buy, how should heinvest his money in order to maximise his profit ? Formulate this problem

mathematically and solve it graphically. Do you think sewing machine isenvironmental friendly ?

16.A housewife wishes to mix together two kinds of foods X and Y, in such away that the mixture contains at least 10 units of vitamin A, 12 units ofvitamin B and 8 units of vitamin C. The vitamin contents of one kg of foodis given below :

Vitamin A Vitamin B Vitamin CFood X 1 2 3

Food Y 2 2 1

One kg of food X costs Rs. 6 and one kg of food Y costs Rs. 10. Formulatethe above problem as a linear programming problem to find the least costof mixture which will produce the diet. Write two lines about the importanceof balanced diet.

17.A company combines two itemsA and B from gift packs during a festivalseason. Each pack must weigh 5 kg and should contain at least 2 kg of Aand not more than 4 kg of B. The net contribution of the company is ` 10per kg of A and ` 12 per kg of B. The company wants to determine theoptimum mix. Formulate the L.P.P. to maximise the net contribution perpack. What is the importance of exchanging gifts with friends andrelatives?

18.A company sells two different products A and B. The two products areproduced in a common production process which has a total capacity of500 man hours. It takes 5 hours to produce a unit of A and 3 hours toproduce a unit of B. The demand in the market shows that maximumnumber of units ofA that can be sold is 70 and that of B is 125. Profit oneach unit of A is Rs. 20 and that on B is Rs. 15. Has many units ofA and B

should be produced to maximise the profit ? Solve it graphically. ConsiderproductsA and B as awareness projects for environment. Name two suchenvironmental needs.

19.Kelloggs is a new cereal formed of a mixture of bran and rice that containat least 88 grams of protein and at least 36 milligrams of iron. Knowingthat bran contains 80 grams of protein and 40 milligrams of iron perkilogram and that rice contains 100 grams of protein and 30 milligrams ofiron per kilogram, find the minimum cost of producing this new cereal, ifbran costs Rs. 5 per kilogram and rice costs Rs. 4 per kilogram. Do youthink new cereal formed is a healthy diet ?


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20.An aeroplane can carry a maximum of 200 passengers. A profit of Rs.400 is made on each first class ticket and a profit of Rs.300 is made oneach economy class ticket. The airline reserves at least 20 tickets for firstclass seats. However, at least 4 times as many passengers prefer to travelby economy class as compared to the first class. Determine how manytickets of each type must be sold in order to maximise the total profit forthe airline. Solve the problem by graphical method. Is an aeroplane Eco-

friendly mode for travelling ?

21.A machine company has factories at two places A and B. From theseplaces, supply is made to each of its three agencies situated at P, Q andR. The monthly requirement of the agencies are respectively 40, 40 and50 packets of machines, while the production capacities of the factories atA and B are 60 and 70 respectively. The transportation cost (in `) perpacket from the factories to agencies are given below :

From

To

A B

P 5 4Q 4 2R 3 5

How many packets from each factory be transported to each agency so that thecost of transportation is minimum ? Also find the minimum cost. What is thesignificance of minimum travel cost ? Is this related to SAVE ENVIRONMENT /

NATURAL RESOURCES ?

22.A firm manufactures jute bags and cloth bags. The total number of items itcan manufacture is at most 24. A Jute bag requires 1 hour to be madewhile a cloth bag requires only half an hour. The maximum number ofhours available per day is 6 hours. If the profit on a jute bag is Rs.30 andon a cloth bag is Rs.20, how many bags of each type must be made formaximum profit? Solve it graphically. The manufacturer wants to replacecloth bags by plastic bags to increase his profit margin. Is it a good idea? Ifnot, give reasons.

23.A manufacturer makes cycles and scooters. Processing of these productsis done on two machines A and B. The cycle parts need 2 hours on

machine A and 6 hours on machine B. Parts of a scooter needs 4 hours onmachine A and 2 hours on machine B. Machine A is available for 16 hoursper day and Machine B is available for 30 hours per day. Profit gained bythe manufacturers from a cycle and a scooter is Rs.1000 and Rs.3000respectively. Find with the help of a graph what should be the dailyproduction of each of the two products to maximize the profit? Which ofthe above modes of transport is a better option and why?

24.There are two types of fertilizers that a farmer uses in his farm namely Aand B. A consists of 10 % of nitrogen and 6% phosphoric acid while Bcontains 5% nitrogen and 10% phosphoric acid. The farmer needs at least

14 kg of nitrogen and 14 kg of phosphoric acid. If A costs Rs. 8/kg and Bcosts Rs. 6/kg, determine how much of each type of fertilizer should beused by the farmer so that the required nutrient levels are met at minimum


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cost. What is the minimum cost? The farmer is considering the option ofusing pesticides to increase his yield. What is your opinion? Can heconvert it into an organic farm?

25.A farmer decides to plant upto 10 hectares with cabbages and potatoes.He decides to grow at least 2 but not more than 8 hectares of cabbagesand at least 1 but not more than 6 hectares of potatoes. He can make a

profit of Rs. 1500 per hectare on cabbages and Rs.2000 per hectare onpotatoes. How should he plan his farming so as to maximize his profit.Keeping in mind the nutritional value of both vegetables, do you think thefarmers production will help the community? Mention one value point thefarmer display?.

26.A manufacturer produces two types of disposable plates, one using plasticand the other using bamboo. Three machines are required to produce theplates and the time in minutes is given below.

MachinesType of Plate I II III

Plastic 12 18 6Bamboo 6 0 9

Each machine is available for a maximum of 6 hours per day. If the profiton each plate of plastic is 75 paise and profit on bamboo plate is 50 paise,how many plates of each type should the factory produce to maximize theprofit. Which type of plates do you think should be promoted more andmention one value point as the reason.

27.A principal decides to buy colour boxes and books as prizes for children. Acolour box costs Rs.5 and a book costs Rs. 10.He wants to buy at least 4of each of them. How many of each should he buy so that the expendituredoes not exceed Rs.100 and at the same time can give maximum numberof prizes? Which of the two , do you think will benefit the children moreand mention one value point as the reason.

28.A diet for a sick person must contain atleast 4000 units of vitamins, 50units of minerals and 1400 calories. Two foods X and Y are available at acost of Rs 4 and Rs 3 per unit respectively. One unit of food X contains200 units of vitamins, 1 unit of minerals and 40 calories, whereas one unit

of food Y contains 100 units of vitamins, 2 units of minerals and 40calories. Find what combination of X and Y should be used to have leastcost, satisfying the requirements? Explain the importance of balanceddiet.

29.A farmer has a supply of chemical fertilizer of type A which contains 10%nitrogen and 5% phosphoric acid, and type B which contains 6% nitrogenand 10% phosphoric acid. After testing the soil conditions of the field, itwas found that at least 14kg of nitrogen and 14 kg of phosphoric acid isrequired for producing a good crop. The fertilizer of type A costs Rs 5 perkg and the type B costs Rs 3 per kg. How many kg of each type of thefertilizer should be used to meet the requirement at the minimum possiblecost ? Using L.P.P. Solve the above problem graphically.Which manure you prefer to be promoted and why ?


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30. If a Youngman rides his motorcycle at 25 km/ hour, he had to spend Rs 2per km on Petrol . If he rides at a faster speed of 40 km/hour, the petrolcost increases at Rs 5 per Km. He has Rs 100 to spend on petrol andwishes to find what is the maximum distance he can travel within onehour . Express this as L.P.P. and solve it graphically. Which mode oftransport you suggest to a young man and why.

31.(a)There are two types of fertilizers F1& F2. F1consists of 10% nitrogen &6% phosphoric acid & F2 consists of 5% nitrogen & 10% phosphoric acid.After testing the soil conditions, a farmer finds that he needs atleast 14 kgof nitrogen & 14 kg of phosphoric acid for his crop. If F1costs Rs. 6/kg &F2costs Rs.5/kg , determine how much of each type of fertilizer should beused so that nutrient requirements are met at a minimum cost. What is theminimum cost.(b)Joseph found that his uncle ,who did not have experience of growingplants, was planting the seeds. He explained his uncle the properprocedure for planting the seeds. His uncle , following the sameprocedure , planted the seeds & the same came out successfully. Whatvalues& qualities you find with Joseph & with his uncle.

32.A man owns a field of area 1000 sq.m. He wants to plant fruit trees in it.He has a sum of Rs. 1400 to purchase young trees. He has the choice oftwo type of trees. Type A requires 10 sq.m of ground per tree and costs Rs20 per tree and type B requires 20 sq.m of ground per tree and costs Rs25 per tree. When fully grown, type A produces an average of 20 Kg offruit which can be sold at a profit of Rs. 2.00 per Kg and type B producesan average of 40 Kg of fruit which can be sold at a profit of Rs. 1.50 per

Kg. How many of each type should be planted to achieve maximum profitwhen the trees are fully grown? What is the maximum profit? What are theadvantages that the man received by the plantation of trees.

33.A catering agency has two kitchens to prepare food at two places A and B.From these places Mid-day Meal is to be supplied to three differentschools situated at P, Q, R. The monthly requirements of the schools arerespectively40, 40 and 50 food packets. A packet contains lunch for 1000students. Preparing capacity of kitchens A and B are 60 and 70 packetsper month respectively. The transportation cost per packet from thekitchens to schools is given below:

Transportation cost per packet (in Rs)

FromTo A B

P 5 3Q 4 2

R 3 5

How many packets from each kitchen should be transported to school so

that the cost of transportation is minimum? Also find the minimum cost.What is the value of giving mid day meals in the schools?


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34.Anils mathematics teacher has given him three very long list of problemswith the instruction to submit not more than 100 of them(correctly solved)for credit. The problem in the first set are worth 5 points each, those in thesecond set are of worth 4 points each, and those are in the third set are ofworth 6 points each. Anil knows from experience that he requires on theaverage 3 minutes to solve a 5 point problem, 2 minutes to solve a 4 pointproblem and 4 minutes to solve a 6 point problem. Because he has other

subjects to worry about, he cannot afford to devote more than 3 hoursaltogether to his mathematics assignment. Moreover, the first two sets ofproblems involve numerical calculations and he knows that he cannotstand more than 2 hours work on this type of problem. Under thesecircumstances, how many problems of these categories shall he do inorder to get maximum possible credit for his efforts? Formulate this as aLPP. What is the importance of time management? According to you whyAnil cant do the entire question in time?

35.A fruit grower can use two types of fertilizer in his garden, brand P andbrand Q. The amounts (in kg) of nitrogen, phosphoric acid, potash, and

chlorine in a bag of each brand are given in the table. Tests indicate thatthe garden needs at least 240 kg of phosphoric acid, at least 270 kg ofpotash and at most 310 kg of chlorine. If the grower wants to minimize theamount of nitrogen added to the garden, how many bags of each brandshould be used? What is the maximum amount of nitrogen added in thegarden?

kg per bagBrand P Brand Q

Nitrogen 3 3.5Phosphoric acid 1 2

Potash 3 1.5Chlorine 1.5 2

In which way the fruit grower is helping the environment?

36.A dietician wishes to mix two types of foods in such away that vitamincontents of the mixture contain atleast 8 units of vitamin A and 10units ofvitamin C. Food I contains 2 units/kg of vitamin A and 1 unit/kg of vitaminC. Food II contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C. Itcosts Rs 50 per kg to purchase Food I and Rs 70 per kg to purchaseFood II. Formulate this problem as a linear programming problem to

minimise the cost of such a mixture. In what way a balanced and healthydiet is helpful in performing your day-to-day activities?

37.A dealer in rural area wishes to purchase a number of sewing machines.He has only 5,760.00 to invest and has space for at most 20 items. Anelectronic sewing machine costs him `360.00 and a manually operatedsewing machine `240.00. He can sell an Electronic Sewing Machine at aprofit of `22.00 and a manually operated sewing machine at a profit of`18.00. Assuming that he can sell all the items that he can buy how shouldhe invest his money in order to maximize his profit. Make it as a linearprogramming problem and solve it graphically. Keeping the rural

background in mind justify the values to be promoted for the selection ofthe manually operated machine.


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38.A company sells two different products A and B. The two products areproduced in a common production process which has a total capacity of500 man hours. It takes 5 hours to produce a unit of A and 3 hours toproduce a unit of B. The demand in the market shows that the maximumnumber of units of A that can be sold is 70 and that of B is 125 . Profit oneach unit of A is Rs. 20 and on B is Rs. 15. How many units of A and B

should be produced to maximize the profit. Form an L.P.P. and solve itgraphically. What safety measures should be taken while working in afactory?

39.A cooperative society of farmers has 50 hectare of land to grow two cropsX and Y. The profit from crops X and Y per hectare are estimated as Rs10,500 and Rs 9,000 respectively. To control weeds, a liquid herbicidehas to be used for crops X and Y at rates of 20 litres and 10 litres perhectare. Further,no more than 800 litres of herbicide should be used inorder to protect fish and wild life using a pond which collects drainagefrom this land.

How much land should be allocated to each crop so as to maximize thetotal profit of the society?How can you protect wildlife from destruction?

40.An oil company has two depots A and B with capacities of 7000 L and4000 L respectively. The company is to supply oil to three petrol pumps, D,E and whose requirements are 4500L, 3000L and 3500L respectively.The distances(in km) between the depots and the petrol pumps is given inthe following table:

Distance in (km.)From

/ To

A B

D 7 3E 6 4F 3 2

Assuming that the transportation cost of 10 litres of oil is Re 1 per km, howshould the delivery be scheduled in order that the transportation cost isminimum?What is the minimum cost?How can you save fuel in your daily routine? any two ways

41.A dealer in rural area wishes to purchase a number of sewing machines.

He only has rupees 5760 to invest and has space for at most 20 items. Anelectronic sewing machine costs him rupees 360 each while a manually

operated sewing machine costs him rupees 240. He can sell an electronic

machine at a profit of rupees 22 and that a manually operated machine at

a profit of rupees 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

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.


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42. If a class XII student aged 17 years, rides his motor cycle at 40km/hr, thepetrol cost is Rs. 2 per km. If he rides at a speed of 70km/hr, the petrolcost increases Rs.7per km. He has Rs.100 to spend on petrol and wishesto cover the maximum distance within one hour.(a) Express this as an L .P.P and solve graphically.(b) What is benefit of driving at an economical speed?(c) Should a child below 18years be allowed to drive a motorcycle? Give

reasons.

43.Vikas has been given two lists of problems from his mathematics teacherwith the instructions to submit not more than 100 of them correctly solvedfor marks. The problems in the first list are worth 10 marks each and thosein the second list are worth 5 marks each. Vikas knows from pastexperience that he requires on an average of 4 minutes to solve a problemof 10 marks and 2 minutes to solve a problem of 5 marks. He has othersubjects to worry about; he cannot devote more than 4 hours to hismathematics assignment. With reference to manage his time in bestpossible way how many problems from each list shall he do to maximize

his marks? What is the importance of time management for students?

44.An NGO is helping the poor people of earthquake hit village by providingmedicines. In order to do this they set up a plant to prepare two medicinesA and B. There is sufficient raw material available to make 20000 bottlesof medicine A and 40000 bottles of medicine B but there are 45000 bottlesinto which either of the medicine can be put. Further it takes 3 hours toprepare enough material to fill 1000 bottles of medicine A and takes 1 hourto prepare enough material to fill 1000 bottles of medicine B and there are66 hours available for the operation. If the bottle of medicine A is used for

8 patients and bottle of medicine B is used for 7 patients.How the NGO should plan his production to cover maximum patients?How can you help others in case of natural disaster?

45.A toy company manufactures two types of dolls, A and

2037977530maths Value Based Question Bank for Class Xii 2013-14

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Transcript of 2037977530maths Value Based Question Bank for Class Xii 2013-14