__Value Based Questions : Maths (Class XII)__

**RELATIONS AND FUNCTIONS**

Q.1 Prove that f : R → R is a bijection given by f(x) = x^{3} + 3 . Find f ^{-1}(x). Does the truthfulness and honesty may have any relation?

Q.2 Set A = { a_{1} , a_{2} , a_{3} , a_{4} , a_{5} } and B = { b_{1} , b_{2} , b_{3} , b_{4} , b_{5} }

when a_{i}‘s and b_{i}‘s Are school going students.

Define a relation from a set A to set B by x R y iff is a true friend of x.

If R = {(a_{1} , b_{1}) , (a_{2} , b_{1}) , (a_{3} , b_{3}) , ( a_{4} , b_{2}) , (a_{5} ,b_{2} )}

Is R a bijective function ? Do you think true friendship important in life ? How ?

Q.3 If h denotes the number of honest people and p denotes the number of punctual people and a relation between honest people and punctual people is given as h = p + 5. If P denotes the number of people who progress in life and a relation between number of people who progress and 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 the punctuality important in the progress of life?

Q.4 let A be the set of all students of class XII in a school and R be the relation, having the same sex on A, and then prove that R is an equivalence relation. Do you think, co-education may be helpful in child development and why?

**MATRICES & DETERMINANTS**

Q.5 Three shopkeepers A, B, C are using polythene, handmade bags (prepared by prisoners), and newspaper’s envelope as carry bags. it is found that the shopkeepers A , B , C are using (20 , 30 ,40) , (30 ,40 ,20) , (40 ,20 ,30) polythene , handmade bags and newspapers envelopes respectively. The shopkeepers A, B, C spent Rs.250, Rs.220 & Rs.200 on these carry bags respectively .Find the cost of each carry bags using matrices. Keeping in mind the social & environmental conditions, which shopkeeper is better? & why ?

Q.6 In a Legislative assembly election, a political party hired a public relation firm to promote its candidate in three ways; telephone, house calls and letters. The numbers of contacts of each type in three cities A, B & C are (500, 1000 and 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?

Q.7 A trust fund has Rs. 30,000 is to be invested in two different types of bonds. The first bond pays 5% interest per annum which will be given to orphanage and second bond pays 7% interest per annum which will be given 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 trust fund obtains an annual total interest of Rs. 1800. What are the values reflected in the question.

Q.8 Using matrix method solve the following system of equations

x + 2y + z = 7

x – y + z = 4

x + 3y + 2z = 10

If X represents the no. of persons who take food at home. Y represents the no. of parsons who take junk food in market and z represent the no. of persons who take food at hotel. Which way of taking food you prefer and way?

Q.9 A school has to reward the students participating in co-curricular activities (Category I) and with 100% attendance (Category II) brave students (Category III) in a function. The sum of the numbers of all the three category students is 6. If we multiply the number of category III by 2 and added to the number of category I to the result, we get 7. By adding second and third category would to three times the first category we get 12.Form the matrix equation and solve it.

Q.10 for keeping Fit X people believes in morning walk, Y people believe in yoga and Z people join Gym. Total no of people are 70.further 20% 30% and 40% people are suffering from any disease who believe in morning walk, yoga and GYM respectively. Total no. of such people is 21. If morning walk cost Rs 0 Yoga cost Rs 500/month and GYM cost Rs 400/ month and total 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?

Q.11 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 want girl child and get the abortion before her birth. Scheme B is for saving of newlywed girls from death due to dowry. Scheme C is planning for good health for senior citizen. Now twice the amount spent on Scheme C together with amount spent on Scheme A is Rs 700 crores. And three times the amount spent on Scheme A together with amount spent on Scheme B and Scheme C is Rs 1200 crores. Find the amount spent on each Scheme using matrices? What is the importance of saving girl child from the cruel parents who don’t want girl child and get the abortion before her birth?

Q.12 There are three families. First family consists of 2 male members, 4 female members and 3 children. Second family consists of 3 male members, 3 female members and 2 children. Third family consists of 2 male members, 2 female members and 5 children. Male member earns Rs 500 per day and spends Rs 300 per day. Female member earns Rs 400 per day and spends 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 of saving in the family ?

**APPLICATION OF DERIVATIVES**

Q.14 A car parking company has 500 subscribers and collects fixed charges of Rs.300 per subscriber per month. The company proposes to increase the monthly subscription and it is believed that for every increase of Re.1, one subscriber will discontinue the service. What increase will bring maximum income of the company? What values are driven by this problem?

Q.15 Check whether the function f(x) = x^{100} + sinx -1 is strictly increasing or strictly decreasing or none of both on (-1 ,1 ). Should the nature of a man be like this function? Justify your answers

Q.16 If y = x^{4} – x^{3}/3 when x denotes the number of hours worked and y denotes the amount (in Rupees) earned. Then find the value of (in interval) for which the income remains increasing? Explain the importance of earning in life?

Q.17 If performance of the students ‘ y ‘ depends on the number of hours ‘ x ‘ of hard work done per day is given by the relation.

y = 4x – x^{2}/2

Find the number of hours, the students work to have the best performance. ‘ Hours of hard work are necessary for success’ Justify.

Q.18 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 sum of 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 and money?

Q.19 Profit function of a company is given as P(x) = 24x/5 – x^{2}/100 – 500 , here x is the number of units produced. What is the maximum profit of the company? Company feels its social responsibility and decided to contribute 10% of his profit for the orphanage. What is the amount contributed by the company for the charity? Justify that every company should do it.

Q.20 In a competition a brave child tries to inflate a huge spherical balloon bearing slogans against child labour at the rate of 900 cubic centimeters of gas 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 skill reflected in this question.

Q.21 In a kite festival, a kite is at a height of 120m and 130m string is out. If the kite is moving horizontally at the rate of 5.2m/sec, find the rate at which the string is being pulled out at that instant. How a festival enhance national integration.

Q.22 An expensive square piece of golden color board of side 24 centimeters. is to be made into a box without top by cutting a square from each corner and 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 volume and minimize the wastage? What is the importance of minimizing the wastage in utilizing the resources?

Q.23 A student is given card board of area 27 square centimeters. He wishes to form a box with square base to have maximum capacity and no wastage of the board. What are the dimensions of the box so formed? Do you agree that students don’t utilize the resources properly? Justify.