VALUE BASED QUESTIONS
CLASS XIIMATHEMATICS
RELATION AND FUNCTIONS
1. (A) Show that the function f :
defined by f(x) = 3x + 4 is an invertible function.
(B) If x represents the number of systematic hours of study that a student puts in and f(x)
represents the marks scored by him, from the graph of the above function, which value will
be rewarded?
Expected answers:

Systematic study

Quality of hard work

Study habit

Time management
2.(A) Consider a relation R in the set A of people in a colony. Defined asaRbiff a and b are
members of joint family. Is R is an equivalence relation?
(B) Staying with Grandparents in a joint family imbibes the moral values in us. Can you
elicit 2 such values?
(a)
(b)
c)
Love and concern for grandparents
Respect for Group parents
Tolerance
3.(A) 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.
(B) If x is a brilliant student and y is a slow learner and x helps y in his studies, what
quality does x possess?
4. (A) Consider the functions f and g,f: {1, 2, 3}
g: {a, b, c}
{a, b, c} and
{punctuality, honesty, sincerity} defined as f(1) = a, f(2) = b, f(3) = c,
g (a) = punctuality, g(b) = honesty, g(c) = sincerity. Show that f, g, gof are invertible.
(B) If a, b, care three students who are awarded prizes for the three values given in the
function g, which value would you prefer to be rewarded and why?
MATRICES AND DETERMINANTS
1.(A) The cost of 4 chocolates, 3 samosas and 2 apples is Rs.60 and that of 2 chocolates, 4
samosas, and 6 apples is Rs.90. The cost of 6 chocolates, 2 samosas, and 3 apples is Rs.70.
Find the cost of each item by matrix method. (B) What do you think is the healthiest diet?
Suggest an item that could replace chocolates and samosas to make the diet healthier?
EXPECTED VALUES:
1.
2.
3.
4.
fruits
sprouts
salads
fresh juices
2.(A) 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 Rs. 11000 for the
three values to 5, 4 and 3 students respectively while school B decided to award Rs. 10700 for
the three values to 4, 3 and 5 students respectively. If all the three prizes together amount to
Rs. 2700, then. Represent the above situation by a matrix equation and form Linear equations
using matrix multiplication.
(B) Is it possible to solve the system of equations so obtained using matrices? Which value
you prefer to be rewarded most and why?
3.(A) A trust fund has Rs 30,000 that is to be invested in two different types of bonds. The first
bond pays 5% p.a. interest which will be given to orphanage and second bond pays 7% interest
p.a. which will be given to financial benefits of the trust. 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.
(B) (i) What are the values reflected in the question?
(ii) Why is it required to help orphan children?
4. (A) 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.(B) Keeping in mind the social &
environmental conditions, which shopkeeper is better? & why?
5.(A) To promote “Compulsory Education” awareness an NGO awards those who take any of
the following subjects as additional subjects. From the table given below, form a set of
simultaneous equations and solve using matrix method to find the amount given exactly to each
subject.(B) Which subject has to be promoted the most and why?
S.No.
Subject
No. of students in A No. of students in B No of students in C
1.
Compulsory education
1
1
3
2.
Adult literacy
1
2
1
Amount received
6,000
7,000
12,000
CONTINUITY AND DIFFERENTIABILITY
 cos 3x  cos x
,x  0

1.(A) f ( x)  
Show that f ( x) is continuous at x  0
x2

 4, x  0
(B) Mention any two factors that will affect the continuity of thought while writing the
examination
2.(A) The path of a moving bike is given by
. Find the dangerous point
on the path.(B) Whether the rider should pass that point or not? Justify your answers
APPLICATION OF DERIVATIVES
1. (A) A window is in the form of rectangle surmounted by a semi-circular opening. Total
perimeter of the window is 10 m. What will be the dimensions of the whole opening to
admit maximum light and air?
(B) (i) How having large windows help us in saving electricity and conserving
environment?
(ii) Why optimum use of energy is required in the Indian context?
2.(A) In a competition, a brave child tries to inflate a huge spherical balloon bearing slogans
against child labour at the rate of 900 cubic centimeter of gas per second. Find the rate at
which the radius of the balloon is increasing when its radius is 15 cm.
(B) (i) Which values have been reflected in this question?
(ii) Why child labour is not good for society?
3.(A) 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. (B) Do you think good planning can
save energy, time and money?
4. (A) 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? (B) What is the importance of minimizing the wastage in
utilizing the resources?
5.(A) A kite is moving horizontally at the height of 151.5. If the speed of the kite is 10m/s how
fast is the string being let out, when the kite is 250 meters away from the boy who is flying the
kite? The height of the boy is 1.5 meters. (B) Do you fly kites? Many accidents have been
reported recently due to kite flying in busy road sides? Suggest some methods to prevent
such road accidents.
Indefinite Integrals, Definite Integrals and Application of Integrals
1.(A) A parking lot in an IT company has an area bounded by the curve y = 4 – x2 and the lines
y = 0 and y = 3. The line y = 3 divides the area into two parts out of which the greater area is
allotted for car owners who practice car pooling. Find this area using integration.
(B) Write any two benefits of carpooling.
Ans : (a) Fuel saving (b) less pollution (c) space management
3
2.(A) Evaluate using limit as a sum :  ( 2x2 + 5x + 1 ) dx
1
(B) Mention two suitable situations in your everyday life (be it food , travel, matters, media,
etc.) where limiting yourself will help you evolve as abetter human being.
3. (A) Evaluate
(B) If the variable x denotes a measure of honesty, suggest a value for the upper limit ‘a’
that you would like to have. Why?
4.(A) If a triangular field is bounded by the lines x + 2y = 2 , y – x = 1 and 2x + y = 7.Using
integration compute the area of the field i) If in each square unit area 4 trees may be planted,find
the number of trees that can be planted in the field.(B) Why plantation of trees is necessary ?
5.(A) A circular Olympic gold medal has a radius 2cm and taking the centre at the origin, finds
its area by method of integration. (B) What is the importance of Olympic Games for a
sportsman and why? Olympic game is a supreme platform for a sportsman. In Olympic
Games all countries of the world participate and try their best and make their country
proud.
DIFFERENTIAL EQUATIONS
1.(A)Show that given differential equation is homogeneous and solve : x 2 dy+ y (x+y) dx = 0.
(B) Which is advantageous to life homogeneity or heterogeneity? Justify your answer.
Homogenity : equal rights, uniformity, oneness, Unity in diversity
Hetrogenity : independently thinking and acting individuals who work for the society.
2.(A) Solve the differential equation
: x ( x 2 – 1) dy/dx =1 ; y =0 when x = 2
If `y’ is distance and x is the time. dy/dx is velocity.
(B) Ravi rides a vehicle beyond the limit in a highway. What suggestions would you give
him to help him understand the risks of over speeding?
3.(A) Form the differential equation of the family of circles touching y axis at origin.
(B) What are the values conveyed by the family of circles formed?.
4.(A) The population grows at the rate of 5% per year. How long does it take for the population
to double?(B) There is always an ‘INCREASE ‘in the population every year? What is the
remedial measure to reduce the growth?
VECTORS
  
a
1(A) .If , b , c are position vectors of vertices A, B, C of a triangle ABC, show that the area of
1
aˆ  bˆ  bˆ  cˆ  cˆ  aˆ
the triangle is 2
.
(B) A student takes honesty, truthfulness and complacency as the three sides of the triangle.
Which side of the triangle do we prefer to take? Give your suggestion.
EXPECTED ANSWER:
I.
Honesty
II.
Truthfulness
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
2.(A) Let A and B be two points whose position vectors are 3i  4 j  8k and 4i  7 j  4k
respectively. Find
and
.
(B) If point A represents a person who is regular and systematic and B represents a lazy
person, which vector
or
would you choose for your success?
EXPECTED ANSWER:
= systematic – laziness = success.
3. (A) Three hoardings are displayed at the points A,B and C displaying A(Do not litter), B(Keep
your place clean) and C(Go green). If these 3 points form a triangle ABC, find the area of the
triangle ABC using method of vectors if points A,B and C are (0,2,1),(4,8,2) and (8,4,3)
respectively.(B) Give your views in two lines about “GO GREEN”.
THREE DIMENSIONAL GEOMETRY
1. (A) Two groups of students representing ‘SAVE MOTHER EARTH’ and ‘GO GREEN’
 ˆ ˆ
ˆ
r
are standing on two planes represented by the equations .(i  j  2k )  5 and

r .(2iˆ  ˆj  kˆ)  8 . What is the angle between the 2 planes?(B) Name few activities
which should be taken up to save mother earth.
EXPECTED ANSWER:
We should be concerned about not wasting natural resources, having development in a
planned manner.
2. (A) The point A(1,8,4) is situated at QutubMinar. Find the coordinates of the foot of the
perpendicular drawn from Ato the line joining the points B(0,-1,3) and C(2,-3,1).
(B)
Do you think that the conservation of monument is important why?.
3. (A) Find the image of the point (1,2,3) in the plane x+2y+4z=38. (B) Represent the
image of the point with one life skill.
EXPECTED VALUES:
I.
Truthfulness
II.
Honesty
LINEAR PROGRAMMING
1. (A) There are two types of fertilizers that a farmer uses in his farm namely A and B. A
consists of 10 % of nitrogen and 6% phosphoric acid while B contains 5% nitrogen and
10% phosphoric acid. The farmer needs at least 14 kg of nitrogen and 14 kg of
phosphoric acid. If A costsRs. 8/kg and B costs Rs. 6/kg, determine how much of each
type of fertilizer should be used by the farmer so that the required nutrient levels are met
at minimum cost. What is the minimum cost? (B) The farmer is considering the option
of using pesticides to increase his yield. What is your opinion? Can he convert it into
an organic farm?
Pesticides may increase the yield but are harmful to mankind. Organic farming is a good
option as it is free of use of any chemicals
2. (A) A dealer in rural area wishes to purchase a number of sewing machines. He has only
Rs.5760.00 to invest and has space for at most 20 items. A electronic sewing machine
costs him Rs.360.00 and a manually operated sewing machine Rs. 240.00. He can sell
an Electronic Sewing Machine at a profit of Rs. 22.00 and a manually operated sewing
machine at a profit of Rs.18.00. 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(B). Keeping the rural background in
mind justify the ‘values’ to be promoted for the selection of the manually operated
machine.
3. (A) 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? (B) Which mode of
transport would you suggest to a student and why?
4. (A) If a class XII student aged 17 years, rides his motor cycle at 40km/hr, the petrol cost
is Rs. 2 per km. If he rides at a speed of 70km/hr, the petrol cost increases Rs.7per km.
He has Rs.100 to spend on petrol and wishes to cover the maximum distance within one
hour. Express this as an L .P.P and solve graphically. (B) What is benefit of driving at
an economical speed? Should a child below 18years be allowed to drive a
motorcycle? Give reasons.
5. (A) A diet for a sick person must contain at least 4,000 units of Vitamins, 50 units of
minerals
and 1400 Calories. Two foods X and Y are available at a cost of Rs: 4.00 and Rs: 3.00
per units respectively. One unit of food X contain 200 units of Vitamins,1 unit of Mineral
and 40 calories, where as one unit of food Y contain 100 units of vitamins,2 units of
minerals and 40 calories. Make an LPP and find the combination of X and Y should be
used to have least cost, satisfying the requirements.(B) Suggest some method for
removing malnutrition among Children in villages? As a student how will you
respond to the under privileged among your schoolmates?
PROBABILITY
1. (A) Three rifle men take one shot each at the same target. The probabilities of the first,
secondand third rifle men hitting the target are 0.4, 0.5, 0.8 respectively. Find the
probability that exactly 2 of them hit the target.
(B) The National Cadet Corps (NCC) provides opportunities for training in gun
firing.Write 2 benefits of students joining NCC.
Ans – 1)Personal discipline 2) acquiring survival skills 3) team spirit and learning to work
as a team 4) patriotism 5) Care for others and social service
2. (A) In an event, a player has to win all 10 rounds continuously. The probability that he
will
win each round successfully is 5/6. What is the probability that he will knock down fewer
than 2 rounds?(B) Write the role of sports in universal brotherhood and peace.
3. (A) 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. (B)
Explain the importance of Nonviolence in patriotism.
4. (A) In answering a question on a MCQ test with 4 choices per question, a student knows
the
answer, guesses or copies the answer. Let ½ be the probability that heknows the answer,
¼ be the probability that he guesses and ¼ that he copies it.Assuming that a student, who
copies the answer, will be correct with theprobability ¾, what is the probability that the
student knows the answer, giventhat he answered it correctly?
(B) 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 characterdevelopment
in the coming years?
5. (A) An insurance Company insured 2000 Honda Activa scooters 3000 Tata Nano cars.
The
probability of an accident involving a scooter is 0.1 and that involving the car is 0.01.An
insured Vehicle met with an accident .Find the probability that an accidented vehicle was
aScooter.(B) Is Two Wheeler riding safe in Indian Roads? What are the precautions
you suggest while riding a Two Wheeler.
6. (A) Of the students in a school; it is known that 30% has 100% attendance and 70%
students areirregular.Previous year results report that 70% of all students who has 100%
attendance attain A grade and 10% irregular students attain A grade in their annual
examination. At the end of the year, one student is chosen at random from the school and
he has A grade. What is the probability that the student has 100% attendance?
(B) (i) Write any two values reflected in this question.
(ii) Is regularity required only in school? Justify your answer
7. (A) A man is known to speak truth 5 out of 6 times. He draws a ball from the bag
containing
4 white and 6 black balls and reports that it is white. Find the probability that it is actually
white? (B) Do you think that speaking truth is always good?
8. (A) A doctor is to visit a patient. From the past experience, it is known that the
probabilities
that he will come by train, bus, and scooter or by other means of transport are
3 1 1
2
1 1
1
respectively
,
, ,
and . The probabilities that he will be late are , and
10 5 10
5
4 3
12
if he comes by train, bus and scooter respectively, but if he comes by other means of
transport, then he will not be late. When he arrives he is late. What is the probability that
he comes by train? (B) Why is the use of generic medicine prescribed by the doctors
preferable to the patients ?
9. (A) A and B throw alternatively with a pair of dice. A wins if he throws 6 before B
throws 7 and B wins if he throws 7 before A throws 6. A begins; show that his chance of
winning is 30/61.(B) How does the knowledge of probability help us to understand
imbalance between success and failure rate in the game of gambling.