Batra Maths Classes.

The most trusted private tuitions in Mathematics ..

Value Based Questions                    Class- XII

Q1   Let A = Set of boys of XII Class in some school. Let a R b, if and only if a and 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

Q2    There are two families P  and Q . There are 3 men, 3 women and 12 children in family

P and 2men, 2 women and 4 children in family Q. The recommended 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 matrix multiplication, calculate

the total  requirement of calories and proteins of each of the two families.

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

Q3   Represent the following  problem by a system of linear equations : Rs  154500 is the

Cost of 3 cycles, 2 motorbikes and one car, the cost of one cycle, one motorbike and

2 cars is Rs 226500.  The cost of 4 cycles and 3 motorbikes is Rs 81000. Use matrix to

Find the cost  of each . Which mode of conveyance preferred the most and why?

Q4   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 to award a total of

Rs 22000 for the three values to 10,8 and 6 employees respectively, while firm Q

decided to award Rs 21400 for  the three values to 8,6 and 10 employees respectively.

If all the three prizes together amount to Rs 2700, then

(i)  Represent the above situation by a matrix equation and form linear equations using

matrix multiplication.

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

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

Q5   Two schools A and B decided to award prizes to their students for the three values Truth

(x), patriotism (y) and Non - violence (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

(i)   Represent the above situation by a matrix equation and form linear equations using

matrix multiplication.

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

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

Q6   A sum of saving amount of  Rs 10000 is put into three investments at the rate of 10%,

12% and 15% p.a. The combined income of first and second investment is Rs 190 less

of the income of third investment. If the combined income is Rs 1310, then find the

Investment in each using matrices. Keeping nation’s growth in mind, justify the value of saving in individual life.

Q7   A  window is in the form of rectangle surmounted by a semicircular opening. The total

perimeter of the window is 10m. Find the dimensions of the window to admit maximum

sunlight through the whole opening. Explain the importance of sunlight.

Q8  A  manufacturer can sell bio gas operated x items at a price of  Rs each. The

cost price of bio gas operated x items is Rs . Find the number of items he

should sell to earn maximum profit. Explain the importance of use of renewable resources of energy.

Q9 Anil wants to invest at most Rs 12000 in Saving Certificates and National Saving Bonds.

According to rules, he has to invest at least Rs 2000 in Saving Certificates and at least

Rs 4000  in National Saving Bonds. If the rate Of interest on Saving Certificate is 8%

Per annum and the rate of interest on National Saving Bonds is 10% per annum, how

much money should he invest to earn maximum yearly income? Find also his maximum

yearly income.

Keeping nation’s growth in mind, justify the values of savings to be promoted in an individual’s life.

Q10 A  diet for a sick person must contain atleast 4000 units of vitamins, 50 units of minerals

and 1400 calories. Two foods X and Y are available at a cost of Rs 4 and Rs 3 per unit

respectively. One unit of food X contains 200 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 40 calories. Find what combination of X and Y should be used to have least cost,

satisfying the requirements? Explain the importance of balanced diet.

Q11   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% nitrogen and 10% phosphoric acid.

After testing the soil conditions of the  field, it was found that at least 14kg of nitrogen

and  14 kg of phosphoric acid is required for producing a good crop. The fertilizer  of type A

costs Rs 5 per kg and the type B costs Rs 3 per kg. How many kg of each type of the fertilizer should be used to meet the requirement at the minimum possible cost ? Using L.P.P.

Solve the above problem graphically.

Which manure you prefer to be promoted and why ?

Q12  If a Youngman rides his motorcycle at 25 km/ hour, he had to spend Rs 2 per km on

Petrol . If he rides at a faster speed of 40 km/hour, the petrol cost increases at Rs 5 per

Km. He has Rs 100 to spend on petrol and wishes to find what is the maximum distance

he can  travel  within one hour . Express this as L.P.P. and solve it graphically.

Which mode of transport you suggest to a young man and why.

Q13  In a school 12 N.C.C cadets of which 3 are reserve for parade selected for the Republic

Explain the importance of being a citizen of republic nation.

Q14 In a girls hostel 60% of the students read Hindi newspaper, 40% read English newspaper

And 20% read both Hindi and English newspapers. A student is selected at random.

(a)  Find the probability that she reads neither Hindi nor English newspapers.

(b)  If she reads Hindi newspaper, find the probability that she reads Hindi newspaper.

(b)  If she reads English newspaper, find the probability that she reads English newspaper.

(c)    Explain the role of newspapers in national integration.

Q15  A man is known to speak the truth 3 out of 5 times. He throws a die and reports that it is

a number greater than 4.

(i)  Find the probability  that it is actually a number greater than 4.

(ii)  Write about ‘ truth’ as essential human value.

Q16   To test the quality of electric bulbs  produced  in a factory , two bulbs are  randomly

selected from a large sample without replacement. If either bulb is defective, the entire

lot is rejected. Suppose a sample of 200 bulbs contains 5 defective bulbs. Find the

probability that the sample will be rejected.

Is a compromise on quality at the cost of quantity justifiable ? explain.

Q17  Paurush throw  a die again and again until three sixes are obtained. Find the probability

Of obtaining the third six in the sixth throw of die by paurush. There is no substitute of

hard work. Comment.

Q18   There are 40 workers in a factory who are participating in strike for increase in wages.

out of them 5 workers are sincere to management  and believe that management know

each thing and do the needful. Management selects 2 workers at random out of them.

Write the probability distribution for the selected worker who are sincere. Also find

the mean of the distribution. Write the importance of sincerity in service.

Q19    There  are 40 workers in a night shift of a factory out of a which 10 are drug- addicted.

Two persons are selected at random out of them. Write the probability distribution for

the selected workers who are drug addicted. Also find the mean of the distribution.

Write the drawbacks of drug addiction.

Q20   There are 80 workers in a publication house. Out of which 20 are hardworking and

honest Three workers are selected at random out of them. Write the probability

distribution for the selected  workers who are hard working  and honest. Also, find

the mean of the distribution. Write the importance of hardworking  and honesty in

One’s life.

Q21  A man is known to speak the truth 5 out of 6 times. He throws a die and reports that

it is a six.

(a)  Find the probability that it is actually a six.

(b)  Find the probability that it is actually not a six.

(c)  How would telling a lie hamper one’s character development in future?

Q22  Suppose that the reliability of a HIV test is specified as follows :

Of people having HIV , 90% of the test detect the disease but 10% go undetected. Of

People free of HIV, 99% of the test are judges HIV  negative but 1% are diagnosed

as  showing HIV positive. From a large population of which 0.1% have HIV,one

Person is selected at random, given the HIV , test and the pathologist reports him /her

as HIV positive. What is the probability that the person actually has HIV ?

(ii) What is the full form of HIV. Write the disease associated with HIV.

Q23  In a town of 6000 people 1200 are blood donors and 2000 are female. It is know that

30%  of the females are blood donors. What is the probability that a random chosen

individual from the town is either female or blood donor ?

(a)  Name the organization world wide helping the victims  in war also ?

(b)  Blood donors and eye donors are helping the society and strengthen the love to

Mankind. Comment.