NBSE Class 12 Question Paper 2022 Fundamentals Of Business Mathematics

Total number of printed pages: 4 NB/XII/FBM/1
2022
FUNDAMENTALS OF BUSINESS MATHEMATICS

Full marks : 80 Time : 3 hours

General instructions:
i) Approximately 15 minutes is allotted to read the question paper and revise the
answers.
ii) The question paper consists of 32 questions.
iii) Marks are indicated against each question.
iv) General choice has been provided in some questions.
N.B: Check to ensure that all pages of the question paper is complete as indicated on the top
left side.

1. What is meant by subset? 1

2. What is non singular matrix? 1

3. Write the formula for finding A-1 1

4. Who is a sleeping partner? 1

5. What is meant by feasible region? 1

Answer any nine (9) from the following questions: 9x4=36

6. Given a relation R  1,2 , 2,3on the set of natural numbers, add a minimum
number of ordered pairs so that the enlarged relation is reflexive, symmetric and
transitive.

7. Write the four characteristics of a function.

8. Using properties of determinant, prove that
21  2 5 3
2  42 10 6 0
3  63 7 3

5 7   3 2  3 5
9. If A  6 9 , B  0 5 and C  1 1
    find the matrix X such
8 3 5 0 2 9
that A˗3B+X=C

-2- NB/XII/FBM/1

10. A shopkeeper has in stock 40 dozen notebooks, 30 dozen pens and 12 dozen
pencils. If the selling prices are 20 per notebook, 10 per pen and 5 per pencil,
find the total amount the shopkeeper will get after selling all the items in the
stock (Apply Matrix Rule).

11. If a banker’s gain on a bill due 4 months hence at 9% per annum is 75, find the
true discount and the amount of bill.

12. What is the actual rate of interest which a banker gets for the money when he
discount a bill legally due in 15 months at 5% per annum?

13. A trader supplies goods and receives cash as follows. On which date the balance
in a lump sum should be paid so that there may be no loss to either party?
Goods supplied in 1941 Cash received in 1941
10th Feb. - 100 12th March - 50
18th March - 200 07th May - 100
08th May - 500 10th June - 200

14. Mr. Maharaj borrowed 5,000 on 15 th January, 1985. He paid back 1,500
after 1 month, 1,600 after 3 months, 2,000 after 4 months and 500
after 5 months. Find the rate of interest.

15. How much 4% stock at 120 can be purchased by investing 48,000. What will
be the income?

16. A man invests 6,750 partly in 4% stock at 90 and partly in 5% stock at 105.
If his total income is 310, find how much he invests in each.

17. In a liquid mixture, 20% is water, and in another mixture, water is 25%. These
two mixture are mixed in the ratio of 5:3. Find the percentage of water in the
final mixture.

18. A shopkeeper mixes 20kg of vegetable ghee with 30kg of pure ghee and sells the
mixture at 140 per kg and gains 10% thereby. Find the cost per Kg of pure ghee
if the vegetable ghee costs him at 100 per kg.

Answer any three (3) from the following questions: 3x5=15

19. Solve by Crammer’s Rule
x  3 y  z  1
2 x  y  4 z  1
6x  7 y  8z  7

-3- NB/XII/FBM/1

20. A company produces 3 products every day. Their total production on a certain
day is 45 tons. It is found that the production of third product exceeds the
production of the first product by 8 tons while the total production of first and
third products is twice the production of second product. Determine the
production level of each product using Cramer’s Rule.

21. Company A pays 6% dividend on share of 100 each, while company B pays
3½% dividend on share of 10 each. If the market values of the shares in A and
B are 120 and 7.20 respectively per share, determine which of these gives a
better return to the share holder. What difference does it make to one investing
80,500?

22. A man sold 5% stock of 8,000 at 110 and purchased 6% stock with sale
proceeds. As a result, his early income increased by 40. What was the market
price of 6% stock?

23. A dealer mixes sugar costing 19 per kg, 20 per kg and 25 per kg and sells
the mixture at 20 and thereby losses 5% on sales price. In what proportion
are they mixed?

24. A grocer sells one kind of pulse at 21per kg and gains 5% and another at
22.50 per kg and losses 10%. How should they be mixed so that the mixture
may be sold at 24.2 per kg at a profit of 10%?

Answer any four (4) from following questions: 4x6=24

25. Out of 300 students in a college, 30 students speak all the 3 languages English,
Nagamese and Hindi, 60 speak English and Nagamese, 90 speak Nagamese and
Hindi, 75 speak English and Hindi, 36 speak English only, 15 speak Nagamese
only and 24 speak Hindi only. How many students do not speak any of the 3
languages?

26. Out of 500 students in a school, 250 played cricket, 220 played football and
180 played volleyball, of the total 160 played both cricket and football,140
played cricket and volleyball, 110 played football and volleyball, 75 played all
three games. How many students (i) did not play any game (ii) played only one
game (iii) played only two games?

27. Find a matrix Q such that
 1  2 3  1  2 3
Q  0 2  1   4 5 2 
 4 5 2   0 2  1

-4- NB/XII/FBM/1

28. Mr. Rao invested a total of 1,500 in 3 different savings accounts with annual
rates of 5%,2% and 1%. The total amount yield from this investment is 38. If
he invested equal amounts in the 5% and 1% accounts, how much amount
would be yield from each investment? Use matrix algebra.

29. A, B, C and D formed a partnership and contributed 40,000, 36,000, 24,000
and 25,000 respectively.They agree to set aside 10% of profit in a year as
reserve and distribute 66 23 % of the balance equally among them. The remaining
profit is divided as interest on respective capitals. If A receives in all 9,600
more than C in a year, find also share of profit earned in that year, find also the
share of profit distributed to A and B in that year.

30. A, B and C are partners in a Business. A contributes 13 rd of the whole capital
while B’s share is twice that of C. At the end of 4 months, A withdraws half of
his capital but refunds it at the end of next 4 months when B withdraws half of
his capital. If C gets 4,800 out of the profits, then ascertain the share of the
profits to which A and B are entitled.

31. Consider two different types of foodstuffs F1 and F2 assume that these food
stuffs contain vitamin V1, V2 and V3 respectively. Minimum daily requirements
of these vitamins are 2mg of V1, 3mg of V2 and 6mg of V3. Assume that these
foodstuff F1 contains 1mg of V1, 3mg of V2 and 4mg of V3 whereas foodstuffs
F2 contains 2mg of V1, 1mg of V2 and 3mg of V3 cost of 1 unit of foodstuff F1
is 4 and that of F2 is 2. Find the minimum cost diet that would supply the
body at least the minimum requirement of each vitamin.

32. The ABC company has been a producer of picture tubes for television sets and
certain printed circuits for radios. The company has just expanded into full
scale production and marketing of AM and AM-FM radios. It has built a new
plant that can operate 48 hours per week. Productions of an AM radio in the
new plant will require 2 hours and production of AM-FM radio will require 3
hours. Each AM radio will contribute 40 to profit while an AM-FM radio will
contributes 80 to profits. The marketing department, after extensive research,
has determined that a maximum of 15 AM radio and 10AM-FM radios can be
sold each week.
(i) Formulate a linear programming model to determine the optimum production
mix of AM-FM radios that will maximize profits.
(ii) Solve the above problem using graphic method.

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