Download SOL Assignment Solved DU Question Papers Answers List 2020
Q.1. (a) “An auditor is a watchdog and not a bloodhound”. Illustrate this statement.
(b) “An internal check means practically a continuous internal auditing carried on by the staff, by means of which the work of each individual is independently checked by other members of the staff”. Elucidate.
Q.2 (a) “Vouching is the backbone of auditing”. Explain this statement. State the general considerations to be borne in mind by the auditor while vouching cash transactions.
(b) Differentiate between vouching and verification. Also, comment on the auditor’s duty regarding verification.
Q.3 (a) Can a properly appointed auditor be removed before the expiry of his term? If so, explain the procedure of removal.
(b) “An auditor’s report may be unqualified, qualified or adverse”. Discuss.
Q.4 (a) Differentiate between cost audit and management audit.
(b) Differentiate between auditing ‘around’ the computer and auditing ‘through’ the
computer.
Q.2. Vitamins A, B and C are found in Foods F1 and F2. One unit of F1 contains 1 mg of A,
100 mg of B and 10 mg of C. One unit of F2 contains 1 mg of A, 10 mg of B and 100 mg
of C. The minimum daily requirement of A, B and C are 1 mg, 50 mg, and 10 mg
respectively. The cost per unit of F1 and F2 are Rs. 1 and Rs. 1.5 respectively. You are
required to (i) formulate the above as a linear programming problem minimizing the cost
per day, (ii) write the dual of the problem and (iii) solve the dual by using simplex
method and read from there the answer to the primal.
Q.3. (a) Suppose that the cost of holding one item in inventory is Rs. 0.50 and that of
placing an order is Rs. 100. Also assume that the annual demand for the item is
4,900 units. Find the economic order quantity.
(b) A firm produces two items 1 X and 2 X . The market prices are given by
1 1 p =100−2x and 2 2 p =125−3x . The cost of production is 1 2 1 2 12x +11x + 4x x for
producing 1 X and 2 X items. Find how many items of each should be produced to
have the joint profit maximum?
(c) Find the consumers’ surplus and producers’ surplus under pure competition for
demand function
8
2
1
p
x
= −
+
and supply function
1
( 3)
2
p = x + , where p is price
and x is quantity.
Q.4. (a) A machine costs a company Rs. 52,000 and its effective life is estimated to be 12
years. A sinking fund is created for replacing the machine by a new model at the
end of its life time, when its scrap realizes a sum of Rs. 5,000 only. The price of
new model is estimated to be 25% higher than the price of the present one. Find
what amount should be set aside at the end of each year, out of the profits, for the
sinking fund, if it accumulates at 10% effective.
(b) Use the assignment method to find the optimum job (A, B, C, D) assignments to
the machines (X, Y, Z, W) so as to minimize total cost. What is the total cost of optimum assignment?
Q.1. (a) An amount of Rs. 65,000 is invested in three investments at the rate of 6%, 8% and 9% per annum, respectively. The total annual income is Rs. 4,800. The income from the third investment is Rs. 600 more than the income from second investment. Using matrix algebra, determine the amount of each investment.
(b) A tour operator charges Rs. 200 per passenger for 50 passengers with a discount of Rs. 5 for each 10 passenger in excess of 50. Determine the number of passengers that will maximize the revenue of the operator.
(c) Which is better investment 8% compounded half-yearly or 7.9% compounded monthly?
Q.2. (a) Discuss the considerations that determine the selection of a suitable average. Explain by giving one example of each case.
(b) The average rainfall for a week, excluding Sunday, was 10 cms. Due to heavy rainfall on Sunday, the average for the week rose to 15 cms. How much rainfall was on Sunday?
(c) For a moderately skewed distribution, the median price of men’s shoes is Rs. 380 and modal price is Rs. 350. Calculate mean price of shoes.
Q.3. (a) The mean and standard deviations of two brands of light bulbs are given below:
Brand I Brand II
Mean 800 hours 770 hours
Standard deviation 100 hours 60 hours
Calculate a measure of relative dispersion for the two brands and interpret the result.
(c) Show that the coefficient of correlation is the geometric mean of the two regression coefficients.
(d) The two regression coefficients are 1.5 and 0.6 and the coefficient of correlation is 0.90. Comment.
Q.4. (a) From the following data, prove that Fisher Ideal Index satisfies both the time reversal and the factor reversal tests:
(b) Fit a straight line trend to the following data and estimate the expected profit for the year 2020. What is the average annual change in profit?
You can check sol.du.ac.in official website for more information.
Download B.Com SOL - School Open Learning (DU) - Delhi University Solved Assignments 2020
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Download SOL (School of Open Learning) Assignment Solved DU (Delhi University) Question Papers Answers List 2020
Paper 3: English Literature-1 B.A. (Hons) English II year Annual Mode
Q.1 Would you call the character of Dr. Faustus ‘heroic’? Give reasons for your answer.
Q.2 Despite the differences in their social status, Desdemona, Bianca, and Emilia are viewed in the same way by the men in the play Othello. Why?
Q.3 Would you agree with the view that As You Like It ridicules and yet at the same time celebrates traditional ideas of romantic love?
Q.4 What is the purpose of the Wife of Bath`s Prologue? Explain.
Paper 4: English Literature-2 B.A. (Hons) English II year Annual Mode
Q.1 Discuss Shakespeare`s portrayal of Rome and Egypt in Antony and Cleopatra.
Q.2 Do you think The Duchess of Malfi manages to rise to the level of a tragedy? If yes, then why?
Q.3 Discuss the importance of The Invocation in Paradise Lost Book I
Q.4 Define and discuss the characteristics of mock-epic poetry with reference to Alexander Pope`s The Rape of the Lock.
English-B B.A. (P) 2nd Year ( Annual Mode )
Q.1(a) The street lights in your locality have not been working for a week. Write a formal letter of complaint to the MCD Commissioner, requesting necessary action to repair the faulty street lights in your locality.
OR
(b) Write a letter to your cousin, who is preparing for her Class XII exams and wants your advice on how to make notes, write answers, and study for competitive exams.
Q.2(a) Write a dialogue, with ten sentences each, that you are having with your friend about the new shopping mall in your locality.
OR
(b) Write an essay, in about 250 words, about the disadvantages of spending too muchtime on your mobile phone.
English Stream C B.A. Programme / 2nd Year Annual Mode
Q.1 Write a letter to your friend who stays in a different city and tell her how you spent your time during the Lockdown period. You can tell her about how you studied, new things you learnt, books you read, hobbies you developed etc.
Q.2 You need to apply for the post of an English teacher in a school. Prepare a bio-data giving all the relevant details.
Q.3 You and your friend Vera are planning to go for a movie. Write out a dialogue in which you two argue about when to go, where to go and which movie to see. You can end the dialogue by finally coming to an agreement.
Q.4 Write a letter to the Commissioner, MCD, complaining about the poor condition of roads and drains in your area.
Classical Literature/ Paper-V(b) B.A. (Hons) English/ 2nd Year Annual Mode
Q.1 Do you think that Medea is a tragic heroine? Give a detailed answer, with references from the text to support your argument.
Q.2 “Achilles is a heroic figure, in spite of his faults.” Discuss the character of Achilles in The Iliad, with reference to this statement.
Q.3 Discuss the structural and thematic significance of the dicing game episode in the Mahabharata.
Q.4 In the character of Dushyanta in AbhijnanaShakuntalam, Kalidasa subjects the ideal of the hero and the ideal of kingship to ironic scrutiny. Would you agree?
(AECC) Hindi B.A. (Prog.) – I Year, Sem-II
B.A. (Hons.) English, (G.E.) I Year, Sem-I
B.A. (Prog.) –I Year, Sem-I
B.A. (Prog.) – II Year (Discipline Hindi)
B.A. (Prog.) – II Year (Code B-136)
B.A(Prog.) SEMESTER - I Mathematics: Calculus (Code: 62351101)
Q.1. Differentiate the following and determine
.
(i)
𝑦 = 𝑐𝑜𝑠 x + 𝑠𝑖𝑛 𝑥 + 𝑐𝑜𝑠 𝑥 + 𝑠𝑖𝑛 𝑥 + √𝑐𝑜𝑠 𝑥 + 𝑠𝑖𝑛 𝑥 + . . .
(ii) yx = e(x + log y)
Q.2. (a) Let f be defined as
𝑓(𝑥) =
3(𝑥– 9)
𝑥 – 3
𝑥 ≠ 3
4 𝑥 = 2
Show that f has removable discontinuity at x = 3.
(b) find
and
if
z = x3 + y3 + 2x2y
where x = 2t + s and y = t – 2s.
Q.3. (a) Find radius of curvature of curve:
x2 + xy + y2 = 4 at point (–2, 0)
(b) Determine the position and nature of the double points on the curve:
2x4 – 8y3 – 12y2 – 4x2 – 2 = 0
Q.4. (a) Find lim
→
(𝑥– 2)( – )
(b) Find the maximum and minimum value of the polynomial.
12x5 – 45x4 – 20x3 + 90x2
B.A(Prog.) SEMESTER-II Mathematics: Algebra (Code: 62351201)
Q.1. (a) If n is a positive integer, show that:
√3 + 𝑖
+ √3– 𝑖
= 2–𝑐𝑜𝑠
𝑛𝜋
6
(b) Find the sum of the cubes of the roots of the equation
x3 – 6x2 + 11x – 6 = 0
Q.2. (a) Express the matrix
3 1 – 7
2 4 8
6 – 1 2
as X + Y, where X is symmetric and Y is
skewsymmetric
(b) Determine the rank of the following matrix.
1 – 1 – 1
– 1 1 1
1 – 1 – 1
– 1 1 1
Q.3. (a) Verify if the set S = {1,−1, i, −i} where √𝑖 = –1, forms an abelian group under
ordinary multiplication.
(b) Let G be the group of all 2×2 non singular matrices with real entries, under the
binary operation of the usual matrix multiplication. Let H consist of all matrices of
the form
𝑎 0
𝑏 1
, a 0. Check if H is a subgroup of G.
Q.4. (a) Suppose V1 and V2 are subspaces of a vector space. Prove that 𝑉 ⋂ 𝑉 is a
subspace of V. Also show that union of two subspaces need not be a subspace.
(b) Show that W = {(x, y, z) ∈ ℝ : x + y + z = 0, x + 2y + 3z = 0} is a subspace of ℝ
B.A(Prog.) 2nd Year Annual Mathematics: Geometry, Vector Calculus & Differential Equation (Code: B-155)
Q.1. (a) Find an equation of the parabola that is symmetric about y-axis has its vertex at the
origin and passes though the point (10, 4). Also show its focus and direction on the
graph.
(b) Find the area of the parallelogram that has 𝑎⃗ and 𝑏 ⃗ as adjacent sides where
𝑎⃗ = 2𝚤̂– 2𝚥̂ + 4𝑘
; 𝑏 ⃗ = 6𝚥̂ + 2𝑘
and find the angle between 𝑎⃗ & 𝑏 ⃗ show that 𝑎⃗ ×𝑏 ⃗ = 0⃗.
Q.2. (a) Solve (D2 – 2D + 1) y = x log x, using the method of variation parameters; where
D =
(b) Solve y = p tan p + log (cos p),
where, 𝑝 =
Q.3. (a) Classify the following partial differential equation into, elliptic, parabolic or
hyperbolic:
sin𝑥
𝜕𝑧
𝜕𝑥 + 2cos 𝑥
𝜕𝑧
𝜕𝑥𝜕𝑦
–
𝜕𝑧
𝜕𝑦 = 0
(b) Find the complete integral of the partial differential equation:
pqz = p2(xq + p2) + q2 (yp + q2).
Where 𝑝 =
, 𝑞 =
Q.4. (a) Let G be a group and a ∈ G. Let C(a) = {x ∈ G | xa = ax}. Show that C(a) is a
subgroup of G. Compute C(a) if S = S3 and a = (12)
(b) Solve the travelling salesperson problem for the cost matrix
To 1 2 3 4
From 1 – 3 9 7
2 3 – 6 5
3 5 6 – 6
4 9 7 4 –
So as to minimize the cost per cycle.
B. Com. Semester-I Business Ogranisation and Management (Code : 52411102)
Q.1 (a) Explain the basic consideration in setting up a business enterprise.
(b) Explain the concept of service. Do you think that the importance of service sector in our economy is on the rise? Give reasons for your answers.
(c) Describe various elements of contemporary business environment.
(d) What is E-Commerce? Discuss the benefits and limitations of E-commerce. How can the safety of E-commerce transactions be ensured? Describe.
Q2. (a) Define Planning. Explain its significance.
(b) What is matrix organisation? Explain its merits and limitations.
(c) Define leadership. What are the styles of leadership.
B.Com. (Hons.) Semester-II Corporate Accounting (Code : 22411201)
Q.1. (a) Discuss the provisions regarding buyback of shares under Companies Act 2013.
(b) Give accounting treatment for debentures issued as Collateral security.
(c) Paras Ltd. issued 40000, 11% debentures of 100 rupees each on 1st April 2015. Half of the debentures were due for redemption on 31st March 2019. The company decided to transfer the minimum required amount to Debenture Redemption Reserve on 31st March, 2018 and invested the necessary amount in debenture Redemption Investments on 30th April, 2018. Pass the necessary journal entries for Redemption of Debentures.
Q.2. (a) Bharat Limited purchased plant and machinery for 20,00,000 rupees from Delhi
machines limited by paying 5,00,000 Rupees by cheque and balance by issue of 11%
debentures of rupees 100 each at a premium of 20%. Pass necessary entry in the books of Bharat Ltd. for the above transactions. Pass necessary entries in the books of Bharat
Limited for the above transactions.
(b) Shubham Limited invited applications for 1,00,000 equity shares of rupees 10 each at
a premium of 2 rupees per share payable as follows: on application 2.50 rupees, on
allotment 4.50 rupees (including premium), on first call 2.50 rupees and on final call
2.50 rupees per share.Applications were received for 1,50,000 shares and shares were
allotted pro-rata to the applicants for 1,20,000 shares and remaining applications were
rejected.A, who was allotted 200 shares could not pay the sum due on
allotment.Shares held by him were forfeited on his failure to pay the first call. B,
holding 300 shares, could not pay the two calls. The company forfeited his shares after
the final call was made.
Pass journal entries for forfeiture and re-issue in the books of Shubham Limited.
Q.3. Priya Ltd. takes over Bhushan Ltd. as at 1st April 2017. The Balance Sheet of Bhushan Ltd.
as at that date was as follows:
Equity and liabilities
Share Capital: Rs.
50,000 Equity Shares of Rs. 10 each fully paid up 5,00,000
General Reserve 2,00,000
Statutory Reserve 1,00,000
12% Debentures (Rs. 100 each, fully paid) 1,00,000
Trade Payables 1,00,000
Total 10,00,000
Assets:
Tangible Fixed Assets 5,00,000
Stock in Trade 2,00,000
Trade Receivables 2,00,000
Cash at Bank 1,00,000
Total 10,00,000
Priya Ltd. agreed to issue 30,000 Equity shares of Rs. 10 each at a premium of Rs. 5 per
share to the shareholders of Bhushan Ltd. 12% Debentures of Bhushan Ltd. will be
converted into equivalent number of 12% Debentures of Rs.100 each. Statutory Reserve of
Bhushan Ltd. is to be maintained for two or more years.
Pass acquisition entries in the books of Priya Ltd.
Q.4. From the following particulars as at 31st March, prepare cash flow statement as per AS-3
using indirect method:
2017 2018
Equity and liabilities:
Equity Share Capital 80,000 55,000
10% Pref. Share Capital 20,000 25,000
General Reserve 7,600 4,000
Surplus in Statement of Profit & Loss 2,400 2,000
15% Debentures 14,000 12,000
Creditors 22,000 24,000
Proposed Dividend 8,000 10,000
Provision for Taxation 8,400 6,000
Total 1,62,400 1,38,000
Assets:
Fixed Assets 80,000 82,000
Less: Accumulated Depreciation 30,000 22,000
50,000 60,000
Stock 70,000 60,000
Debtors 34,400 15,000
Cash 7,000 2,400
Prepaid Expenses 1,000 600
Total 1,62,400 1,38,000
Additional information:
i. Provision for tax made Rs. 9,400.
ii. Fixed assets costing Rs. 20,000 (accumulated depreciation till date of sale on then Rs.
6,000) were sold Rs. 10,000.
iii. Interim dividend paid during the year Rs. 9,000. Proposed dividend of last year was
declared and paid during the year. Ignore corporate dividend tax.
iv. New Debentures were issued on 31st March, 2017.
B.Com. (Hons.) Semester-II Corporate Accounting (Code :22411201)
Q.1. (a) Discuss the provisions regarding buyback of shares under Companies Act 2013.
(b) Give accounting treatment for debentures issued as Collateral security.
(c) Paras Ltd. issued 40000, 11% debentures of 100 rupees each on 1st April 2015. Half
of the debentures were due for redemption on 31st March 2019. The company decided
to transfer the minimum required amount to Debenture Redemption Reserve on 31st
March, 2018 and invested the necessary amount in debenture Redemption Investments
on 30th April, 2018. Pass the necessary journal entries for Redemption of Debentures.
Q.2. (a) Bharat Limited purchased plant and machinery for 20,00,000 rupees from Delhi
machines limited by paying 5,00,000 Rupees by cheque and balance by issue of 11%
debentures of rupees 100 each at a premium of 20%. Pass necessary entry in the books
of Bharat Ltd. for the above transactions. Pass necessary entries in the books of Bharat
Limited for the above transactions.
(b) Shubham Limited invited applications for 1,00,000 equity shares of rupees 10 each at
a premium of 2 rupees per share payable as follows: on application 2.50 rupees, on
allotment 4.50 rupees (including premium), on first call 2.50 rupees and on final call
2.50 rupees per share.Applications were received for 1,50,000 shares and shares were
allotted pro-rata to the applicants for 1,20,000 shares and remaining applications were
rejected.A, who was allotted 200 shares could not pay the sum due on
allotment.Shares held by him were forfeited on his failure to pay the first call. B,
holding 300 shares, could not pay the two calls. The company forfeited his shares after
the final call was made.
Pass journal entries for forfeiture and re-issue in the books of Shubham Limited.
Q.3. Priya Ltd. takes over Bhushan Ltd. as at 1st April 2017. The Balance Sheet of Bhushan Ltd.
as at that date was as follows:
Equity and liabilities
Share Capital: Rs.
50,000 Equity Shares of Rs. 10 each fully paid up 5,00,000
General Reserve 2,00,000
Statutory Reserve 1,00,000
12% Debentures (Rs. 100 each, fully paid) 1,00,000
Trade Payables 1,00,000
Total 10,00,000
Assets:
Tangible Fixed Assets 5,00,000
Stock in Trade 2,00,000
Trade Receivables 2,00,000
Cash at Bank 1,00,000
Total 10,00,000
Priya Ltd. agreed to issue 30,000 Equity shares of Rs. 10 each at a premium of Rs. 5 per
share to the shareholders of Bhushan Ltd. 12% Debentures of Bhushan Ltd. will be
converted into equivalent number of 12% Debentures of Rs.100 each. Statutory Reserve of
Bhushan Ltd. is to be maintained for two or more years.
Q.4. From the following particulars as at 31st March, prepare cash flow statement as per AS-3
using indirect method:
2017 2018
Equity and liabilities:
Equity Share Capital 80,000 55,000
10% Pref. Share Capital 20,000 25,000
General Reserve 7,600 4,000
Surplus in Statement of Profit & Loss 2,400 2,000
15% Debentures 14,000 12,000
Creditors 22,000 24,000
Proposed Dividend 8,000 10,000
Provision for Taxation 8,400 6,000
Total 1,62,400 1,38,000
Assets:
Fixed Assets 80,000 82,000
Less: Accumulated Depreciation 30,000 22,000
50,000 60,000
Stock 70,000 60,000
Debtors 34,400 15,000
Cash 7,000 2,400
Prepaid Expenses 1,000 600
Total 1,62,400 1,38,000
Additional information:
i. Provision for tax made Rs. 9,400.
ii. Fixed assets costing Rs. 20,000 (accumulated depreciation till date of sale on then Rs.
6,000) were sold Rs. 10,000.
iii. Interim dividend paid during the year Rs. 9,000. Proposed dividend of last year was
declared and paid during the year. Ignore corporate dividend tax.
iv. New Debentures were issued on 31st March, 2017.
B.Com (H) – Semester-II Corporate Laws (Code : 22411202)
Q.1 (A) What is lifting of Corporate Veil? Explain the Statutory Provisions under which the Corporate Veil of the Company May be lifted.
(B) Explain the Procedure of on line Registration of Company.
(C) “A Promoter is Neither a trustee Nor on agent of the Company he Promotes but he stands in a fiduciary Position towards the Company and the original allotted of shares: Comment on the statement.
(D) What are Preliminary Contracts? Discuss the legal effects of Preliminary Contracts.
Q.2 (A) Define a Private Company and distinguse it from a Producer Company.
(B) Write a Short Note on one Person Company.
(C) Explain the Doctrine of Indoor Management. State the Exceptions, if any to the Doctrine of Indoor Management.
(D) Write a Short Note on Independent Director.
Q.3 (A) Write a Note on Employees Stock Option Scheme.
(B) What do you mean by a misleading Prospectus? What are the remedy is available to shareholders against the Company for Mist-Statement in the Prospectus?
(C) Write a Note on Issue of sweat equity shares.
(D) Describe the statutory Provisions Regarding Quorums at the general meeting of a Company. Can are member Constitute Quorum?
Q.4 (A) What is an Extraordinary General Meeting? By whom can an extraordinary general meeting be called?
(B) Who can be a Director? Explain the Provision of Companies Act Relating to the Appointment of Directors by the Board of Directors.
(C) Describe the General Powers Vested in the Board. Under what exceptional situations, the shareholders in General Meeting is Competent to Act even on the matters delegating to the Board?
(D) Write a Note on Compulsory Winding of a Company.
B.Com/(Hons.)/II Year / NS E-Commerce (Code : ECOM)
Q.1. (a) Privacy is a basic human value that is inadequately addressed in e-commerce. What measures can you suggest to protect privacy in internet transactions?
(b) What is the difference between pure online and bricks and mortar store?
Q2. (a) Elaborate the challenges of the design and marketing phases of the online business life cycle.
(b) What do you mean by e-money? What are its benefits and limitations?
Q.3. (a) Explain the concept of virtual office. What are the advantages offered by a virtual office?
(b) How can you protect your business from cyber frauds and virus attacks?
Q4. (a) What are the advantages and disadvantages of encryption?
(b) Explain the B2B and C2C models of e-commerce.
B.Com. (Hons.) New Annual - II Auditing (Code : AUDT)
Q.1. (a) “An auditor is a watchdog and not a bloodhound”. Illustrate this statement.
(b) “An internal check means practically a continuous internal auditing carried on by the staff, by means of which the work of each individual is independently checked by other members of the staff”. Elucidate.
Q.2 (a) “Vouching is the backbone of auditing”. Explain this statement. State the general considerations to be borne in mind by the auditor while vouching cash transactions.
(b) Differentiate between vouching and verification. Also, comment on the auditor’s duty regarding verification.
Q.3 (a) Can a properly appointed auditor be removed before the expiry of his term? If so, explain the procedure of removal.
(b) “An auditor’s report may be unqualified, qualified or adverse”. Discuss.
Q.4 (a) Differentiate between cost audit and management audit.
(b) Differentiate between auditing ‘around’ the computer and auditing ‘through’ the
computer.
B.Com. (Hons.) New Annual-II
Business Mathematics
(Code : B Maths)
Q.1. (a) A person has Rs. 35,000 that he has divided into three investments. Part of the money is invested in a savings account with annual rate of interest of 6%, part in 7% annual yield bonds, and the remainder in a business. In 2006, when he lost 6% of the money that he invested in that business, his net income from all three investments was Rs. 660. If he invested Rs. 3,000 more in the business than in savings account, how much was invested in each? Use matrix method.
(b) Suppose that the final demand for steel, coal and electricity in an economy consisting only of three sectors are Rs. 10 crores, Rs. 5 crores and Rs. 6 crores, respectively. A rupee worth of steel requires 20 paise, 40 paise and 10 paise worth of steel, coal and electricity respectively as inputs; A rupee worth of coal requires 30 paise, 10 paise and 30 paise worth of steel, coal and electricity respectively as inputs and A rupee worth of electricity requires 20 paise, 20 paise and 20 paise worth of steel, coal and electricity respectively as inputs. How much of steel, coal and electricity should be produced to satisfy for both final and intermediate demands?
100 mg of B and 10 mg of C. One unit of F2 contains 1 mg of A, 10 mg of B and 100 mg
of C. The minimum daily requirement of A, B and C are 1 mg, 50 mg, and 10 mg
respectively. The cost per unit of F1 and F2 are Rs. 1 and Rs. 1.5 respectively. You are
required to (i) formulate the above as a linear programming problem minimizing the cost
per day, (ii) write the dual of the problem and (iii) solve the dual by using simplex
method and read from there the answer to the primal.
Q.3. (a) Suppose that the cost of holding one item in inventory is Rs. 0.50 and that of
placing an order is Rs. 100. Also assume that the annual demand for the item is
4,900 units. Find the economic order quantity.
(b) A firm produces two items 1 X and 2 X . The market prices are given by
1 1 p =100−2x and 2 2 p =125−3x . The cost of production is 1 2 1 2 12x +11x + 4x x for
producing 1 X and 2 X items. Find how many items of each should be produced to
have the joint profit maximum?
(c) Find the consumers’ surplus and producers’ surplus under pure competition for
demand function
8
2
1
p
x
= −
+
and supply function
1
( 3)
2
p = x + , where p is price
and x is quantity.
Q.4. (a) A machine costs a company Rs. 52,000 and its effective life is estimated to be 12
years. A sinking fund is created for replacing the machine by a new model at the
end of its life time, when its scrap realizes a sum of Rs. 5,000 only. The price of
new model is estimated to be 25% higher than the price of the present one. Find
what amount should be set aside at the end of each year, out of the profits, for the
sinking fund, if it accumulates at 10% effective.
(b) Use the assignment method to find the optimum job (A, B, C, D) assignments to
the machines (X, Y, Z, W) so as to minimize total cost. What is the total cost of optimum assignment?
B.Com. Part-2
Business Mathematics and Statistics
(Code : 52411202)
Q.1. (a) An amount of Rs. 65,000 is invested in three investments at the rate of 6%, 8% and 9% per annum, respectively. The total annual income is Rs. 4,800. The income from the third investment is Rs. 600 more than the income from second investment. Using matrix algebra, determine the amount of each investment.
(b) A tour operator charges Rs. 200 per passenger for 50 passengers with a discount of Rs. 5 for each 10 passenger in excess of 50. Determine the number of passengers that will maximize the revenue of the operator.
(c) Which is better investment 8% compounded half-yearly or 7.9% compounded monthly?
Q.2. (a) Discuss the considerations that determine the selection of a suitable average. Explain by giving one example of each case.
(b) The average rainfall for a week, excluding Sunday, was 10 cms. Due to heavy rainfall on Sunday, the average for the week rose to 15 cms. How much rainfall was on Sunday?
(c) For a moderately skewed distribution, the median price of men’s shoes is Rs. 380 and modal price is Rs. 350. Calculate mean price of shoes.
Q.3. (a) The mean and standard deviations of two brands of light bulbs are given below:
Brand I Brand II
Mean 800 hours 770 hours
Standard deviation 100 hours 60 hours
Calculate a measure of relative dispersion for the two brands and interpret the result.
(c) Show that the coefficient of correlation is the geometric mean of the two regression coefficients.
(d) The two regression coefficients are 1.5 and 0.6 and the coefficient of correlation is 0.90. Comment.
Q.4. (a) From the following data, prove that Fisher Ideal Index satisfies both the time reversal and the factor reversal tests:
(b) Fit a straight line trend to the following data and estimate the expected profit for the year 2020. What is the average annual change in profit?
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