This is the official December 2025 question paper for BECE-015 Elementary Mathematical Methods in Economics under IGNOU's Bachelor's Degree Programme. The BECE 015 Question Paper December 2025 covers input-output matrix analysis, partial derivatives, Young's theorem, second-order optimisation conditions, Kuhn-Tucker conditions, the Simplex method, Cobweb model stability, Shephard's lemma, matrix inversion, and limit evaluation. This paper demands both mathematical accuracy and conceptual understanding. Having solved answers alongside the actual questions is the most effective way to prepare.
| Prepared by | Unnati Education, IGNOU-experienced academic content writer |
|---|---|
| Qualification | Graduate with specialisation in Economics and Mathematical Methods |
| Programme | IGNOU Bachelor of Arts BDP |
| Institution Reference | IGNOU Term-End Examination December 2025 |
What is BECE 015 December 2025 Question Paper?
The BECE-015 December 2025 question paper is a 100-mark IGNOU examination for Elementary Mathematical Methods in Economics under BDP, combining numerical problem solving and theoretical derivations across three structured sections.
This is one of the more technically demanding papers in the BDP Economics elective stream. It requires you to apply mathematical tools directly to economic problems. Most students notice that Section A questions, especially the input-output matrix and the Kuhn-Tucker problem, need careful stepwise working. Here is the important part: even if your final answer is slightly off, showing the correct method and intermediate steps earns substantial partial marks.
About IGNOU BECE-015 — Elementary Mathematical Methods in Economics
BECE-015 bridges mathematics and economics. It equips students with the quantitative tools needed to analyse economic problems rigorously. The course covers matrix algebra including input-output analysis, partial and total differentiation, optimisation theory for unconstrained and constrained problems, Kuhn-Tucker conditions for non-linear programming, the Simplex method for linear programming, dynamic models like the Cobweb model, game theory concepts like perfect Bayesian equilibrium, and foundational topics like limits, determinants, and vector mathematics.
In practice, this course demands regular practice with problems rather than just reading theory. Every topic has a calculation component that needs to be worked through repeatedly before the exam.
BECE 015 Exam Pattern and Marks Breakdown
Section A carries 40 marks total. You attempt any 2 questions from 4, each worth 20 marks. These are long answers that combine numerical computation with theoretical explanation. Plan your time carefully because these questions take the most working space.
Section B carries 48 marks total. You attempt any 4 questions from 6, each worth 12 marks. These are medium-length answers mixing theory and calculation. Focus on showing all steps clearly.
Section C carries 12 marks total. Both questions are compulsory, each worth 6 marks. These include both short conceptual answers and direct calculations.
Total: 100 marks, 3 hours.
All Questions — BECE 015 Question Paper December 2025 IGNOU
Section A — Attempt any two questions from this Section. 2x20=40
The input coefficient matrix for a two-sector economy is given as under:
A = [0.20 0.20] [0.70 0.20]
The final demand for the two goods is Rs. 400 crore and Rs. 4,650 crore respectively. Calculate the total outputs of the two sectors. Also estimate their input requirements.
Find all possible partial derivatives of the of the function:
e raised to 3x squared plus 2xy plus 5y squared.
Also verify if Young's theorem is satisfied here.
Consider the objective function in three variables:
Z = f(x1, x2, x3)
Find out second order condition for maximum value.
Suppose the problem is minimize:
C = f(x1, x2, ...., xn)
subject to:
g raised to i (x1, ..., xn) is greater than or equal to ri,
where ri is a constant in the ith constraint and xj is greater than or equal to 0, i = 1, 2, ...., m and j = 1, 2, ..., n.
(a) Write out the expanded version of the Kuhn-Tucker minimum condition. (b) Write out the dual of the problem and write the Kuhn-Tucker condition for the dual.
Section B — Answer any four questions from this Section. 4x12=48
Explain the Simplex method of solving linear programming problems.
Explain the concept of perfect Bayesian equilibrium.
Find the total derivative dz/dt, given that:
z = x squared minus 8xy minus y cubed,
where x = 3t and y = 1 minus t.
Find the inverse of the matrix:
A = [4 1 -1] [0 3 2] [3 0 7]
Solve the following Cobweb model and determine whether the equilibrium is stable or not:
Q subscript t superscript d = 19 minus 6P subscript t
Q subscript t superscript s = 6P subscript t-1 minus 5.
Derive Shephard's lemma.
Section C — Answer both questions from this Section. 2x6=12
(a) Evaluate:
lim as V approaches 1 of (1 minus V squared) divided by (1 minus V)
(b) If A = [7 -1] and B = [8 3], then find C = 3A + 2B. [6 9] [6 1]
(a) What are orthogonal vectors? Explain. (b) What is a determinant? Does every matrix have a determinant? Give reasons.
BECE 015 Syllabus Topics Covered
This paper draws from the full BECE-015 syllabus. Key areas include input-output analysis using matrix algebra, partial derivatives of multivariable functions including exponential terms, verification of Young's theorem, second-order conditions for maximisation in three variables, Kuhn-Tucker conditions for constrained minimisation, the dual problem formulation, the Simplex method for linear programming, perfect Bayesian equilibrium from game theory, total derivative calculation using chain rule, matrix inversion, Cobweb model stability analysis, derivation of Shephard's lemma, limit evaluation, matrix scalar multiplication, orthogonal vectors, and the concept of determinants.
Sample Answer Preview — BECE-015 Mathematical Methods Solved Paper
Here is a brief look at how a high-scoring answer to Question 1 would begin.
To find total outputs for the two sectors, we use the Leontief input-output model. The total output vector X is given by X = (I minus A) inverse multiplied by D, where I is the identity matrix, A is the input coefficient matrix, and D is the final demand vector. We first compute I minus A, then find its inverse, and finally multiply by D to get total outputs for both sectors. Input requirements are then calculated by multiplying A by X.
A complete answer shows the full matrix calculation with intermediate steps. Get the full BECE-015 solved question paper for complete stepwise solutions for all sections.
How to Write High-Scoring Answers in BECE 015 Question Paper
For Section A numerical questions, never skip steps. Write the formula first, define all variables, substitute values, and show every arithmetic step. Matrix problems need to show row operations or cofactor expansion clearly. For the Kuhn-Tucker question, write all conditions explicitly with proper notation.
For Section B, theory questions like the Simplex method need a logical sequence: standard form, initial tableau, pivot selection, and iterations. For Section C, calculation questions need clean working. Conceptual answers like orthogonal vectors need a definition followed by one illustrative example. Clarity in layout earns marks even when the method is partially correct.
Who Should Use This BECE-015 Solved Question Paper?
This solved paper is most useful for BDP students taking BECE-015 as an elective who need to see how mathematical problems are solved within IGNOU's examination context. Students who find the matrix and optimisation chapters difficult will benefit most from seeing complete stepwise solutions. It is also valuable for anyone attempting a back paper who wants a clear benchmark for how answers should be structured and presented.
Why This is Better Than Free BECE-015 December 2025 PDFs and Telegram Files
Mathematical questions cannot be half-answered. Free Telegram files for BECE-015 almost never include complete solutions with all steps shown. Even when answers are present, they often skip intermediate working, which is exactly what IGNOU examiners check. Unnati Education's solved paper shows every step for every numerical problem. The Simplex method, matrix inverse, total derivative, and Cobweb model are all solved from scratch with full working, not just final answers.
Student Reviews — BECE-015 Solved Question Paper by Unnati Education
How to Get the BECE-015 Solved Question Paper December 2025
The process is quick and simple. First, contact Unnati Education through the WhatsApp link or contact form on this page. Second, share your course code BECE-015 and confirm the December 2025 session. Third, receive your complete solved paper with full stepwise solutions for all three sections. Most students receive their paper within minutes of reaching out.
Frequently Asked Questions
What is BECE-015?
BECE-015 is Elementary Mathematical Methods in Economics, an elective course under IGNOU's Bachelor's Degree Programme. It applies mathematical tools including matrix algebra, calculus, optimisation theory, linear programming, and dynamic models to economic problems. The course is designed for economics students who want to develop quantitative analytical skills alongside their economic theory knowledge.
What is the exam pattern and marks distribution for BECE-015?
The paper carries 100 marks and is 3 hours long. Section A has four questions and you attempt any two, each worth 20 marks, covering major numerical and theoretical problems. Section B has six questions and you attempt any four, each worth 12 marks, mixing theory and calculation. Section C has two compulsory questions, each worth 6 marks, covering shorter conceptual and computational topics.
What are the most important mathematical topics for BECE-015 December 2025?
Based on the actual December 2025 question paper, the most tested topics include input-output matrix analysis, partial derivatives and Young's theorem verification, second-order conditions for maximisation, Kuhn-Tucker conditions for constrained minimisation, the Simplex method, total derivatives using the chain rule, matrix inversion, Cobweb model equilibrium and stability, Shephard's lemma derivation, limit evaluation, matrix operations, orthogonal vectors, and determinants.
How can I access the IGNOU BECE-015 question paper with solved answers?
You can get the complete BECE-015 solved question paper through Unnati Education by following the three-step process described in Section 14 above. The solved paper includes full stepwise numerical solutions, complete derivations, and conceptual explanations for all sections of the December 2025 exam.
About Unnati Education — IGNOU Study Material Experts
Unnati Education has been supporting IGNOU students across programmes for years. Every solved paper is prepared by an IGNOU-experienced academic content writer with graduate-level specialisation in economics and mathematical methods. Our content aligns with the IGNOU Term-End Examination December 2025 official schedule and follows IGNOU's BDP assessment framework. We serve students across BDP, BAG, BAECH, BAFEC, and other IGNOU undergraduate economics programmes.
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You have the questions. You know what each section demands. Now prepare with solutions that show every step, every derivation, and every calculation written for IGNOU's examination format. Get the BECE-015 solved question paper from Unnati Education and walk into your exam with real mathematical confidence.