If your BEY-018 exam is scheduled for 2026 or any later session, the BEY 018 Question Paper December 2025 is one of the most practical revision tools you can keep beside your notebook. It tells you exactly how IGNOU frames matrix, vector, and calculus questions, which topics carry real weight, and how to manage three hours without panic. Unnati Education has built this solved paper for students who want genuine clarity before they sit for the actual term end exam.
About This Solved Paper
| Prepared by | Unnati Education, IGNOU-experienced academic content writer |
|---|---|
| Subject expert qualification | Graduate team with specialisation in Mathematics and Applied Science |
| Programme | IGNOU Bachelor of Science Applied Science Energy (BSCAEY) |
| Institution Reference | IGNOU December 2025 Term-End Examination |
You can download the BEY 018 Solved Question Paper December 2025 directly from this page as a clean PDF file. The PDF opens on any phone, tablet, or laptop and stays with you through every revision round. Students who study with actual previous year papers almost always score higher than those who only read textbook exercises. That's why starting your revision with a properly solved paper changes the last month of your preparation entirely.
What is BEY 018 Question Paper December 2025 Definition
The BEY 018 December 2025 question paper is the official IGNOU Term End Examination paper for Linear Algebra and Calculus, conducted in December 2025 for BSCAEY students. It carries 70 marks, runs for three hours, and asks you to attempt any seven questions of equal marks, with a non programmable scientific calculator allowed.
The paper tests how well you handle matrices, vectors, limits, differentiation, maxima minima, differential equations, partial derivatives and multivariable calculus. You are expected to write clearly, justify each step and reach the final answer with proper working.
About IGNOU BEY-018 Linear Algebra and Calculus
BEY-018 is a core mathematical paper in the Bachelor of Science (Applied Science Energy) programme. It covers matrices, vectors, limits, differentiation, maxima minima, differential equations, partial derivatives, and multivariable calculus. In practice, this is the paper that strengthens the mathematical backbone you need for thermodynamics, fluid mechanics, and energy systems later. Most students manage vectors comfortably but slow down on differential equations. A well worked solved paper closes that gap with less stress.
BEY 018 Question Paper December 2025 Exam Pattern and Marks Breakdown (BEY-018 December 2025 Question Paper)
The paper runs for three hours and carries a total of 70 marks. Question 1 is compulsory with five small parts worth 10 marks together, built to test quick concept recall. You then attempt any six questions from Questions 2 to 9, each worth 10 marks. Here's the important part, most of these longer questions split into two subparts, so time management per subpart matters more than rushing through the whole paper in one attempt.
All Questions BEY 018 Question Paper December 2025 IGNOU (Complete List)
Below is the full paper exactly as it appeared in the IGNOU Term End Examination December 2025. The attached PDF shows the original paper with proper mathematical formatting.
Note: (i) Question No. 1 is compulsory. (ii) Attempt any six questions from the remaining question nos. 2 to 9. (iii) Use of scientific calculator (non programmable) is allowed in exam. (iv) Symbols have their usual meanings.
Question 1 (Compulsory, 10 marks)
(a) If A = [[2, 3],[5, 4]], show that (1/2)(A + A′) is symmetric and (1/2)(A – A′) is skew symmetric.
(b) Show that the vectors 2î – ĵ + k̂, î + 2ĵ – 3k̂ and 3î – 4ĵ + 5k̂ are coplanar vectors.
(c) Expand y = sin x about x = 0 using Maclaurin's formula upto 2 terms.
(d) Evaluate: lim (x→1, y→2) (2x2 + y2)/(2xy).
(e) Solve: dx/x = tan y · dy.
Question 2 (10 marks)
(a) Find the coordinates of the point, where the tangent is parallel to the x axis for the curve: y3 = x2(2 – x).
(b) Find the points of maximum and minimum for the function: f(x) = x5 – 5x4 + 5x3 – 1.
Question 3 (10 marks)
Solve the following system of equations: 3x + 6y – 4z = 3; 3x – z = 0; 12x – 6y – z = – 3.
Question 4 (10 marks)
(a) Solve the differential equation: x2y″ + 4xy′ + 2y = 0, x > 0.
(b) Solve: y″ + 2y′ = 4 sin 2x.
Question 5 (10 marks)
(a) Find the volume of the tetrahedron whose three sides are given by: 2î – 3ĵ + 4k̂, î + 2ĵ – k̂ and 3î – ĵ + 2k̂.
(b) A particle is acted upon by constant forces –3î + 2ĵ + 5k̂ and 2î + ĵ – 3k̂ and is displaced from the point (2, –1, –3) to the point (4, –3, 7). Find the total work done by the forces.
Question 6 (10 marks)
(a) Prove that: (a × b) × c = a × (b × c) if and only if a and c are collinear vectors.
(b) Check the applicability of the Rolle's theorem in the function: f(x) = x2 + 4, x ∈ [–2, 2]. Find 'c' in case it is applicable.
Question 7 (10 marks)
(a) Find ∂u/∂r and ∂u/∂θ, if: u = e(r cos θ) · cos (r sin θ).
(b) If x = r cos θ, y = r sin θ, z = z, then find: ∂(x, y, z)/∂(r, θ, z).
Question 8 (10 marks)
(a) Prove that: |1 x x2; 1 y y2; 1 z z2| = (x – y)(y – z)(z – x).
(b) Show by vector method that the diagonals of a rhombus are at right angles.
Question 9 (10 marks)
(a) Solve: d2y/dx2 + 6 dy/dx + 9y = 5e(3x).
(b) Solve: (x + 1) dy/dx – y = ex (x + 1)2.
BEY 018 Question Paper December 2025 Syllabus Topics Covered
The December 2025 paper pulls from almost every important unit of the BEY-018 syllabus. You will notice questions on symmetric and skew symmetric matrices, coplanar vectors, Maclaurin series, limits, curve tangents, maxima and minima, system of linear equations, second order differential equations, tetrahedron volume, work done by forces, Rolle's theorem, partial derivatives, Jacobians, determinants, rhombus geometry, and variable coefficient differential equations. The balance between algebra, vectors, and calculus stays steady across recent BSCAEY sessions.
Sample Answer Preview BEY-018 Linear Algebra and Calculus Solved Question Paper Explanation
Take Question 1(c) as an example. For y = sin x expanded about x = 0 using Maclaurin's formula, you start with f(0) = 0, then f′(0) = 1, and stop after two terms. The answer reads sin x equals x plus zero times x squared by two factorial, which simplifies neatly to x for the first two terms requested. Our solved paper shows the derivation step by step, including why the even power term vanishes. Every solution carries this same careful structure, formula, substitution, final answer.
How to Write High-Scoring Answers in BEY 018 Question Paper December 2025
Always begin a numerical with the relevant theorem or formula written on a fresh line. Substitute values clearly before reaching the final answer. For vector questions, draw a small diagram showing direction, even if it is rough. For matrix proofs, write the transpose step separately instead of squeezing it into the main line. Most students lose marks not because they do not know the method, but because their presentation is cluttered. Underline final results. Keep decimal values consistent. State assumptions in a single line wherever needed.
Who Should Use This BEY-018 Solved Question Paper December 2025?
This solved paper is built for IGNOU BSCAEY students appearing in June 2026, December 2026, or later sessions. It suits first time exam takers who want direction, repeaters aiming to close past weak areas, and working students who get only a few hours per week for revision. If vectors and matrices feel easier than differential equations, the worked solutions will balance your preparation. If calculus is your strength, the algebra sections will sharpen your speed and accuracy.
Why This is Better Than Free BEY-018 December 2025 Question Paper PDFs and Telegram Files
Free files shared on Telegram channels often carry wrong signs, missing steps, or scans so faded you cannot read the exponents. Some PDFs mix answers from different years. A few skip the compulsory question entirely. Unnati Education's solved paper is checked by writers who have worked with IGNOU mathematical papers for years. You get clean notation, proper symbols, correct derivations, and answers that follow IGNOU's marking pattern closely. The small fee you pay saves weeks of wasted revision.
Student Reviews BEY-018 Solved Question Paper by Unnati Education
Rohit from Chandigarh said the tetrahedron volume answer finally made him confident with scalar triple products. Kavya, a BSCAEY student from Kochi, wrote that the Rolle's theorem explanation was clearer than her reference book. Arjun from Bhopal appreciated how the Jacobian solution walked through each partial derivative without skipping steps. These small notes reach our team every week, and they keep us committed to checked, classroom style solutions instead of quick keys.
How to Get the BEY-018 Solved Question Paper December 2025 Step by Step
First, click the download or buy button visible on this page. Second, pay through UPI, debit card, credit card, or net banking, whichever suits you best. Third, your PDF link arrives in your email within minutes, and the same link stays active on your account page for repeat downloads anytime. No subscription trap. No monthly charge. No waiting for someone to share the file through WhatsApp late at night before your exam.
Frequently Asked Questions BEY 018 Question Paper December 2025 IGNOU
Is this the official IGNOU BEY 018 December 2025 paper?
Yes, this is the actual Term End Examination paper conducted by IGNOU in December 2025 for BEY 018 under the Bachelor of Science Applied Science Energy BSCAEY programme. Every question on this page is reproduced exactly as it appeared in the official paper, which makes it a reliable source for your 2026 exam preparation and for any future Term End attempt you may plan later in your studies.
Will this paper help me for my 2026 exam?
It will help you strongly. IGNOU often repeats question themes in BEY 018, especially on matrices, vectors, limits, differentiation, maxima minima, differential equations, Jacobians and Rolle's theorem. By practicing the December 2025 paper with solved answers, you understand the examiner style, the expected length for a 10 mark question, and how to structure both theory and calculation based answers for full marks in your Term End exam.
Are all numerical questions solved with full working?
Yes. Every numerical question in our solved paper carries complete step by step working. You see the starting formula, intermediate algebra, substitution of values, and the final answer. Our team prefers teaching the method rather than offering a short answer key, so even weak students can follow along and reproduce the answer on their own in the exam hall.
Does it cover all major units of the syllabus?
Yes. The December 2025 paper itself covers a broad range, including matrices, vectors, limits, differentiation, maxima minima, differential equations, partial derivatives, determinants, and multivariable calculus. Our solutions treat every unit seriously, so by the time you finish the solved paper, you have effectively revised most core areas of the BEY-018 syllabus in one focused sitting.
Is the download instant after payment?
Yes, delivery is instant. Once your payment is confirmed, the BEY 018 solved question paper PDF is sent to your registered email and also saved inside your Unnati Education account dashboard. You can open it on mobile, tablet or laptop, and there is no limit on how many times you download, print or revise the paper during your BSCAEY preparation journey in any upcoming Term End exam cycle across years.
About Unnati Education IGNOU Study Material Experts
Unnati Education is an academic resource platform built for IGNOU students across India. Our team includes graduates, postgraduates, engineers and subject mentors who have personally handled IGNOU coursework. We prepare solved question papers, handwritten assignments and revision notes in student friendly language. Our focus is simple, we want you to stop depending on unreliable free files and start preparing with material you can actually trust during your exam cycle.
Explore More IGNOU BEY-018 Solved Papers and Study Material
You can also explore BEY 018 solved assignments, previous year question papers from June and December cycles, important questions lists, and short revision notes on our website. Together, these resources give you a complete preparation package for Linear Algebra and Calculus, from the first reading of the course to your final revision the night before your IGNOU BSCAEY Term End examination in any upcoming session.