BCOC 134 key facts
- Course code: BCOC 134
- Subject: Business Mathematics and Statistics
- Programme: Bachelor of Commerce (General), BCOMG
- Credits: 6
- Syllabus: 18 units in two parts (Part A Units 1 to 11, Part B Units 12 to 18)
- Maximum marks: 100
- Duration: 3 hours
- Questions in the paper: 9 (attempt 5: Q1 compulsory, any 2 from Part A, any 2 from Part B)
- Samples shown on this page: 2 (Question 2 and Question 8); all 9 in the paid file
BCOC 134 Solved Question Paper for June 2026 is our complete, examiner-style solution to IGNOU's latest Business Mathematics and Statistics term-end paper. This page shows two full answers, lists the other seven questions exactly as printed, and explains how to get the whole file on WhatsApp 9899436384.
1. What the June 2026 Paper Covers
BCOC 134 Business Mathematics and Statistics is a core course of IGNOU's Bachelor of Commerce (General) programme that joins matrices, calculus and interest mathematics with business statistics.
The June 2026 paper tests both halves in one sitting. Question 1 is compulsory and holds ten short parts, five from mathematics and five from statistics, and you answer any four from each group. After that you pick any two questions from Part A and any two from Part B, and every question carries 20 marks.
The paper this session leans hard on computation. Part A asks for a 3 × 3 inverse, four limits, four derivatives and a simple versus compound interest comparison, while Part B mixes a theory essay on statistics with standard deviation, least squares regression and index number tests.
If you are putting together a revision set for the whole programme, the BCOMG Question Paper collection sits alongside this one, so you can line up BCOC 134 with the other B.Com core courses you are writing this term.
2. Two Answers Solved in Full, Seven Held Back
Two questions from the June 2026 BCOC 134 paper are solved in full below: Question 2 from Part A and Question 8 from Part B.
We chose one question from each part so you can judge the working style for both mathematics and statistics. Each answer names the method, shows every line of arithmetic and ends with a check, which is exactly where IGNOU evaluators award method marks.
Inverse of a 3 × 3 matrix, with proof
Question 2: Find the inverse of matrix A = [3 2 4; 6 2 1; 1 2 3] and hence show that A × A−1 = A−1 × A = I3. (20)
| 3 | 2 | 4 |
| 6 | 2 | 1 |
| 1 | 2 | 3 |
Step 1: find |A| by expanding along the first row
|A| = 3(2 × 3 − 1 × 2) − 2(6 × 3 − 1 × 1) + 4(6 × 2 − 2 × 1) = 3(4) − 2(17) + 4(10) = 12 − 34 + 40 = 18.
Since |A| = 18 ≠ 0, A is a non-singular matrix, so its inverse exists.
Step 2: find the cofactors
Here Cij = (−1)i+j × Mij.
- Row 1: C11 = +(2·3 − 1·2) = 4; C12 = −(6·3 − 1·1) = −17; C13 = +(6·2 − 2·1) = 10
- Row 2: C21 = −(2·3 − 4·2) = 2; C22 = +(3·3 − 4·1) = 5; C23 = −(3·2 − 2·1) = −4
- Row 3: C31 = +(2·1 − 4·2) = −6; C32 = −(3·1 − 4·6) = 21; C33 = +(3·2 − 2·6) = −6
Check: 3(4) + 2(−17) + 4(10) = 18, which matches |A|, so the first-row cofactors are right.
Step 3: write adj A, the transpose of the cofactor matrix
| 4 | 2 | −6 |
| −17 | 5 | 21 |
| 10 | −4 | −6 |
Step 4: divide by |A|
A−1 = (1/|A|) × adj A = (1/18) × adj A:
| 2/9 | 1/9 | −1/3 |
| −17/18 | 5/18 | 7/6 |
| 5/9 | −2/9 | −1/3 |
Step 5: show that A × A−1 = I3
It is cleaner to multiply A by adj A first and divide by 18 at the end.
- Row 1 of A (3, 2, 4): 12 − 34 + 40 = 18; 6 + 10 − 16 = 0; −18 + 42 − 24 = 0
- Row 2 of A (6, 2, 1): 24 − 34 + 10 = 0; 12 + 10 − 4 = 18; −36 + 42 − 6 = 0
- Row 3 of A (1, 2, 3): 4 − 34 + 30 = 0; 2 + 10 − 12 = 0; −6 + 42 − 18 = 18
So A × adj A = 18 I3, and A × A−1 = (1/18)(18 I3) = I3.
Step 6: show that A−1 × A = I3
- Row 1 of adj A (4, 2, −6): 12 + 12 − 6 = 18; 8 + 4 − 12 = 0; 16 + 2 − 18 = 0
- Row 2 of adj A (−17, 5, 21): −51 + 30 + 21 = 0; −34 + 10 + 42 = 18; −68 + 5 + 63 = 0
- Row 3 of adj A (10, −4, −6): 30 − 24 − 6 = 0; 20 − 8 − 12 = 0; 40 − 4 − 18 = 18
So adj A × A = 18 I3, and A−1 × A = I3.
Conclusion: A−1 = (1/18) × adj A as found in Step 4, and since both products equal the identity matrix, A × A−1 = A−1 × A = I3. Hence proved.
Regression equation of y on x by least squares
Question 8: Find the regression equations of y on x using method of Least Square. (20)
| x | 3 | 5 | 6 | 8 | 9 | 11 |
|---|---|---|---|---|---|---|
| y | 2 | 3 | 4 | 6 | 5 | 8 |
Method. The regression line of y on x is y = a + bx. By the method of least squares, a and b come from the two normal equations: Σy = na + bΣx and Σxy = aΣx + bΣx².
| x | y | x² | xy |
|---|---|---|---|
| 3 | 2 | 9 | 6 |
| 5 | 3 | 25 | 15 |
| 6 | 4 | 36 | 24 |
| 8 | 6 | 64 | 48 |
| 9 | 5 | 81 | 45 |
| 11 | 8 | 121 | 88 |
| Σx = 42 | Σy = 28 | Σx² = 336 | Σxy = 226 |
Step 1: substitute into the normal equations (n = 6)
- 28 = 6a + 42b … (i)
- 226 = 42a + 336b … (ii)
Step 2: solve
Multiply (i) by 7: 196 = 42a + 294b … (iii). Subtract (iii) from (ii): 30 = 42b, so b = 5/7 = 0.714. Put b in (i): 28 = 6a + 30, so 6a = −2 and a = −1/3 = −0.333.
Regression equation of y on x: y = −0.333 + 0.714x, which can also be written as 21y = 15x − 7.
Step 3: check with means
x̄ = 42/6 = 7 and ȳ = 28/6 = 4.667. Putting x = 7 gives y = −0.333 + 5 = 4.667, so the line passes through (x̄, ȳ), as every least squares regression line must.
Step 4: cross-check the slope
byx = (Σxy − n x̄ ȳ) / (Σx² − n x̄²) = (226 − 196)/(336 − 294) = 30/42 = 0.714, the same value as Step 2.
Interpretation. Each one-unit rise in x raises the estimated value of y by about 0.71 units. For example, at x = 10 the estimate is y = −0.333 + 7.143 = 6.81.
For completeness. Since the question says "equations", some evaluators also expect the line of x on y. With Σy² = 154, bxy = 30/(154 − 130.667) = 9/7 = 1.286, giving x − 7 = 1.286(y − 4.667), that is x = 1.286y + 1. Then r = √(0.714 × 1.286) = 0.958, a strong positive correlation.
3. Questions Answered Only in the Full File
The seven questions below are shown as question text only, exactly as printed in the June 2026 paper. Their complete answers are in the full solved file.
Question 1 (a): Answer the following (any four). (4 × 2.5 = 10)
(i) Write a 3 × 3 matrix whose elements aij = 2i + j. Here i is row and j is column.
(ii) What is the transpose of A = [2 3; 1 5]?
(iii) Find all the cofactors of [3 −3; 2 1].
(iv) Find dy/dx of y = x(x + 1)(x + 2).
(v) Find limx→3 (x² − 3x − 10)/(x² − 6x + 5).Question 1 (b): Answer the following (any four). (4 × 2.5 = 10)
(i) Define quartiles.
(ii) Meaning of dispersion.
(iii) What is Simple Regression?
(iv) Define Simple Price and Quantity Index Number.
(v) What are different components of time series?
Question 3: Find the limit of the following (any four). (4 × 5 = 20)
(i) limx→5 (x² − 9x + 20)/(x² − 6x + 5)
(ii) limx→2 [1/(x − 2) − 2/(x² − 2x)]
(iii) limx→0 [√(2 + x) − √2]/x
(iv) limx→1 (x15 − 1)/(x10 − 1)
(v) limx→0 (e2x − 1)/(e3x − 1)
Question 4: Find dy/dx (any four). (4 × 5 = 20)
(i) y = x³ + 2x² − 8x + 15
(ii) y = [(x + 7)(x − 3)]/[(x + 3)(x − 7)]
(iii) y² + x² = 2xy
(iv) y = x5 + 5x + log 5
(v) y = (ex − 1)/(ex + 1)
Question 5: Arun borrows ₹12,000 for 3 years at 10.5% p.a. simple interest, while Kiran borrows the same amount for the same period at 10% compounded annually. Who pays more and by how much? (20)
Question 6: What is Statistics? Explain some of the important functions of Statistics. (20)
Question 7 (a): What are the requisites of a good measure of central tendency? (10)
Question 7 (b): Calculate standard deviation from the following data. (10)
Class 0–5, frequency 2; 5–10, frequency 5; 10–15, frequency 7; 15–20, frequency 13; 20–25, frequency 21; 25–30, frequency 16; 30–35, frequency 8; 35–40, frequency 3.
Question 9 (a): Explain different tests of consistency of Index Number Formula. (10)
Question 9 (b): Explain different components of a time series. (10)
4. Paper Pattern and Marks Distribution
The June 2026 BCOC 134 paper runs for 3 hours and carries 100 marks, and you attempt 5 of its 9 questions at 20 marks each.
| No. | Part | What it asks | Choice | Marks |
|---|---|---|---|---|
| Q1 | Compulsory | (a) five maths short parts, (b) five statistics short parts | Any four from (a) and any four from (b) | 4 × 2.5 + 4 × 2.5 = 20 |
| Q2 | Part A | Inverse of a 3 × 3 matrix and proof of A × A−1 = I3 | Any two of Q2 to Q5 | 20 |
| Q3 | Part A | Limits | Any four of five parts | 4 × 5 = 20 |
| Q4 | Part A | dy/dx | Any four of five parts | 4 × 5 = 20 |
| Q5 | Part A | Simple versus compound interest on ₹12,000 | Any two of Q2 to Q5 | 20 |
| Q6 | Part B | Meaning and functions of statistics | Any two of Q6 to Q9 | 20 |
| Q7 | Part B | (a) Requisites of a good average, (b) standard deviation | Any two of Q6 to Q9 | 10 + 10 |
| Q8 | Part B | Regression of y on x by least squares | Any two of Q6 to Q9 | 20 |
| Q9 | Part B | (a) Consistency tests of index numbers, (b) time series components | Any two of Q6 to Q9 | 10 + 10 |
Reading the paper by structure shows one change from December 2025. That paper gave Question 1 as two 10-mark theory parts, while June 2026 goes back to the 2.5-mark short-answer format last used in June 2024.
The Question 1 plus two-from-each-part layout has held since December 2022, so working through the IGNOU Previous Year Question Paper set is a direct rehearsal for this format.
5. Most Repeated Topics in Past BCOC 134 Papers
Across five official BCOC 134 papers we checked (December 2022, June 2023, June 2024, June 2025 and December 2025), index numbers, time series and functions appeared in every one.
| Topic | Sessions where it appeared | Count (of 5) | In June 2026 |
|---|---|---|---|
| Index numbers: Fisher's index, reversal tests, construction problems | Dec 2022, Jun 2023, Jun 2024, Jun 2025, Dec 2025 | 5 | Yes: Q9(a), Q1(b)(iv) |
| Time series: components, least squares trend, additive and multiplicative models | Dec 2022, Jun 2023, Jun 2024, Jun 2025, Dec 2025 | 5 | Yes: Q9(b), Q1(b)(v) |
| Functions: composite f∘g, cost, revenue and demand functions | Dec 2022, Jun 2023, Jun 2024, Jun 2025, Dec 2025 | 5 | — |
| Derivatives: a set of dy/dx problems | Jun 2023, Jun 2024, Jun 2025, Dec 2025 | 4 | Yes: Q4, Q1(a)(iv) |
| Simple and compound interest | Dec 2022, Jun 2023, Jun 2024, Jun 2025 | 4 | Yes: Q5 |
| Regression: coefficients, equations, properties | Dec 2022, Jun 2023, Jun 2024, Jun 2025 | 4 | Yes: Q8 (Sample 2), Q1(b)(iii) |
| Correlation: Karl Pearson's r and its meaning | Dec 2022, Jun 2023, Jun 2024, Dec 2025 | 4 | No separate question |
| Dispersion: variance, SD, quartile deviation, combined variance | Dec 2022, Jun 2023, Jun 2024, Jun 2025 | 4 | Yes: Q7(b), Q1(b)(i) and (ii) |
| Central tendency: averages, merits and demerits, AM versus HM | Dec 2022, Jun 2023, Jun 2024, Dec 2025 | 4 | Yes: Q7(a) |
| Matrix definitions and types: diagonal, scalar, unit, transpose, inverse | Dec 2022, Jun 2024, Jun 2025 | 3 | Yes: Q1(a)(i) to (iii) |
| Matrix algebra in business: billing by multiplication, finding A and B | Dec 2022, Jun 2023, Jun 2025 | 3 | — |
| Linear equations by matrix method or Cramer's rule | Jun 2023, Jun 2024, Dec 2025 | 3 | Related: Q2 asks for a 3 × 3 inverse (Sample 1) |
| Maxima, minima, increasing and decreasing functions | Dec 2022, Jun 2025, Dec 2025 | 3 | — |
| Present value, discount, nominal and effective rates | Jun 2023, Jun 2025, Dec 2025 | 3 | — |
| Meaning, importance and uses of statistics | Jun 2023, Jun 2025, Dec 2025 | 3 | Yes: Q6 |
| Limits of functions | None of the five | 0 | Yes: Q3 (20 marks), Q1(a)(v) |
A topic is counted once per paper, whether it came as a short part or a full question. The biggest surprise in June 2026 is Question 3: none of the five earlier papers had a full limits question, yet this paper gives limits 20 marks, while functions, seen in all five, were left out entirely.
Use these counts as a priority list, not a prediction. Our IGNOU Solved Guess Paper sets are built the same way, from official papers only, so a topic seen four times ranks above one seen once.
We could not find the December 2023 and December 2024 BCOC 134 papers on ignou.ac.in or webservices.ignou.ac.in, so the counts cover five sessions rather than every exam since the course began.
6. Unit Wise Syllabus
BCOC 134 has 18 units split into Part A Business Mathematics (Units 1 to 11) and Part B Business Statistics (Units 12 to 18).
| Part | Unit | Title | Key topics |
|---|---|---|---|
| Part A: Business Mathematics | Unit 1 | Introduction to Matrices | Order of a matrix; row, column, diagonal, scalar and identity types; equality and transpose |
| Part A: Business Mathematics | Unit 2 | Determinants | Expanding 2 × 2 and 3 × 3 determinants; minors and cofactors; properties of determinants |
| Part A: Business Mathematics | Unit 3 | Inverse of Matrices | Adjoint method; singular versus non-singular matrices; checking A × A−1 = I |
| Part A: Business Mathematics | Unit 4 | Application of Matrices in Business and Economics | Matrix method and Cramer's rule for linear equations; input-output analysis; billing by matrix multiplication |
| Part A: Business Mathematics | Unit 5 | Mathematical Functions | Linear, quadratic and exponential functions; composite and inverse functions; cost, revenue and demand functions |
| Part A: Business Mathematics | Unit 6 | Limit and Continuity | Limits by factorisation and rationalisation; standard limit results; continuity of a cost function at break points |
| Part A: Business Mathematics | Unit 7 | Concept of Differentiation | Power, product, quotient and chain rules; implicit differentiation; derivatives of ex, ax and log x |
| Part A: Business Mathematics | Unit 8 | Maxima and Minima of Functions | First and second derivative tests; increasing and decreasing intervals; local maxima and minima |
| Part A: Business Mathematics | Unit 9 | Application of Derivatives | Marginal cost and marginal revenue; profit maximisation; price and income elasticity of demand |
| Part A: Business Mathematics | Unit 10 | Interest Rates | Simple interest; compound interest with changing rates; nominal versus effective rate |
| Part A: Business Mathematics | Unit 11 | Compounding and Discounting | Present value and discount factor; equation of value; types of discount |
| Part B: Business Statistics | Unit 12 | Introduction to Statistics | Meaning and definitions; functions and scope in business; limitations and misuse |
| Part B: Business Statistics | Unit 13 | Measures of Central Tendency | Arithmetic, geometric and harmonic means; median and quartiles; requisites of a good average |
| Part B: Business Statistics | Unit 14 | Measures of Dispersion | Range and quartile deviation; standard deviation and coefficient of variation; combined variance of two groups |
| Part B: Business Statistics | Unit 15 | Simple Linear Correlation | Scatter diagram; Karl Pearson's coefficient; effect of change of origin and scale on r |
| Part B: Business Statistics | Unit 16 | Simple Linear Regression | Least squares regression lines; properties of regression coefficients; link between r, byx and bxy |
| Part B: Business Statistics | Unit 17 | Index Numbers | Simple and weighted price and quantity indices; Laspeyres, Paasche and Fisher; time and factor reversal tests |
| Part B: Business Statistics | Unit 18 | Time Series Analysis | Trend, seasonal, cyclical and irregular components; least squares trend; additive and multiplicative models |
Unit titles follow IGNOU's course listing; the topic notes are ours. You can read the official unit PDFs on eGyanKosh's BCOC 134 course page before you start practising.
By our mapping, June 2026 drew on 12 of the 18 units; Units 4, 5, 8, 9, 11 and 15 had no question this time. Our BCOC 134 Study Material follows the same unit order, so you can go from a weak unit straight to the matching question type.
7. How Our Answers Are Written and Checked
Every answer in the BCOC 134 Solved Question Paper is worked in full, checked step by step by a second person and laid out the way IGNOU evaluators mark numericals.
Numericals open with the formula, then the substitution, then the arithmetic, and close with a check line. For Question 2 that check is multiplying A back into its inverse; for regression it is confirming that the line passes through the two means. A wrong final digit still earns method marks when the steps are visible.
Theory answers for questions such as the functions of statistics or the tests of index numbers use a definition, headed points, a short business example and a closing line. Length is matched to marks: roughly a page for 20 marks, half a page for 10, and three or four lines for a 2.5-mark part.
Answers were written after studying earlier BCOC 134 papers, so repeated question types get the fuller treatment evaluators have rewarded before.
8. Solved File Index by Question and Unit
BCOC 134 has no practical or record file, so instead of a practical index here is the solved file index for all 9 questions of the June 2026 paper.
| No. | Topic | Course unit (our mapping) | Where the answer is |
|---|---|---|---|
| Q1 | Ten short parts: matrix construction, transpose, cofactors, a derivative, a limit; quartiles, dispersion, regression, index numbers, time series components | Units 1, 2, 6, 7, 13, 14, 16, 17, 18 | Full file |
| Q2 | Inverse of a 3 × 3 matrix and proof that A × A−1 = A−1 × A = I3 | Units 2 and 3 | Sample 1 above |
| Q3 | Five limits, answer any four | Unit 6 | Full file |
| Q4 | Five dy/dx problems including implicit and exponential forms, answer any four | Unit 7 | Full file |
| Q5 | Arun's simple interest loan versus Kiran's compound interest loan on ₹12,000 | Unit 10 | Full file |
| Q6 | Meaning of statistics and its important functions | Unit 12 | Full file |
| Q7 | Requisites of a good average; standard deviation for an 8-class distribution | Units 13 and 14 | Full file |
| Q8 | Regression equation of y on x by least squares for six pairs | Unit 16 | Sample 2 above |
| Q9 | Consistency tests of index number formulae; components of a time series | Units 17 and 18 | Full file |
That is 2 answers on this page and 7 in the full file, 9 in total. The full file also repeats the two sample answers, so you have one complete document to revise from.
9. Programmes That Include BCOC 134
BCOC 134 is a core course of IGNOU's Bachelor of Commerce (General), programme code BCOMG, and the June 2026 paper is printed for that programme.
If you are enrolled in the Bachelor of Commerce (General), this is the one course where mathematics and statistics are examined together, so its numericals carry more weight than in any other core paper of the degree.
IGNOU also places the BCOC 134 assignment in the third-semester folder of its four-year undergraduate B.Com. If you are in that programme, confirm in your programme guide that you sit the same BCOC 134 paper.
10. How to Get the Full Solved Question Paper
Message WhatsApp 9899436384 with the code BCOC 134 and the session June 2026 to get the full solved file covering all 9 questions.
- Save 9899436384 in your phone and open WhatsApp.
- Send "BCOC 134 June 2026 solved paper" along with your name.
- Our team confirms the price and the PDF format.
- After you confirm, the full file is sent to you on WhatsApp.
The full file carries the 2 answers you have read here plus the 7 questions shown above as text only, so every question you might choose in the exam hall is covered.
11. BCOC 134 Frequently Asked Questions
Quick answers to what students ask most about the BCOC 134 June 2026 solved paper.
What does the Solved Question Paper for June 2026 include?
It includes complete answers to all 9 questions of the June 2026 BCOC 134 term-end paper, from the ten short parts of Question 1 to the Part B statistics numericals. Each numerical shows the formula, every step of working and a final check. This page shows 2 of those answers in full, and the other 7 are available only in the full file on WhatsApp.
How do I get the full solved paper on WhatsApp?
Send a message to WhatsApp 9899436384 with the course code BCOC 134 and the session June 2026. Our team replies with the price and the file format, and after you confirm, you receive the full solved PDF. It contains answers to all 9 questions in the paper: the 2 solved on this page and the 7 listed here as question text only.
Which June 2026 questions are solved on this page?
Question 2 and Question 8 are solved in full on this page. Question 2 finds the inverse of a 3 × 3 matrix by the adjoint method and proves A × A−1 = A−1 × A = I3, and Question 8 fits the regression equation of y on x by least squares. Questions 1, 3, 4, 5, 6, 7 and 9 appear here as question text only.
How many questions must I attempt in the BCOC 134 exam?
You attempt 5 of the 9 questions in the June 2026 BCOC 134 paper. Question 1 is compulsory, and inside it you answer any four short parts from group (a) and any four from group (b). You then choose any two questions from Part A, Questions 2 to 5, and any two from Part B, Questions 6 to 9. Each question carries 20 marks, making 100.
Which BCOC 134 topics repeat most?
In the five official papers we checked, from December 2022 to December 2025, index numbers, time series and functions appeared every time. Derivatives, simple and compound interest, regression, correlation, dispersion and central tendency each appeared four times. Treat these as your first revision priorities, but keep limits ready as well, because June 2026 gave them a full 20-mark question.
Were limits asked in earlier BCOC 134 papers?
Not as a full question in the five papers we checked. December 2022, June 2023, June 2024, June 2025 and December 2025 had no dedicated limits question, while June 2026 asks for any four of five limits in Question 3 and adds another limit in Question 1(a)(v). That makes Unit 6, Limit and Continuity, a part of the course you should not skip.
Is the question paper printed in Hindi as well?
Yes. The June 2026 BCOC 134 paper prints the English questions on pages 1 to 6 and the Hindi version on pages 7 to 12. Read both carefully, because a few lines differ: in Question 4(ii) the Hindi text prints (x + 5) in the denominator where the English prints (x + 3), and Question 1(a)(ii) asks for the transpose in English but uses the Hindi word for inverse.
Who prepared and reviewed the solutions?
The BCOC 134 solutions were prepared by Prateek Talwar for Unnati Educations and reviewed by Sheetal Kirola before release. The review covers every numerical step, including the matrix inverse, the regression line and the standard deviation table, to catch arithmetic slips. Theory answers were matched against the IGNOU course units so that the definitions read the way evaluators expect to see them.
12. Who Wrote and Checked the BCOC 134 Answers
The BCOC 134 solutions were prepared by Prateek Talwar and reviewed by Sheetal Kirola at Unnati Educations.
Prateek Talwar is a Company Secretary who prepares IGNOU commerce solved papers from the course blocks and the official term-end paper. Sheetal Kirola, Academic Head (M.Ed.), re-works every numerical step, including the matrix inverse, the regression line and the standard deviation table, before the file is released.