BCOC-134: Business Mathematics and Statistics Question Papers

Welcome to our comprehensive collection of BCOC-134 Business Mathematics and Statistics past question papers for B.Com students. These previous term-end examination papers serve as an excellent resource to understand the exam pattern, recurring question types, marks distribution, and core mathematical and statistical concepts for your upcoming IGNOU examinations.

📘 BCOC 134 Question Paper December 2025

Note:

Question No. 1 is compulsory.
Attempt both Part A and Part B as directed.
All questions carry equal marks.

1. (a) Explain the following terms with example for each: 10

Cost function
Composite function
Inverse function
Demand function

(b) Discuss briefly the importance of statistics in the following disciplines: 10

Business and Management
Accountancy and Auditing

Part-A

Note: Answer any two questions from this Part.

2. (a) Explain the different properties of determinants. 10

(b) Solve the following system of equations by Cramer's rule: 10

$2x + 5y = 1$
$3x + 2y = 7$

3. Find $\frac{dy}{dx}$ for any four from the following: 4 × 5 = 20

(a) $x^2 + xy + y^2 = 100$
(b) $y = e^{x^3} + e^{x^2} + e^x$
(c) $y = \sqrt{(x - 3)(x^2 + 4)}$
(d) $x^y + y^x = a^b$
(e) $x = at^2$ and $y = 2at$
(f) $y = x^3 \cdot \log x$

4. (a) Find the intervals in which the function $f(x)$ given by $f(x) = 4x^3 - 6x^2 - 72x + 30$ is (i) increasing, and (ii) decreasing. 10

(b) Find local maxima and local minima values of the function $f(x)$ by using second order derivative: 10

$f(x) = 3x^4 + 4x^3 - 12x^2 + 12$

5. Write notes on the following: 20

(i) Nominal and effective rate of interest (5)
(ii) Present value (5)
(iii) Types of discounts (10)

Part-B

Note: Attempt any two questions from this Part.

6. What is the meaning of measurement of central tendency? Explain different measures of central tendency with their merits and demerits. 20

7. Calculate the correlation coefficient from the following data: 20

X	y
12	14
9	8
8	6
10	9
11	11
13	12
7	3

What will be correlation coefficient of $2x + 6$ and $2y - 2$?

8. What is an Index Number? What are the different uses of it? Briefly explain different criteria (tests) for a good index number. 20

9. Fit a linear trend to the following data by the least square method. Also estimate the production for the year 2025: 20

Year	Production (in '000 tons)
2019	18
2020	21
2021	23
2022	27
2023	16

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📘 BCOC 134 Question Paper June 2025

Note:

Question No. 1 is compulsory.
Attempt both Part A and Part B as directed.
All questions carry equal marks.

1. (a) Define the following terms with example for each: 10

Diagonal matrix
Scalar matrix
Unit matrix
Transpose of a matrix
Inverse of a matrix

(b) Define the word 'Statistics'. Write in brief the uses and misuses of Statistics. 10

Part-A

Note: Attempt any two questions from this Part.

2. (a) Three shopkeepers A, B and C go to a store to buy stationery. A purchases 12 dozen notebooks, 5 dozen pens and 6 dozen pencils. B purchases 10 dozen notebooks, 6 dozen pens and 7 dozen of pencils. C purchases 11 dozen notebooks, 13 dozen pens and 8 dozen pencils. A notebook costs 40, a pen costs 12.50 and a pencil costs 3.50. Use matrix multiplication to find individual's bills. 10

(b) Specify the conditions under which a function $f(x)$ is increasing or decreasing. Find the value of $X$ for which $f(x) = 2x^2 - 8x + 80$ is decreasing. 10

3. Find $\frac{dy}{dx}$ for any four from the following: 4 × 5 = 20

(a) $x^3 + x^2y + xy^2 + y^3 = 81$
(b) $y = (x+3)^2 (x+4)^3 (x+5)^4$
(c) $x = 2at^2$, $y = at^4$
(d) $y = \frac{5 + \sqrt{x}}{5 - \sqrt{x}}$
(e) $y = (2x + 1)^3 (2x - 1)^4$
(f) $y = \sqrt{\frac{x + 1}{x - 1}}$

4. (a) Find $fog$ and $gof$, given $f(x) = x^2 + 2$ and $g(x) = \frac{x}{x-1}$. 10

(b) If demand function of a firm is given by $P = 8000 - 40X - X^2$, find Total Revenue (TR) and Marginal Revenue (MR) and comment on the nature of the firm. 10

5. (a) Explain the differences between simple interest and compound interest with examples. If principal is 10,000; time is 5 years and rate of interest is 10%, calculate simple interest and compound interest. 10

(b) Explain the meaning of 'present value' and 'equation of value' with suitable example for each. 10

Part-B

Note: Attempt any two questions from this Part.

6. What is Simple Linear Regression? Explain the different properties of regression coefficients. 20

7. For two firms A and B, the following details are given: 20

Particulars	Firm A	Firm B
Number of employees	100	200
Average Salary	16,000	18,000
Standard Deviation ($\sigma$)	160	180

Which firm pays larger total salary?
Which firm shows greater variability in the distribution of salary?
Compute the combined average salary and combined variance of both the firms.

8. What is Index number? Explain different types of Index numbers. Also explain the problems in the construction of Index number. 20

9. Below are given the figures of production (in thousand kilograms) of a sugar factory: 20

Year	Production
2017	77
2018	88
2019	94
2020	85
2021	56

Fit a straight line trend using method of least squares.
Find out the trend value for the year 2025.

📘 BCOC 134 Question Paper December 2024

Note:

Question No. 1 is compulsory. Attempt both Part A and Part B as directed.
All questions carry equal marks.

1. (a) Answer the following (any four): 2.5 × 4 = 10

Under what conditions two matrices are said to be equal?
What is inverse matrices?
Give one example from linear function and quadratic function.
What is the $\frac{dy}{dx}$ of $y = f(x) \cdot g(x)$?
Write formula for simple interest and compound interest.

(b) Answer the following (any four): 2.5 × 4 = 10

What are data in Statistics?
What is relationship between A.M. and G.M.?
Write the formula for Spearman's rank correlation coefficient.
What are base year and current year in Index number?
What are the two models for analyzing time series?

Part-A

Note: Attempt any two of the following questions.

2. Explain in detail the Input-Output analysis in the context of Matrix Algebra. 20

3. The following data is given: 20

Fixed Cost = ₹ 9,00,000
Variable Cost = ₹ 300 per unit
Selling Price = ₹ 750 per unit

Calculate the Cost Function $C(X)$ and Revenue Function $R(X)$ for $X$ units of the product. Also find the break-even point and the profit at quantity $= 1000$.

4. Find the $\frac{dy}{dx}$ of the following (any four): 5 × 4 = 20

(i) $y = \left(\frac{1-x}{1+x}\right)^{1/2}$
(ii) $y = x^x$
(iii) $x^2 + y^2 = 25$
(iv) $y = u^3$ and $u = 3x + 9$
(v) $y = \log u$ and $u = (x^2 + 5)$

5. Calculate the amount and compound interest on ₹ 12,500 for 3 years, the rates of interest for successive years being 6%, 8% and 10% respectively. 20

Part-B

Note: Attempt any two of the following questions.

6. What is Statistics? Discuss its scope and limitations in brief. 20

7. Find the median and mean deviation about median for the following data: 20

Size	Frequency
0-10	6
10-20	7
20-30	15
30-40	16
40-50	4
50-60	2

8. Explain the term "Index Number". Discuss the steps and problems involved in the construction of Index Numbers. 20

9. Below are given the figures of production (in m. tons) of a certain industry: 20

Year	Production (in m. tons)
2018	80
2019	90
2020	92
2021	83
2022	94
2023	99
2024	92

Fit a straight line trend by the method of least squares.
Monthly increase in production.
Estimate the trend value for 2026.

📘 BCOC 134 Question Paper June 2024

Note:

Question No. 1 is compulsory. Attempt both Part A and Part B as directed.
All questions carry equal marks.

1. (a) Answer the following (any four): 2.5 × 4 = 10

Construct a $3 \times 4$ matrix $A = [a_{ij}]$ whose elements are given by $a_{ij} = i \times j$.
Find the value of : $$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$
Define inverse matrix.
If $y = x \cdot \log x$, find $\frac{dy}{dx}$.
What is the difference between simple interest and compound interest?

(b) Answer the following (any four): 2.5 × 4 = 10

List out various measures of central tendency.
What is positive and negative correlation?
Define Price Indices.
Name the four components of time series.
What is the meaning of linear relationship between two variables X and Y?

Part-A

Note: Attempt any two of the following questions.

2. Use matrix method to solve the following system of equations using Cramer's rule: 20

$5X - 7Y = 11$
$7X - 5Y = 25$

3. Find $\frac{dy}{dx}$ of the following: 5 × 4 = 20

(a) $y = (x^2 + 5)^3$
(b) $y = (x^2 + 5x + 6)(x^2 - 3x + 8)$
(c) $y = 3^x + x^3 + 3x + 3$
(d) $y = 4u^3$ and $u = 3x^3 + 5x + 1$

4. (a) If the function $f:R \rightarrow R$ be given by $f(x) = x^2 + 2$ and $g:R \rightarrow R$ be given by $g(x) = \frac{x}{x-1}$, find $fog$ and $gof$. 10

(b) Explain cost function, revenue function and profit function. 10

5. Calculate the amount and the compound interest on 8,000 for 2 years, the rates of interest for the successive years being 5% and 6% per annum respectively. 20

Part-B

Note: Attempt any two of the following questions.

6. Age distribution of 200 employees of a firm is given below. Calculate quartile deviation $\frac{Q_3 - Q_1}{2}$ from it: 20

Age (in years)	No. of Employees
20-25	10
25-30	25
30-35	75
35-40	130
40-45	170
45-50	189
50-55	200

7. Explain the concept of correlation and regression and point out their usefulness in dealing with business problems. 20

8. On the basis of the following information, calculate the Fisher's ideal price index number: 20

Commodities	Base Year		Current Year
Commodities	Price	Quantity	Price	Quantity
A	2	40	6	50
B	4	50	8	40
C	6	20	9	30
D	8	10	6	20
E	10	10	3	20

9. What is a time series? Discuss briefly the importance of time series analysis in business and economics. 20

📘 BCOC 134 Question Paper December 2023

Note:

Question No. 1 is compulsory. Attempt both Part A and Part B.
All questions carry equal marks.

1. (a) Explain the following matrix with example for each: 10

Identity Matrix
Rectangular Matrix
Orthogonal Matrix
Scalar Matrix
Transpose of Matrix

(b) Discuss the limitations of statistics. 10

Part-A

Note: Answer any two of the following questions.

2. Solve by Cramer's rule: 20

$2x - y = 17$
$3x + 5y = 6$

3. Find all the points of local maxima and minima and the corresponding maximum and minimum values of the function: 20

$f(x) = 2x^3 - 21x^2 + 36x - 20$

4. Find $\frac{dy}{dx}$ of the following: 20

(a) $y = \frac{(x+3)(x-1)}{(x+2)(x+4)}$
(b) $y = (x^2 + 3x + 4)(2x^2 - 8x)$
(c) $y = \log u$ and $u = (x^2 + 5)$
(d) $y = x^x$

5. How long would it take for a principal P to be double if rate of interest is 6% per annum compounded annually? 20

Given: $\log 2 = 0.3010$, $\log(1.06) = 0.0253$

Part-B

Note: Attempt any two of the following questions.

6. Explain various measures of central tendency with their merits, demerits and use. 20

7. For the following data, calculate the coefficient of rank correlation: 20

X	Y
80	123
91	135
99	154
71	110
61	105
81	134
70	121
59	106

8. From the data given below find the quantities of different commodities and then compute Fisher's ideal price index number: 20

Commodities	Base Year		Current Year
Commodities	Price per unit	Expenditure	Price per unit	Expenditure
A	2	40	5	75
B	4	16	8	40
C	1	10	2	24
D	5	25	10	60

9. Write short notes on the following: 20

(i) Moving Average Method
(ii) Utility of Time Series

📘 BCOC 134 Question Paper June 2023

Note:

Question No. 1 is compulsory. Attempt both Part A and Part B as directed.
All questions carry equal marks.

1. (a) Discuss application and use of Matrices for Economic decision making. 10

(b) Define statistics. Explain the importance and scope of statistics in Business and Economic decision making. 10

Part-A

Note: Answer any two questions.

2. Solve the following system of equations, using matrix method: 20

$x + 2y + z = 7$
$x + 3z = 11$
$2x - 3y = 1$

3. Find $\frac{dy}{dx}$ for any four from the following: 5 × 4 = 20

(a) $y = u^4$ and $u = (x^2 + x + 1)$
(b) $x^2 + y^2 = 2xy$
(c) $y = \frac{(x+1)(x+2)}{(x+3)(x+4)}$
(d) $y = (1 + e^x)(1 - e^x)$
(e) $y = \frac{1 + \sqrt{x}}{1 - \sqrt{x}}$
(f) $y = x^{1/x}$

4. (a) Given $f(x) = 2x + 3$ and $g(x) = 2x^2 + 5$, then find $f \circ g(x)$ and $g \circ f(x)$. 10

(b) Given total cost function $C = 15 + 3x$, find total cost, average cost and marginal cost when output $x = 5$. 10

5. Explain the following: 10 + 10 = 20

(a) Present value and Equation of value
(b) Types of Annuities

Part-B

Note: Answer any two questions.

6. Distinguish between primary and secondary data. Discuss various methods of collecting primary data. 20

7. Compute the missing frequencies in the following distribution, given that the median is 32 and total frequency is 100: 20

Class Interval	Frequency
0-10	10
10-20	?
20-30	25
30-40	30
40-50	?
50-60	10

8. What is correlation? Distinguish between Karl Pearson's coefficient of correlation and Spearman's rank correlation. When is rank correlation preferred over Karl Pearson's coefficient? 20

9. Compute Laspeyre's, Paasche's and Fisher's price index number for the year 2021 from the following data: 20

Commodity	2011 (Base Year)		2021 (Current Year)
Commodity	Price (₹)	Quantity	Price (₹)	Quantity
A	4	10	10	12
B	3	8	8	9
C	2	12	5	15
D	5	5	12	6

BCOC-134: Business Mathematics and Statistics Question Papers [IGNOU BCOM Courses]

BCOC-134: Business Mathematics and Statistics Question Papers

📑 Table of Contents

📘 BCOC 134 Question Paper December 2025

Bachelor of Commerce (General) [B. Com. (G)]

Term-End Examination | December, 2025

📘 BCOC 134 Question Paper June 2025

Bachelor of Commerce (General) [B. Com. (G)]

Term-End Examination | June, 2025