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BA · End Term · 31 Aug 2025 (Forenoon)

32 questions · 45 marks · 90 min

Answer key Take as mock

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Business Analytics

End Term · 31 Aug 2025 (Forenoon)

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
MSQ: One or more options correct. Select all to score.
NAT: Numerical response. No negative marking.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

Read the passage below, then answer Q1–Q5
The Following Comprehension and Related Questions are Purely Hypothetical
MiloBurgers, a fast-food restaurant sells two types of products: “Double Cheese Veggy” (DCV) burgers and “Cheese Veggy” (CV) burgers. The DCV uses 0.5Kg of cheese and the CV uses only 0.2kg of cheese. The restaurant starts the day with 200Kg of cheese but may order more at an additional cost of ₹25 per Kg to cover the delivery cost. Any surplus cheese at the end of the day is donated to charity. MiloBurgers sells a DCV for ₹100 and a CV for ₹80. All in all, MiloBurgers does not expect to sell more than 900 items in total during a day and the owner wants to maximizes the profit for the coming day. Assume that whatever combination is made (a solution to the problem) can be sold. Given this information, answer the given subquestions.
Q1NAT1 Mark·Write the number
Asked 3 times Key ↓
How many decision variables are present in the standard form of the primal, if the given problem is formulated as a Linear Programming Problem?
Your answer:
Q2NAT1 Mark·Write the number
Asked 2 times Key ↓
How many decision variables are present in the Dual form (which is formulated based on the standard form of the primal) if the given problem is formulated as Linear Programming Problem?
Your answer:
Q3NAT1 Mark·Write the number
Asked 3 times Key ↓
If the restaurant decides to make 450 DCVs and 450 CVs, then what is the value of the objective function for the linear program which is in the standard form of the primal? [Note: Enter your answer in decimal rounded to two decimal places. For example, if your answer is 1.235 then enter the answer as “1.24”]
Your answer:
Q4NAT1 Mark·Write the number
Asked 3 times Key ↓
If the restaurant decides to make 450 DCVs and 450 CVs, then how many decision variables in the Dual form (which is formulated based on the standard form of the primal) will have a value of “0”, if the given problem is formulated as Linear Programming Problem?
Your answer:
Q5MCQ1 Mark·Choose one option
Asked 2 times Key ↓
If the restaurant decides to make 450 DCVs and 450 CVs, then which of the following option is correct
1. AThe restaurant will order more cheese in addition to the cheese available in stock
2. BThe restaurant will not order more cheese and will completely consume the available cheese
3. CThe restaurant will donate some cheese to charity as it has surplus
4. DCannot say as more information is required
Read the passage below, then answer Q6–Q8
The Following Comprehension and Related Questions are Purely Hypothetical
A company has collected data on the average monthly electricity consumed for air conditioning (dependent variable) relative to (i) Average ambient temperature of the month, (ii) Total number of working days in the month and (iii) Average number of employees who have worked in that month. This data is provided in Table-1. Additionally, the correlation matrix for the different variables in Table-1 is provided in Figure-1. Given this information, answer the given subquestions.
Q6NAT2 Marks·Write the number
Asked 2 times Key ↓
What is the total variability in the dependent variable? [Note: Enter your answer in decimal rounded to two decimal places. For example, if your answer is 1.235 then enter the answer as “1.24”]
Your answer:
Q7NAT2 Marks·Write the number
Asked 3 times Key ↓
What is the expected percentage inflation (increase) in the standard error of the beta value corresponding to “Average Number of Employees who have Worked” due to “Total Number of Working Days” if a model with only these two variables is built for predicting “Average Electricity Consumed”? [Note: Enter your answer in “PERCENTAGE” rounded to two decimal places without the percentage symbol. For example, if your answer is 1.235% then enter the answer as “1.24”]
Your answer:
Q8MSQ1 Mark·Choose all correct options
Key ↓
Based on the expected percentage inflation (increase) in the standard error of the beta value corresponding to “Average Number of Employees who have Worked” due to “Total Number of Working Days” if a model with only these two variables is built for predicting “Average Electricity Consumed”, which of the following statements is/are TRUE (choose all that is applicable)?
1. AThe t-statistic corresponding to the “Beta value of Average Number of Employees who have Worked” will increase. Hence, the corresponding NULL HYPOTHESIS will be REJECT
2. BThe t-statistic corresponding to the “Beta value of Average Number of Employees who have Worked” will increase. Hence, the corresponding NULL HYPOTHESIS will NOT BE REJECTED
3. CThe t-statistic corresponding to the “Beta value of Total Number of Working Days” will increase. Hence, the corresponding NULL HYPOTHESIS will be REJECT
4. DThe t-statistic corresponding to the “Beta value of Total Number of Working Days” will increase. Hence, the corresponding NULL HYPOTHESIS will NOT be REJECT
Q9MSQ1 Mark·Choose all correct options
Asked 4 times Key ↓
The computed p-value of a chi-square goodness-of-fit test is 0.167. Then, which of the following statements are TRUE
1. AAt a 5% level of significance, the null hypothesis is rejected
2. BAt a 5% level of significance, the null hypothesis is not-rejected
3. CAt a 10% level of significance, the null hypothesis is rejected
4. DAt a 10% level of significance, the null hypothesis is not-rejected
5. EAt a 5% level of significance, the alternative hypothesis is rejected
6. FAt a 5% level of significance, the alternative hypothesis is not-rejected
7. GAt a 10% level of significance, the alternative hypothesis is rejected
8. HAt a 10% level of significance, the alternative hypothesis is not-rejected
9. ICannot conclude only based on the P-value and Significance Level. Need the computed Chi-Square value as well.
Q10MCQ1 Mark·Choose one option
Key ↓
Say you build a multiple regression model using 6 independent variables and 20 data points. This is called Model-1. The R-Square for Model-1 is 94%. You then decide to add four more variables (such that the sample size is still 20) to the model and develop a new model called Model-2. The R- Squared for Model-2 is 95%. Then which of the following statements is/are TRUE?
1. AModel-1 is better as it has lower R-Squared
2. BModel-1 is better as it has lower Adjusted R-Square
3. CModel-1 is better as it has higher Adjusted R-Square
4. DModel-2 is better as it has higher R-Square
5. EModel-2 is better as it has lower Adjusted R-Square
6. FModel-2 is better as it has higher Adjusted R-Square
7. GNone of these
Q11MCQ1.5 Marks·Choose one option
Asked 3 times Key ↓
The Following Question is Purely Hypothetical Your family is seeking an alliance for you and has found three matrimonial services “X”, “Y” and “Z”. Assume that the enrolment in the matrimonial services is mutually exclusive. A market survey indicates that 40% of total enrolments are in “X”, 35% are in “Y” and the remaining are in “Z”. The market survey also indicates that 25% of registrations in “X” find a suitable match, 40% in “Y” find a suitable match, and 30% in “Z” find a suitable match. Recently, your family has heard the news that a relative “P” has not found a suitable match after enrolling in one of the matrimonial services. Then which matrimonial service would you suspect “P” to have enrolled in?
1. AZ
2. BY
3. CX
4. DCannot say as I am already married (This is not the correct answer to this question. Just relax, think and choose from the other three)
Read the passage below, then answer Q12–Q16
The Following Comprehension and Related Questions are Purely Hypothetical
A manufacturer produces lenses for sunglasses. In a given day, a total of 100 products were produced. Products produced can have anywhere between no scratches to 3 scratches. From past experience, it is seen that the lenses break if it has more than 3 scratches. Broken lenses are not included in the 100 units which are provided to you. On examining the 100 units, the below Table- 2 on the products with scratches is determined. Based on the production lot of 100 units (given sample), you are asked to check if the “Number of Scratches on produced lenses” follows a Poisson Distribution. Given this information, answer the given subquestions.
Q12NAT1 Mark·Write the number
Asked 2 times Key ↓
What would be the mean of the distribution, if you want to check the hypothesis “The number of scratches on a produced lens follows a Poisson Distribution”? [Note: Enter your answer rounded to two decimal places. For example, if your answer is 1.235 then enter the answer as “1.24”]
Your answer:
Q13MCQ0.5 Marks·Choose one option
Key ↓
Which of the following is the correct PMF formula for a Poisson Distribution?
1. A
2. B
3. C
4. D
5. E
Q14NAT0.5 Marks·Write the number
Asked 5 times Key ↓
How many (count) of degrees of freedom will be presented for the computed test statistic for this problem if you want to check the hypothesis “The number of scratcheson a produced lens follows a Poisson Distribution”?
Your answer:
Q15NAT3 Marks·Write the number
Asked 4 times Key ↓
What is the value of the computed test statistic for the test to be performed if you want to check the hypothesis “The number of scratches on a produced lens follows a Poisson Distribution”? [Note: Enter your answer rounded to two decimal places. For example, if your answer is 1.235 then enter the answer as “1.24”]
Your answer:
Q16MSQ1 Mark·Choose all correct options
Asked 4 times Key ↓
Based on the computed test statistic for the test to be performed, using Figure-2, at a significance level of 10% what will be concluded (choose all that are correct)?
1. AReject the Null Hypothesis
2. BDo not Reject the Null Hypothesis
3. CReject the Alternative Hypothesis
4. DDo not Reject the Alternative Hypothesis
5. EAccept the Null Hypothesis
6. FAccept the Alternative Hypothesis
Read the passage below, then answer Q17–Q23
Assume that you have trained a logistic regression model on a training dataset containing features X1 and X2. The coefficients obtained and threshold are given in Table 1.
Predict the target variable (y_pred) in the test dataset (Table 2) using the available information.
Based on the available information, answer the given subquestions:
Q17NAT1 Mark·Write the number
Asked 5 times Key ↓
What is the accuracy of the logistic regression model? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 0.635450, then enter the answer as “63.5450”]
Your answer:
Q18NAT1.5 Marks·Write the number
Asked 8 times Key ↓
What is the precision of class 1? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 0.635450, then enter the answer as “63.5450”]
Your answer:
Q19NAT1.5 Marks·Write the number
Asked 8 times Key ↓
What is the recall of class 1? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 0.635450, then enter the answer as “63.5450”]
Your answer:
Q20NAT1.5 Marks·Write the number
Asked 8 times Key ↓
What is the precision of class 0? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 0.635450, then enter the answer as “63.5450”]
Your answer:
Q21NAT1.5 Marks·Write the number
Asked 8 times Key ↓
What is the recall of class 0? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 0.635450, then enter the answer as “63.5450”]
Your answer:
Q22MSQ1.5 Marks·Choose all correct options
Asked 6 times Key ↓
What is the correct interpretation of the coefficient β1? (Select all that apply)
1. AIf the X1 increases by 1 unit, the log of odds of the positive outcome increases by 0.6 assuming X2 to be constant.
2. BIf the X1 increases by 1 unit, the odds of the positive increase by 82% (e ^(0.6)= 1.82) assuming X2 to be constant.
3. CHigher values of X1 are associated with an increased likelihood of the positive outcome
4. DNone of these
Q23MSQ1.5 Marks·Choose all correct options
Asked 6 times Key ↓
What is the correct interpretation of the coefficient β2? (Select all that apply)
1. AIf the X2 increases by 1 unit, the log of odds decreases by 0.65, assuming X1 to be constant.
2. BIf the X2 increases by 1 unit, the odds decrease by 48% (e^(−0.65) ≈ 0.52), assuming X1 to be constant.
3. CHigher values of X2 are associated with a decreased likelihood of the positive outcome.
4. DNone of these
Read the passage below, then answer Q24–Q25
There are six business units. There are two outputs and one input under consideration. You are solving the optimization problem for business unit 3, and you find that the efficiency is 0.9. You see that the dual variables corresponding to the constraints of business units 2 and 5 are non- zero, and the dual variables corresponding to the constraints of other units are zero. The dual variables corresponding to the constraints of business units 2 and 5 are 0.55 and 0.35, respectively. Based on Table 4, answers the given subquestions.
Hint: At every step, round off your answers to 4 decimal places.
Q24NAT2 Marks·Write the number
Asked 8 times Key ↓
How much will the Output 1 in HCU 3? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 1000.63545, then enter the answer as “1000.6355”]
Your answer:
Q25NAT2 Marks·Write the number
Asked 8 times Key ↓
How much will the Output 2 in HCU 3? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 1000.63545, then enter the answer as “1000.6355”]
Your answer:
Read the passage below, then answer Q26–Q28
We are interested in understanding the efficiency of 5 Sales Offices. Each of the Sales Offices has an approved budget and a team size for achieving a fixed target of 10,00,000. As a Business Analyst, you must formulate a DEA problem using Linear programming for the Sales Office 2. Answer the given subquestions using the Table below.
Q26MCQ1.5 Marks·Choose one option
Asked 3 times Key ↓
What is the objective function?
1. A
2. B
3. C
4. D
5. E
Q27MCQ1.5 Marks·Choose one option
Asked 3 times Key ↓
What is the type constraint?
1. A
2. B
3. C
4. D
Q28MSQ1.5 Marks·Choose all correct options
Asked 3 times Key ↓
Which of them is not a constraint for the LP problem pertaining to Sales Office 2? (Select all that apply)
1. A
2. B
3. C
4. D
5. E
6. F
Read the passage below, then answer Q29–Q32
You are in the process of selecting an ideal car when a lot of options are available. For example, the three brands that have been on top of your mind are: Maruti, Hyundai, and Volkswagen. Similarly, there are 2 engine options that are highly efficient: 1000 CC and 1500 CC. Lastly, the type of automatic gearbox is another important variable in deciding the ideal car. There are 3 gearbox options available: AMT, AT and DSC. Also, assume that Maruti is the least preferred brand, and assume AMT is the least preferred gearbox. Based on the inputs available, you build a regression model, and the coefficients are given below in Figure 1.
Based on the above data, answer the given subquestions.
Q29NAT1 Mark·Write the number
Asked 2 times Key ↓
What is the part worth to customers if he/she upgrades from Maruti to Volkswagen? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 1000.63545, then enter the answer as “1000.6355”]
Your answer:
Q30NAT2 Marks·Write the number
Asked 6 times Key ↓
How much is the weightage provided by the customer for the Brand? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 0.635450, then enter the answer as “63.5450”]
Your answer:
Q31NAT2 Marks·Write the number
Asked 6 times Key ↓
How much is the weightage provided by the customer for the Engine? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 0.635450, then enter the answer as “63.5450”]
Your answer:
Q32NAT2 Marks·Write the number
Asked 6 times Key ↓
How much is the weightage provided by the customer for the Gearbox? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 0.635450, then enter the answer as “63.5450”]
Your answer:

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q14

Q22

Q378125

Q40

Q5A

Q63900 to 3904

Q711 to 11.5

Q8B, D

Q9B, D

Q10C

Q11C

Q121.3 to 1.5

Q13A

Q142

Q155.2 to 5.5

Q16A

Q1757.1 to 57.2

Q1866.65 to 66.71

Q1950

Q2050

Q2166.65 to 66.71

Q22A, B, C

Q23A, B, C

Q246915 to 6918

Q2527.5 to 27.9

Q26C

Q27A

Q28F

Q291.832 to 1.834

Q3020.35 to 20.39

Q3125.9 to 25.96

Q3253.65 to 53.75

Questions and answer keys are reproduced from the official IIT Madras BS papers. BTechi is not affiliated with IIT Madras.