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BA · End Term · 31 Aug 2025 (Afternoon)

30 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 (Afternoon)

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.

Q1MSQ1 Mark·Choose all correct options
Key ↓
Which of the following Regression equations is/are MLR? (Choose all that is/are applicable)
1. A
2. B
3. C
4. D
5. E
6. F
Read the passage below, then answer Q2–Q5
Given the confusion matrix in Table-1, answer the given subquestions
Q2NAT1 Mark·Write the number
Asked 5 times Key ↓
What is the number of False Positives for Class-A?
Your answer:
Q3NAT1 Mark·Write the number
Asked 8 times Key ↓
What is the precision for predicting Class-D? [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:
Q4NAT1 Mark·Write the number
Asked 8 times Key ↓
What is the recall for predicting Class-B? [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:
Q5NAT1 Mark·Write the number
Asked 5 times Key ↓
What is the accuracy of the model? [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:
Read the passage below, then answer Q6–Q9
The Following Comprehension and Related Subquestions are Purely Hypothetical A manufacturer produces lenses for sunglasses. In a given day, a total of 100 products were produced. Products produced usually can have scratches. The manufacturer is interested to see if the length of the scratches on produced lenses is normally distributed. Hence, based on the production of 100 lenses, he has identified the length of scratch on each lens and the grouped data is presented to you in Table-2. Further, from sample, the manufacturer has computed the standard deviation to be 1.00. Based on the production lot of 100 units (given sample), you are asked to check if the “Length of Scratches on produced lenses” follows a Normal Distribution. Given this information, answer the given subquestions.
Q6NAT2 Marks·Write the number
Asked 2 times Key ↓
What would be the mean of the distribution, if you want to check the hypothesis “The length of scratches on a produced lens follows a Normal 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:
Q7NAT1 Mark·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 length of scratches on a produced lens follows a Normal Distribution”?
Your answer:
Q8NAT2 Marks·Write the number
Asked 2 times Key ↓
What would be expected frequency in the last bin of the frequency table (Hint: The frequency table is obtained by only modifying Table-2 without adding any new bins)? [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:
Q9MSQ1 Mark·Choose all correct options
Asked 4 times Key ↓
Say the computed test statistic for the test is 12.3. Then, 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 Q10–Q12
The Following Comprehension and Related Subquestions are Purely Hypothetical Table-2 provides the Cumulative Television Rating Points (CTRP), money spend on promotion (in Lakhs, denoted by “P”), and the advertisement revenue (in Lakhs, denoted by “R”) generated over a one-month period for 8 different television programs. The Revenue a TV show makes is the Dependent Variable. Using this data, answer the given subquestions.
Q10NAT2 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:
Q11NAT1 Mark·Write the number
Asked 2 times Key ↓
The correlation coefficient between “CTRP” and “P” is 0.19. Then, what will be the Adjusted R- Square for the model (built using data in Table-2), where “CTRP” is the response variable and “P” is the predictor? [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:
Q12NAT2 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q13–Q17
The Following Comprehension and Related Subquestions are Purely Hypothetical Milo The Goofball (MTG) is a company that makes footballs for “Recreation (R)” games and “Professional (P)” games. The process of making a football involves the following three stages Stage-1: Cutting and Dyeing
Stage-2: Sewing
Stage-3: Inspection
It is seen that making a R-game football requires 6 minutes in Stage-1, 15 minutes in Stage-2 and 6 minutes in Stage-3. On the other hand, the football for a P-game requires 12 minutes, 9 minutes and 6 minutes in Stages 1,2 and 3 respectively.
For the coming planning period of 4 weeks, MTG has 340 hours available in Stage-1, 480 hours available in Stage-2 and 300 hours available in Stage-3. Moreover, if required, MTG can avail more hours in Stage-1 at an additional cost of Rs. 200 per hour.
Moreover, a R-game football generates a profit of Rs. 500 per piece and a P-game football generates a profit of Rs. 800 per piece. Furthermore, MTG has forecasted that the maximum number of footballs it can sell is 3000. With an objective to maximize the profit, formulate the problem as a Linear Program and answer the given subquestions.
Q13NAT1 Mark·Write the number
Asked 3 times Key ↓
How many decision variables are present in the standard form of the primal linear Programming Problem?
Your answer:
Q14NAT1 Mark·Write the number
Asked 2 times Key ↓
How many decision variables are present in the Dual Linear Programming Problem (which is developed based on the standard form of the problem)?
Your answer:
Q15NAT1 Mark·Write the number
Asked 3 times Key ↓
If the company decides to make 1500 P-game footballs, 1000 R-game footballs, then how many decision variables in the Dual Linear Programming Problem (which is developed based on the standard form of the problem) will have a value of “0”?
Your answer:
Q16NAT1 Mark·Write the number
Asked 3 times Key ↓
If the company decides to make 1500 P-game footballs, 1000 R-game footballs, then what is the objective function value for the primal linear programming problem (which is in the standard form)? [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:
Q17MSQ1 Mark·Choose all correct options
Asked 2 times Key ↓
If the MTG decides to make 1500 P-game footballs, 1000 R-game footballs, then which of the following options is/are correct
1. AMTG will purchase addition capacity in Stage-1
2. BMTG will not purchase addition capacity in Stage-1
3. CMTG will have excess capacity in Stage-1
4. DMTG will have excess capacity in Stage-2
5. EMTG will have excess capacity in Stage-3
6. FMTG will have deficit capacity in Stage-2
7. GMTG will have deficit capacity in Stage-3
8. HMTG cannot make 1500 P-game footballs and 100 R-game footballs as it is an infeasible solution
9. ICannot say as more information is required
Read the passage below, then answer Q18–Q19
Assume that you have trained a logistic regression model on a training dataset containing features X1 and X2. The coefficients obtained are given in Table 1.
Based on the above data, answer the given subquestions.
Q18MSQ1.5 Marks·Choose all correct options
Asked 6 times Key ↓
What is the correct interpretation of the coefficient β1?
1. AIf the X1 increases by 1 unit, the log of odds of the positive outcome increases by 0.3, assuming X2 to be constant.
2. BIf the X1 increases by 1 unit, the odds of the positive outcome increases by 35% (e^(0.3) = 1.35), assuming X2 to be constant.
3. CHigher values of X1 are associated with an increased likelihood of the positive outcome
4. DNone of these
Q19MSQ1.5 Marks·Choose all correct options
Asked 6 times Key ↓
What is the correct interpretation of the coefficient β2?
1. A
2. B
3. C
4. D
Q20MCQ1.5 Marks·Choose one option
Key ↓
Assume that you are working on a classification problem where you are predicting whether the patient is suffering from cancer or not. As a business analyst, select the metric that is most appropriate.
1. APrecision
2. BRecall
3. CR2
4. DMAPE
5. EAll of these
Q21MCQ1.5 Marks·Choose one option
Key ↓
Assume that you are working on a classification problem where you are predicting whether the email is spam or not. As a business analyst, select the metric that is most appropriate.
1. APrecision
2. BRecall
3. CR2
4. DMAPE
5. EAll of these
Read the passage below, then answer Q22–Q23
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 0.8. 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 0.25, respectively. Based on Table 4, answers the given subquestions.
Hint: At every step, round off your answers to 4 decimal places.
Q22NAT2 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:
Q23NAT2 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 Q24–Q26
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 3. Answer the given subquestions using the Table below.
Q24MCQ2 Marks·Choose one option
Asked 3 times Key ↓
What is the objective function?
1. A
2. B
3. C
4. D
5. E
Q25MCQ2 Marks·Choose one option
Asked 3 times Key ↓
What is the type constraint?
1. A
2. B
3. C
4. D
Q26MCQ2 Marks·Choose one option
Asked 3 times Key ↓
Which of them is not a constraint for the LP problem pertaining to Sales Office 3?
1. A
2. B
3. C
4. D
5. E
6. F
Read the passage below, then answer Q27–Q30
You are in the process of selecting an ideal Laptop when a lot of options are available. For example, the three brands that have been on top of your mind are Acer, HP, and Dell. Similarly, there are 2 RAM options available: 8 GB and 16 GB. Lastly, the processor is another important variable in deciding the ideal laptop. There are 3 processors available: i3, i5, and i7. Also, assume that Acer is the least preferred brand. 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.
Q27NAT2 Marks·Write the number
Asked 2 times Key ↓
What is the part worth to customers if he/she upgrades from an i3 to an i7 processor? [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:
Q28NAT2 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 0.63545, then enter the answer as “63.55”]
Your answer:
Q29NAT2 Marks·Write the number
Asked 6 times Key ↓
How much is the weightage provided by the customer for the RAM? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 0.63545, then enter the answer as “63.55”]
Your answer:
Q30NAT2 Marks·Write the number
Asked 6 times Key ↓
How much is the weightage provided by the customer for the processor? [Note: Enter your answer in decimal rounded to four decimal places. For example, if your answer is 0.63545, then enter the answer as “63.55”]
Your answer:

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q1A, B, C, D

Q220

Q350 to 52

Q487 to 89

Q564 to 66

Q61.6 to 1.9

Q71

Q818 to 19

Q9A

Q1018 to 21

Q11-0.14 to -0.12

Q1211 to 12

Q133

Q144

Q151

Q16-1238000 or 1238000

Q17A, D, E

Q18A, B, C

Q19A, B, C

Q20B

Q21A

Q227874 to 7876

Q2317.1 to 17.3

Q24C

Q25A

Q26F

Q274.82 to 4.84

Q2820.35 to 20.39

Q2925.9 to 25.96

Q3053.65 to 53.75

Detailed Answer Notes & Working

Q16Answer: -1238000 or 1238000: Official answer key accepts -1238000 or 1238000.

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