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BA · End Term · 22 Dec 2024 (Afternoon)

31 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 · 22 Dec 2024 (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.

Q1NAT2 Marks·Write the number
Key ↓
Two factories “A” and “B” produce radios. Each radio produced at factory-A is defective with probability 0.05, whereas each radio produced at factory-B is defective with probability 0.1. You purchase two radios that were produced in the same factory (which is equally likely to have been either factory-A or factory-B). If the first radio that you check is defective, what is the conditional probability that the second radio is also defective? (Note: Enter your answer in decimals rounded to two decimal places. For example, if your answer is “0.456” then enter it as “0.46”)
Your answer:
Read the passage below, then answer Q2–Q5
Milo’s Survey Services (MSS) specializes in evaluating the reaction of customers to new products. A client has hired MSS to ascertain customer reaction to a recently launched product (Frying Pan). During meeting with the client, MSS agreed to conduct door-to-door personal interviews to obtain responses from households with children and without children. In addition, MSS agreed to conduct both “Daytime” and “Evening time” interviews. Specifically, the client’s contract called for MSS to conduct 1000 interviews under the following quota guidelines
i. Interview at least 400 households with children
ii. Interview at least 400 households without children
iii. The total number of households interviewed during evening must be at least as great as the number of households interviewed during the day
iv. At least 40% of the interviews for households with children must be conducted during the evening
v. At least 60% of the interviews for households without children must be conducted during evening
Because the interviews for households with children take additional interview time and because evening interviewers are paid more than daytime, the cost varies with type of interview. Based on previous surveys conducted, MSS estimates the interview costs as given in Table-1
MSS wanted to conduct the interviews so that the overall cost for conducting the survey is minimized. Given this information, answer the subquestions.
Q2NAT1.5 Marks·Write the number
Asked 3 times Key ↓
How many (count of) decision variables are present in the standard form of the primal?
Your answer:
Q3NAT1.5 Marks·Write the number
Key ↓
Excluding the non-negativity constraint, how many (count of) constraints are present in the standard form of the primal?
Your answer:
Q4NAT1 Mark·Write the number
Asked 3 times Key ↓
MSS has decided to conduct 400 interviews for Households with children and 600 interviews for households without children. Moreover, of the 400, 240 are to be conducted in the daytime. Similarly, of the 600 interviews, 360 are going to be conducted in the evening. Then, what is the total cost that would be incurred by MSS? (Note: enter your answer in “Rupees” rounded to two decimal places without the “₹” symbol. For example, if your answer is “₹123.456” then enter it as “123.46”)
Your answer:
Q5NAT2 Marks·Write the number
Asked 3 times Key ↓
MSS has decided to conduct 400 interviews for Households with children and 600 interviews for households without children. Moreover, of the 400, 240 are to be conducted in the daytime. Similarly, of the 600 interviews, 360 are going to be conducted in the evening. Then, how many (count of) decision variables will have a NON-ZERO VALUE in dual formulation which is obtained based on the standard form of the primal?
Your answer:
Read the passage below, then answer Q6–Q10
The BS program coordinators wanted to understand the difficulty level of the BA course. Hence, past learners of the BA course were asked to give a rating (on a scale of 1 to 5, 1 meaning “least difficult” and 5 implying “most difficult”). A total of 200 students (100 male and 100 female) were approached for the survey and the result of the same is provided in Table-2. Given this data, answer the sub-questions.
Q6NAT1 Mark·Write the number
Asked 3 times Key ↓
If the aim is to determine if the difficulty level is independent of gender, then how many male responses would you expect to choose the rating value of “3”? (Note: Enter your answer in decimal value rounded to two decimal places. For example, if your answer is “123.456” then enter it as “123.46”)
Your answer:
Q7NAT1 Mark·Write the number
Asked 3 times Key ↓
If the aim is to determine if the difficulty level is independent of gender, then how many female responses would you expect to choose the rating value of “5”? (Note: Enter your answer in decimal value rounded to two decimal places. For example, if your answer is “123.456” then enter it as “123.46”)
Your answer:
Q8NAT2 Marks·Write the number
Asked 2 times Key ↓
If the aim is to find if the difficulty level is independent of gender, then what is the value for the test statistic? (Enter your answer in decimals rounded to two decimal places. Eg: If your answer is 10.256, then enter it as 10.26)
Your answer:
Q9NAT2 Marks·Write the number
Asked 4 times Key ↓
Assuming that each difficulty level splits the probability space into equal areas, the general belief is that the level of difficulty across all learners follows a normal distribution. To validate this belief, what is the value of the computed test statistic? (Enter your answer in decimals rounded to two decimal places. Eg: If your answer is 10.256, then enter it as 10.26)
Your answer:
Q10NAT1 Mark·Write the number
Asked 5 times Key ↓
For the hypothesis test focusing on whether the data is distributed normally, how many (count of) degrees of freedoms is present?
Your answer:
Read the passage below, then answer Q11–Q12
A doctor is of the opinion that “Blood Pressure (BP)” is affected by “Age” and “Weight”. Based on past data, the correlation between these three variables is identified and provided in Table-3. Then answer the given subquestions.
Q11NAT1 Mark·Write the number
Asked 2 times Key ↓
If a linear regression model is built between “BP” and “Age”, then how much percentage of variability in BP can be explained by Age? (Note: Enter your answer in percentage rounded to two decimal places. Eg: If your answer is “10.256%”, then enter the answer as “10.26”)
Your answer:
Q12NAT1 Mark·Write the number
Asked 3 times Key ↓
What is the VIF for “Weight” with respect to “Age”? (Note: Enter your answer in decimal rounded to two decimal places. Eg: If your answer is “10.256”, then enter it as “10.26”)
Your answer:
Read the passage below, then answer Q13–Q14
A logistic model is built to classify three types of animals: “Cat”, “Dog” and “Pig”. The confusion matrix for the model based on 30 samples is presented in Table-4.
Based on the above data, answer the given subquestions
Q13NAT1 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. Eg: If your answer is “10.256%”, then enter the answer as “10.26”)
Your answer:
Q14NAT2 Marks·Write the number
Asked 8 times Key ↓
What is the precision of the model for predicting “Dog”? (Note: Enter your answer in percentage rounded to two decimal places. Eg: If your answer is “10.256%”, then enter the answer as “10.26”)
Your answer:
Read the passage below, then answer Q15–Q17
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 20,00,000. As a Business Analyst, you must formulate a DEA problem using Linear programming for the Sales Office 3. Answer subquestions using the Table below.
Q15MCQ1 Mark·Choose one option
Asked 3 times Key ↓
What is the objective function?
1. A
2. B
3. C
4. D
5. E
Q16MCQ1 Mark·Choose one option
Asked 3 times Key ↓
What is the type constraint?
1. A
2. B
3. C
4. D
Q17MCQ1 Mark·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 Q18–Q19
There are 5 business units. There are two outputs and one input under consideration. You are solving the optimization problem for business unit 3 and find that the efficiency to be 0.6. You find that the dual variables corresponding to the constraints of business units 2 and 4 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 4 are 0.25 and 0.35, respectively. You are given the following table where sales and number of leads are the two outputs.
Based on the above data, answer the given subquestions.
Q18NAT1.5 Marks·Write the number
Asked 8 times Key ↓
How much will the Output 1 in HCU 3? NOTE: For every step performed round off 4 decimal places.
Your answer:
Q19NAT1.5 Marks·Write the number
Asked 8 times Key ↓
How much will the Output 2 in HCU 3? NOTE: For every step performed round off 4 decimal places.
Your answer:
Read the passage below, then answer Q20–Q22
As a Business Analyst, we are trying to find the DMUs that are efficient, where there are 2 inputs (Team Size & Budget) and one constant output. Based on the graph given below, answer the subquestions
Q20MCQ1 Mark·Choose one option
Asked 2 times Key ↓
Which DMUs are in the economic frontier?
1. A(1,2,4)
2. B(1,3,5)
3. C(1,2,4,5)
4. D(1,3,4)
Q21MCQ1 Mark·Choose one option
Asked 4 times Key ↓
Which DMUs are the reference units for DMU 2?
1. A(1,4)
2. B(1,3)
3. C(3,5)
4. D(3,4)
Q22MCQ1 Mark·Choose one option
Asked 4 times Key ↓
Which DMUs are the reference units for DMU 4?
1. A(1,4)
2. B(1,3)
3. C(3,5)
4. D(3,4)
Read the passage below, then answer Q23–Q27
The table below contains the details of 6 customers who have applied for a bike loan. Based on the 2 inputs (X1 & X2), the bank must decide whether to provide the bike loan or not. In addition, the actual decision on the loan is provided in the column (Y_act).
A senior Business Analyst used logistic regression and computed the below values. Based on the data provided answer the subquestions
Q23NAT2 Marks·Write the number
Asked 5 times Key ↓
What is the accuracy of the logistic regression model? Hint: Round off your answer to two decimal places and if your answer is 0.5543, please enter it as 55.43
Your answer:
Q24NAT2 Marks·Write the number
Asked 8 times Key ↓
What is the precision of class 1? Hint: Round off your answer to two decimal places and if your answer is 0.5543, please enter it as 55.43
Your answer:
Q25NAT2 Marks·Write the number
Asked 8 times Key ↓
What is the sensitivity? Hint: Round off your answer to two decimal places and if your answer is 0.5543, please enter it as 55.43
Your answer:
Q26NAT2 Marks·Write the number
Asked 8 times Key ↓
What is the precision of class 0? Hint: Round off your answer to two decimal places and if your answer is 0.5543, please enter it as 55.43
Your answer:
Q27NAT2 Marks·Write the number
Asked 8 times Key ↓
What is the specificity? Hint: Round off your answer to two decimal places and if your answer is 0.5543, please enter it as 55.43
Your answer:
Q28MSQ2 Marks·Choose all correct options
Key ↓
What is the format of data needed for performing the conjoint analysis using the Statistical or Linear Regression Approach?
1. AConsumer Choice Data is Ratings
2. BValue of the attributes are continuous
3. CConsumer Choice Data is Pairwise Comparison
4. DValue of the product attributes are categorical
Q29MCQ1 Mark·Choose one option
Key ↓
The objective function of the linear programming model using pair-wise judgments:
1. AMinimize the poorness of fit
2. BMaximize the distance from the ideal point
3. CMinimize the distance from the ideal point
4. DBoth Minimize the poorness of fit & Minimize the distance from the ideal point
5. EBoth Maximize the distance from the ideal point & Minimize the distance from the ideal point
Q30MCQ1 Mark·Choose one option
Asked 2 times Key ↓
If the attribute values in the conjoint analysis is a continuous variable and the data is collected in a pairwise order, then what approach can be used:
1. AOptimization approach
2. BRegression approach
3. CStatistical approach
4. DOptimization approach or Statistical approach
Q31MCQ2 Marks·Choose one option
Key ↓
In a conjoint problem with 4 products and 2 attributes, how many pair-wise preferences are possible?
1. A4
2. B14
3. C10
4. D6

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q10.04 to 0.05

Q24

Q37

Q420320 or -20320

Q52

Q617 to 18

Q720

Q814.5 to 15

Q921 to 22

Q102

Q1148.3 to 48.32

Q121.3 to 1.4

Q1346 to 47

Q1455 to 56

Q15C

Q16A

Q17F

Q187541 to 7542

Q1911.13 to 11.23

Q20B

Q21B

Q22C

Q2333.3 to 33.4

Q2425

Q2550

Q2650

Q2725

Q28A, D

Q29A

Q30A

Q31D

Detailed Answer Notes & Working

Q4Answer: 20320 or -20320: Official answer key accepts 20320 or -20320.

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