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BA · End Term · 13 Apr 2025 (Forenoon)

33 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 · 13 Apr 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.

Q1MSQ1 Mark·Choose all correct options
Asked 2 times Key ↓
Which of the following distributions is/are not symmetric in nature (choose all that are applicable)?
1. AStandard Normal distribution
2. BStandard Binomial distribution
3. CUniform distribution
4. DPoisson distribution
Q2MSQ1 Mark·Choose all correct options
Key ↓
Which of the following is/are required to build an empirical distribution? (choose all that are applicable)
1. APDF or PMF
2. BSample data
3. CSummary Statistics
4. DNone of these
Q3MSQ1 Mark·Choose all correct options
Asked 4 times Key ↓
Given the Chisquare table in Figure-2, what is the conclusion from the test at a 95% significance level? (choose all that may be applicable)
1. AREJECT the NULL HYPOTHESIS and conclude that the number of defects FOLLOWS a poisson distribution
2. BDO NOT REJECT the NULL HYPOTHESIS and conclude that the number of defects FOLLOWS a poisson distribution
3. CREJECT the NULL HYPOTHESIS and conclude that the number of defects DOES NOT FOLLOW a poisson distribution
4. DDO NOT REJECT the NULL HYPOTHESIS and conclude that the number of defects DOES NOT FOLLOW a poisson distribution
5. EREJECT the ALTERNATIVE HYPOTHESIS and conclude that the number of defects FOLLOWS a poisson distribution
6. FDO NOT REJECT the ALTERNATIVE HYPOTHESIS and conclude that the number of defects FOLLOWS a poisson distribution
7. GREJECT the ALTERNATIVE HYPOTHESIS and conclude that the number of defects DOES NOT FOLLOW a poisson distribution
8. HDO NOT REJECT the ALTERNATIVE HYPOTHESIS and conclude that the number of defects DOES NOT FOLLOW a poisson distribution
Q4MSQ1.5 Marks·Choose all correct options
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 (choose all that is/are applicable)
1. AOptimization approach
2. BRegression approach
3. CStatistical approach
4. DNone of these
Q5MSQ1.5 Marks·Choose all correct options
Key ↓
The part worth can be defined as (choose all that may be applicable)
1. ALevel utilities
2. BThe utility for that level of attribute
3. CUtility for separate parts of the products
4. DNone of these
Q6MCQ1 Mark·Choose one option
Key ↓
In Figure-3 the customer wants to decide between the products O1 & O2, and x denotes the coordinates of the ideal product. Which of the following is/are true?
1. ACustomers will prefer O1 when d2>d1
2. BCustomers will prefer O2 when d1<d2
3. CBoth Customers will prefer O1 when d2>d1 & Customers will prefer O2 when d1<d2
4. DNone of these
Q7MSQ2 Marks·Choose all correct options
Key ↓
There are 7 business units and you are using the DEA to compare them. You solve the LP for business unit 5. You find from the constraint expression that business unit 1 has obtained an efficiency of 1 and business unit 2 has obtained an efficiency of 1 with the optimal weights of business unit 5. Which of the following statements is correct? (choose all that is/are applicable)
1. ABusiness unit 5 is inefficient
2. BBusiness unit 1 is efficient
3. CBusiness unit 5 is efficient
4. DBusiness unit 2 is efficient
Q8MSQ2 Marks·Choose all correct options
Key ↓
In DEA, when can the Linear Programming model be used for calculating the weights of efficiency (weighted outputs/weighted inputs)? (choose all that is/are applicable)
1. AAfter converting the ratio into the linear objective function
2. BAfter normalizing the denominator
3. CBy setting a constraint on the efficiency of all DMUs to be lesser than or equal to 1
4. DNone of these
Read the passage below, then answer Q9–Q13
(The following is a purely imaginary scenario)
A demand response curve is modelled using linear regression. The partial regression output is given in Figure-1 below. Given this information, answer the subquestions.
Q9NAT1.5 Marks·Write the number
Asked 2 times Key ↓
What is the elasticity of the demand response curve at a price of Rs. 50? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Your answer:
Q10NAT0.5 Marks·Write the number
Asked 2 times Key ↓
What is the market size? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Your answer:
Q11NAT0.5 Marks·Write the number
Asked 2 times Key ↓
What is the satiating price? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Your answer:
Q12MCQ0.5 Marks·Choose one option
Key ↓
Based on the elasticity, which of the following statements are TRUE
1. AThe demand is elastic
2. BThe demand is inelastic
3. CThe price is elastic
4. DThe price is inelastic
Q13NAT1 Mark·Write the number
Key ↓
What percentage of the total linear variability in demand is captured by this model (given in figure-1)? (Note: Enter the answer in “percentage rounded to two decimal places without the percentage sign. For example, if the answer is “1.234%”, then enter it as “1.23”)
Your answer:
Read the passage below, then answer Q14–Q16
(The following is a purely imaginary scenario)
A survey was conducted among 100 students who participated in all events at IITMs recent “Saarang” event. The students were asked to rate various aspects of their experience on a scale of “-5 to +5”, where “-5” indicates a very negative experience and “+5” indicates a very positive experience. The average student rating for each event was taken across four key parameters: “Event Ambience”, “Fairness of Event Judges”, “Event Conduct”, “Event Prize Money”. The target variable was “Event Performance” which measures the overall performance of each event. Based on the collected data, a correlation matrix as specified in Table-2 is obtained for the independent variables. With this information, answer the given sub-questions
Q14NAT1 Mark·Write the number
Asked 2 times Key ↓
What would be the R-Square value if a model is built with “Event Conduct” as the independent variable and “Event Prize Money” as the dependent variable? (Note: Enter the answer in percentage rounded to two decimal places without the “%” symbol. For example, if the answer is “1.234%”, then enter it as “1.23”)
Your answer:
Q15NAT1 Mark·Write the number
Asked 2 times Key ↓
What would be the Adjusted R-Square value if a model is built between “Fairness of Event Judges” as the independent variable and “Event Ambience” as the dependent variable? (Note: Enter the answer in percentage rounded to two decimal places without the “%” symbol. For example, if the answer is “1.234%”, then enter it as “1.23”)
Your answer:
Q16NAT2 Marks·Write the number
Asked 3 times Key ↓
What will be the percentage increase in the standard error corresponding to the beta value of “Event Ambience”, if a multiple linear regression model where both “Event Ambience” and “Event Price Money” are used as explanatory variables to predict “Event Performance”? (Note: Enter the answer in percentage rounded to two decimal places. For example, if the answer is “1.234%”, then enter it as “1.23”)
Your answer:
Read the passage below, then answer Q17–Q18
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 0.5 and 0.3, respectively. Based on Table 6, answers the given sub-questions
Q17NAT2 Marks·Write the number
Asked 8 times Key ↓
How much will the Output 1 in HCU 3?
Your answer:
Q18NAT2 Marks·Write the number
Asked 8 times Key ↓
How much will the Output 2 in HCU 3?
Your answer:
Read the passage below, then answer Q19–Q21
(The following is a purely imaginary scenario)
Ms. Teddy, is the owner of a toy manufacturing company. The company produces its iconic “Teddy Bear” toys in a facility that operates for 8 hours a day, and 20 days in month. Ms. Teddy has recently completed the BA course and wants to see if her manufacturing facility is producing toys where the defects per ship follows a Poisson distribution. Accordingly, she collected data for the past month indicating the number of defects produced in a shift. This is provided in Table-1. Using this information answer the given sub-questions
Q19NAT1 Mark·Write the number
Key ↓
How many bins will be present in the frequency table for the statistical test to be conducted? (Note: Enter an INTEGER answer)
Your answer:
Q20NAT3 Marks·Write the number
Asked 4 times Key ↓
What is the value of the computed test statistic for the statistical test that is to be performed by Ms. Teddy to very her claim? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Your answer:
Q21NAT1 Mark·Write the number
Asked 5 times Key ↓
How many degrees of freedom is present for the test statistic that is to be conducted by Ms. Teddy? (Note: Enter an INTEGER answer)
Your answer:
Read the passage below, then answer Q22–Q23
(The following is a purely imaginary scenario)
The relationship between Demand “D” and Selling Price “P” is given by the equation D(p) = 780 – 9*P. Then answer the given sub-questions.
Q22NAT2 Marks·Write the number
Key ↓
If the intention is to maximize the profit, then what is the optimal selling price if the item is going to be made at Rs. 30 per unit? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Your answer:
Q23NAT1 Mark·Write the number
Key ↓
What is the maximum profit that can be generated? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Your answer:
Read the passage below, then answer Q24–Q26
As a Business Analyst, we are trying to find the DMUs that are efficient, where there are 2 outputs (Number of Leads & Sales) and one constant input. Based on the graph given in Figure-4 below, answer the given sub-questions
Q24MCQ1 Mark·Choose one option
Asked 2 times Key ↓
Which DMUs are in the economic frontier?
1. A(3,2,1)
2. B(3,2,5)
3. C(4,5,2)
4. D(3,4,1)
Q25MCQ1 Mark·Choose one option
Asked 4 times Key ↓
Which DMUs are the reference units for DMU 2?
1. A(5,4)
2. B(4,1)
3. C(3,5)
4. D(3,1)
Q26MCQ1 Mark·Choose one option
Asked 4 times Key ↓
Which DMUs are the reference units for DMU 5?
1. A(1,4)
2. B(1,3)
3. C(3,4)
4. DNone of these
Read the passage below, then answer Q27–Q28
(The following is a purely imaginary scenario)
An insurance company believes that people can be divided into two classes: “Class-1: Those who are accident prone” and “Class-2: Those who are not accident prone”. The company’s statistics show that an accident-prone person will have an accident at sometime within a faxed 1-year period with probability 0.4, whereas this probability decreases to 0.2 for a person who is not accident prone. It is assumed that 30 percent of the human population is accident prone. Given this information, answer the sub-questions
Q27NAT1 Mark·Write the number
Asked 2 times Key ↓
What is the probability that a new policyholder will have an accident within a year of purchasing a policy? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Your answer:
Q28NAT1 Mark·Write the number
Asked 3 times Key ↓
Suppose a new policyholder has an accident within a year of purchasing a policy. Then, what is the probability that the person is accident prone? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Your answer:
Read the passage below, then answer Q29–Q33
A fintech company wants to assess the performance of its classification model, which predicts loan approval (positive class) or rejection (negative class). Table 3 presents the data used for model development, while Table 4 provides the estimated coefficients from the logistic regression model. To validate the model, the actual loan decisions made by the fintech company are shown in Table 5.
Based on the provided data, answer the given sub-questions
Q29NAT2 Marks·Write the number
Asked 8 times Key ↓
What is the precision of class 1? (Note: Enter the answer in percentage rounded to two decimal places. For example, if the answer is “10.235%”, then enter it as “10.24”)
Your answer:
Q30NAT2 Marks·Write the number
Asked 8 times Key ↓
What is the sensitivity of the model? (Note: Enter the answer in percentage rounded to two decimal places. For example, if the answer is “10.235%”, then enter it as “10.24”)
Your answer:
Q31NAT2 Marks·Write the number
Asked 8 times Key ↓
What is the specificity of the model? (Note: Enter the answer in percentage rounded to two decimal places. For example, if the answer is “10.235%”, then enter it as “10.24”)
Your answer:
Q32MSQ1.5 Marks·Choose all correct options
Asked 6 times Key ↓
What is the correct interpretation of the coefficient b1? (Choose that is/are applicable)
1. AIf the salary increases by 1 unit, the log of odds of the application acceptance increases by 0.04.
2. BIf the salary increases by 1 unit, the odds of the application getting accepted increase by 4% (e^(0.4) = 1.04)
3. CNone of these
Q33MSQ1.5 Marks·Choose all correct options
Asked 6 times Key ↓
What is the correct interpretation of the coefficient b2? (Choose that is/are applicable)
1. AIf the age increases by 1 unit, the log of odds of the application acceptance decreases by 0.03.
2. BIf the age increases by 1 unit, the odds of the application getting accepted decrease by 3% (e^(-0.03) = 0.97).
3. CNone of these

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q1D

Q2A, B, C

Q3C

Q4A

Q5A, B, C

Q6A

Q7B, D

Q8A, B, C

Q90.02 to 0.05

Q1039942

Q111352 to 1355

Q12B

Q1398 to 99

Q1425 to 27

Q1515 to 16

Q1618 to 20

Q178061 to 8064

Q1810.5 to 11

Q196

Q20589 to 592

Q214

Q2258 to 59

Q2320424 to 20425

Q24D

Q25B

Q26C

Q270.25 to 0.27

Q280.44 to 0.48

Q2933.32 to 33.34

Q3049.95 to 50.05

Q3149.95 to 50.05

Q32A, B

Q33A, B

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