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BA · Most repeated questions

122 questions · 173 marks · 6 papers · 36 question types

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Business Analytics

Most repeated questions

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.

Type 1 · asked 8 times · Logistic regression & classification

Compute precision of a class from a confusion matrix

Read the passage below, then answer Q1
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
Q1NAT2 Marks·Write the number
End Term · 22 Dec 2024 (AN)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 Q2–Q3
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
Q2NAT2 Marks·Write the number
End Term · 22 Dec 2024 (AN)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:
Q3NAT2 Marks·Write the number
End Term · 22 Dec 2024 (AN)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:
Read the passage below, then answer Q4
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
Q4NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)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:
Read the passage below, then answer Q5
A matrimonial site has built a logistic classification model to predict if a person will get married or not (Married =1 and Not Married =0). The parameters used for this model are Age (in tens of years, that is, the data for a person who is “40 years old” is recorded as “4”) and Height (in feet). The built model’s coefficients are provided in Table-1. The model is being tested using matrimonial profile data available in Table-2.
Given this information, answer the given subquestions
Q5NAT1 Mark·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
At a threshold of 0.8, what is the PRECISION of the model for predicting the Negative Class? (Note: Enter the answer in “%” rounded to two decimal places without the “%” symbol. For example, if the answer is “1.234%”, then enter it as “1.23”)
Your answer:
Read the passage below, then answer Q6
Given the confusion matrix in Table-1, answer the given subquestions
Q6NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)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:
Read the passage below, then answer Q7–Q8
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:
Q7NAT1.5 Marks·Write the number
End Term · 31 Aug 2025 (FN)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:
Q8NAT1.5 Marks·Write the number
End Term · 31 Aug 2025 (FN)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:

Type 2 · asked 8 times · Logistic regression & classification

Compute recall, sensitivity or specificity from a confusion matrix

Read the passage below, then answer Q9–Q10
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
Q9NAT2 Marks·Write the number
End Term · 22 Dec 2024 (AN)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:
Q10NAT2 Marks·Write the number
End Term · 22 Dec 2024 (AN)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:
Read the passage below, then answer Q11–Q12
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
Q11NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)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:
Q12NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)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:
Read the passage below, then answer Q13
A matrimonial site has built a logistic classification model to predict if a person will get married or not (Married =1 and Not Married =0). The parameters used for this model are Age (in tens of years, that is, the data for a person who is “40 years old” is recorded as “4”) and Height (in feet). The built model’s coefficients are provided in Table-1. The model is being tested using matrimonial profile data available in Table-2.
Given this information, answer the given subquestions
Q13NAT1 Mark·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
At a threshold of 0.8, what is the RECALL of the model for predicting the Positive Class? (Note: Enter the answer in “%” rounded to two decimal places without the “%” symbol. For example, if the answer is “1.234%”, then enter it as “1.23”)
Your answer:
Read the passage below, then answer Q14
Given the confusion matrix in Table-1, answer the given subquestions
Q14NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)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:
Read the passage below, then answer Q15–Q16
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:
Q15NAT1.5 Marks·Write the number
End Term · 31 Aug 2025 (FN)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:
Q16NAT1.5 Marks·Write the number
End Term · 31 Aug 2025 (FN)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:

Type 3 · asked 8 times · Data envelopment analysis (DEA)

Find output targets for an inefficient unit from DEA dual values

Read the passage below, then answer Q17–Q18
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.
Q17NAT1.5 Marks·Write the number
End Term · 22 Dec 2024 (AN)Key ↓
How much will the Output 1 in HCU 3? NOTE: For every step performed round off 4 decimal places.
Your answer:
Q18NAT1.5 Marks·Write the number
End Term · 22 Dec 2024 (AN)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 Q19–Q20
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
Q19NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
How much will the Output 1 in HCU 3?
Your answer:
Q20NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
How much will the Output 2 in HCU 3?
Your answer:
Read the passage below, then answer Q21–Q22
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.
Q21NAT2 Marks·Write the number
End Term · 31 Aug 2025 (AN)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:
Q22NAT2 Marks·Write the number
End Term · 31 Aug 2025 (AN)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 Q23–Q24
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.
Q23NAT2 Marks·Write the number
End Term · 31 Aug 2025 (FN)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:
Q24NAT2 Marks·Write the number
End Term · 31 Aug 2025 (FN)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:

Type 4 · asked 6 times · Logistic regression & classification

Interpret a logistic regression coefficient (log-odds and odds)

Read the passage below, then answer Q25–Q26
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
Q25MSQ1.5 Marks·Choose all correct options
End Term · 13 Apr 2025 (FN)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
Q26MSQ1.5 Marks·Choose all correct options
End Term · 13 Apr 2025 (FN)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
Read the passage below, then answer Q27–Q28
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.
Q27MSQ1.5 Marks·Choose all correct options
End Term · 31 Aug 2025 (AN)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
Q28MSQ1.5 Marks·Choose all correct options
End Term · 31 Aug 2025 (AN)Key ↓
What is the correct interpretation of the coefficient β2?
1. A
2. B
3. C
4. D
Read the passage below, then answer Q29–Q30
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:
Q29MSQ1.5 Marks·Choose all correct options
End Term · 31 Aug 2025 (FN)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
Q30MSQ1.5 Marks·Choose all correct options
End Term · 31 Aug 2025 (FN)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

Type 5 · asked 6 times · Conjoint analysis

Find importance weight of an attribute in conjoint analysis

Read the passage below, then answer Q31–Q33
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.
Q31NAT2 Marks·Write the number
End Term · 31 Aug 2025 (AN)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:
Q32NAT2 Marks·Write the number
End Term · 31 Aug 2025 (AN)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:
Q33NAT2 Marks·Write the number
End Term · 31 Aug 2025 (AN)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:
Read the passage below, then answer Q34–Q36
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.
Q34NAT2 Marks·Write the number
End Term · 31 Aug 2025 (FN)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:
Q35NAT2 Marks·Write the number
End Term · 31 Aug 2025 (FN)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:
Q36NAT2 Marks·Write the number
End Term · 31 Aug 2025 (FN)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:

Type 6 · asked 5 times · Chi-square goodness-of-fit tests

Find degrees of freedom for a chi-square goodness-of-fit test

Read the passage below, then answer Q37
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.
Q37NAT1 Mark·Write the number
End Term · 22 Dec 2024 (AN)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 Q38
(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
Q38NAT1 Mark·Write the number
End Term · 13 Apr 2025 (FN)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 Q39
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.
Q39NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)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:
Read the passage below, then answer Q40
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.
Q40NAT0.5 Marks·Write the number
End Term · 31 Aug 2025 (FN)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:
Read the passage below, then answer Q41
(The following is a partially imaginary scenario)
The BA discourse is often cluttered with queries / requests related to solutions for Past Year Question Papers (PYQP). The course instructor, Dr. Milo, had been informing that students need to put in effort to find solutions by searching the discourse. However, the results seem to be disappointing. Therefore, Dr. Milo wanted to do a few basic analytics on discourse behaviour of students. Past student data was collected for the analysis.
Past data was collected for the BA terms in Jan-2022, May-2022, Sep-2022, Jan-2023, May-2023 and Sep-2023. For each term, 150 randomly selected unique student IDs were sampled. Of the 150 student IDs, 75 were “Male” and the remaining were “Female”. The learners in the discourse have either “followed the instructions” or “not followed the instructions” or “have not accessed the discourse at all” (these three are referred to as access categories). Specifically, for the sample data in the different terms (in sequence of earliest term to later term i.e. Jan-2022 to Sep-2023) it was observed that
1. For the Male sample: 30, 20, 35, 35, 45 and 35 had not followed the instructions respectively in each term (i.e 30 male learners had not followed the instructions in Jan-2022 term and so on) 2. For the Male sample: 20, 10, 15, 15, 15 and 10 had not accessed discourse at all respectively in each term (i.e 20 male learners had not accessed discourse at all in Jan-2022 term and so on) 3. For the female sample: 15, 22, 33, 25, 20 and 20 had followed the instructions respectively in each term (i.e 15 female learners had followed the instructions in Jan-2022 term and so on) 4. For the female sample: 30, 20, 25, 25, 25 and 10 had not accessed discourse at all respectively in each term (i.e 30 female learners had not accessed discourse at all in Jan-2022 term and so on) Moreover, Dr. Milo assumes that all learners in the “followed the instructions” category are Uniformly distributed between 4 and 75. A total of 6 bins of equal area are created for performing the appropriate statistical test. Each term is a sample point.
Given this information, answer the sub questions.
Q41NAT1 Mark·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
How many degrees of freedom is present for the hypothesis test used to check if Dr. Milo’s assumption that all learners in the “followed the instructions” category are Uniformly distributed?
Your answer:

Type 7 · asked 5 times · Logistic regression & classification

Count TP, TN, FP or FN from predictions or a confusion matrix

Read the passage below, then answer Q42–Q45
A matrimonial site has built a logistic classification model to predict if a person will get married or not (Married =1 and Not Married =0). The parameters used for this model are Age (in tens of years, that is, the data for a person who is “40 years old” is recorded as “4”) and Height (in feet). The built model’s coefficients are provided in Table-1. The model is being tested using matrimonial profile data available in Table-2.
Given this information, answer the given subquestions
Q42NAT1 Mark·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
At a threshold of 0.8, how many “True Positives” is the model predicting?
Your answer:
Q43NAT1 Mark·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
At a threshold of 0.8, how many “True Negatives” is the model predicting?
Your answer:
Q44NAT1 Mark·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
At a threshold of 0.8, how many “False Positives” is the model predicting?
Your answer:
Q45NAT1 Mark·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
At a threshold of 0.8, how many “False Negatives” is the model predicting?
Your answer:
Read the passage below, then answer Q46
Given the confusion matrix in Table-1, answer the given subquestions
Q46NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
What is the number of False Positives for Class-A?
Your answer:

Type 8 · asked 5 times · Logistic regression & classification

Compute accuracy of a classifier from a confusion matrix

Read the passage below, then answer Q47
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
Q47NAT1 Mark·Write the number
End Term · 22 Dec 2024 (AN)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:
Read the passage below, then answer Q48
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
Q48NAT2 Marks·Write the number
End Term · 22 Dec 2024 (AN)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:
Read the passage below, then answer Q49
A matrimonial site has built a logistic classification model to predict if a person will get married or not (Married =1 and Not Married =0). The parameters used for this model are Age (in tens of years, that is, the data for a person who is “40 years old” is recorded as “4”) and Height (in feet). The built model’s coefficients are provided in Table-1. The model is being tested using matrimonial profile data available in Table-2.
Given this information, answer the given subquestions
Q49NAT1 Mark·Write the number
Quiz 2 · 3 Aug 2025 (AN)Key ↓
At a threshold of 0.8, what is the ACCURACY of the model? (Note: Enter the answer in “%” rounded to two decimal places without the “%” symbol. For example, if the answer is “1.234%”, then enter it as “1.23”)
Your answer:
Read the passage below, then answer Q50
Given the confusion matrix in Table-1, answer the given subquestions
Q50NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)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 Q51
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:
Q51NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)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:

Type 9 · asked 4 times · Chi-square goodness-of-fit tests

Compute the chi-square goodness-of-fit test statistic

Read the passage below, then answer Q52
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.
Q52NAT2 Marks·Write the number
End Term · 22 Dec 2024 (AN)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:
Read the passage below, then answer Q53
(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
Q53NAT3 Marks·Write the number
End Term · 13 Apr 2025 (FN)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:
Read the passage below, then answer Q54
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.
Q54NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)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:
Read the passage below, then answer Q55
(The following is a partially imaginary scenario)
The BA discourse is often cluttered with queries / requests related to solutions for Past Year Question Papers (PYQP). The course instructor, Dr. Milo, had been informing that students need to put in effort to find solutions by searching the discourse. However, the results seem to be disappointing. Therefore, Dr. Milo wanted to do a few basic analytics on discourse behaviour of students. Past student data was collected for the analysis.
Past data was collected for the BA terms in Jan-2022, May-2022, Sep-2022, Jan-2023, May-2023 and Sep-2023. For each term, 150 randomly selected unique student IDs were sampled. Of the 150 student IDs, 75 were “Male” and the remaining were “Female”. The learners in the discourse have either “followed the instructions” or “not followed the instructions” or “have not accessed the discourse at all” (these three are referred to as access categories). Specifically, for the sample data in the different terms (in sequence of earliest term to later term i.e. Jan-2022 to Sep-2023) it was observed that
1. For the Male sample: 30, 20, 35, 35, 45 and 35 had not followed the instructions respectively in each term (i.e 30 male learners had not followed the instructions in Jan-2022 term and so on) 2. For the Male sample: 20, 10, 15, 15, 15 and 10 had not accessed discourse at all respectively in each term (i.e 20 male learners had not accessed discourse at all in Jan-2022 term and so on) 3. For the female sample: 15, 22, 33, 25, 20 and 20 had followed the instructions respectively in each term (i.e 15 female learners had followed the instructions in Jan-2022 term and so on) 4. For the female sample: 30, 20, 25, 25, 25 and 10 had not accessed discourse at all respectively in each term (i.e 30 female learners had not accessed discourse at all in Jan-2022 term and so on) Moreover, Dr. Milo assumes that all learners in the “followed the instructions” category are Uniformly distributed between 4 and 75. A total of 6 bins of equal area are created for performing the appropriate statistical test. Each term is a sample point.
Given this information, answer the sub questions.
Q55NAT3 Marks·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
What is the value of the computed test statistic which will be used to check if Dr. Milo’s assumption that all learners in the “followed the instructions” category are Uniformly distributed? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.235”, then enter it as “1.24”)
Your answer:

Type 10 · asked 4 times · Chi-square goodness-of-fit tests

Decide reject / do not reject H0 from chi-square table or p-value

Q56MSQ1 Mark·Choose all correct options
End Term · 13 Apr 2025 (FN)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
Read the passage below, then answer Q57
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.
Q57MSQ1 Mark·Choose all correct options
End Term · 31 Aug 2025 (AN)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
Q58MSQ1 Mark·Choose all correct options
End Term · 31 Aug 2025 (FN)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.
Read the passage below, then answer Q59
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.
Q59MSQ1 Mark·Choose all correct options
End Term · 31 Aug 2025 (FN)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

Type 11 · asked 4 times · Data envelopment analysis (DEA)

Find reference units for an inefficient DMU from a DEA graph

Read the passage below, then answer Q60–Q61
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
Q60MCQ1 Mark·Choose one option
End Term · 22 Dec 2024 (AN)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)
Q61MCQ1 Mark·Choose one option
End Term · 22 Dec 2024 (AN)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 Q62–Q63
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
Q62MCQ1 Mark·Choose one option
End Term · 13 Apr 2025 (FN)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)
Q63MCQ1 Mark·Choose one option
End Term · 13 Apr 2025 (FN)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

Type 12 · asked 3 times · Probability, Bayes & distributions

Use Bayes' theorem to find the posterior probability of a class

Read the passage below, then answer Q64
(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
Q64NAT1 Mark·Write the number
End Term · 13 Apr 2025 (FN)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:
Q65MCQ1.5 Marks·Choose one option
End Term · 31 Aug 2025 (FN)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 Q66
(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 fixed 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.
Q66NAT1 Mark·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Suppose you learn that 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 “1.235”, then enter it as “1.24”)
Your answer:

Type 13 · asked 3 times · Chi-square test of independence

Find expected frequency in a cell for a chi-square independence test

Read the passage below, then answer Q67–Q68
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.
Q67NAT1 Mark·Write the number
End Term · 22 Dec 2024 (AN)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:
Q68NAT1 Mark·Write the number
End Term · 22 Dec 2024 (AN)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:
Read the passage below, then answer Q69
(The following is a purely imaginary scenario)
A company sells two products (A and B) in four different marketplaces. In the first marketplace, the sales are made at the Forenoon (FN). In the second marketplace, sales are made during the Afternoon (AN). In the third marketplace, sales are made during the Evening (E). In the fourth marketplace, sales are made during the Night (N). Table-2 provides the data on the sales in the four marketplaces for the two products in the first 5 days on January 2023. Using this data, answer the given subquestions.
Q69NAT2 Marks·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
The question of whether total sales in different marketplaces for product A and total sales in different marketplaces for product B are independent across the different days is being checked. Then what is the expected frequency for “Product-B” on “03-01-2025”? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.235”, then enter it as “1.24”)
Your answer:

Type 14 · asked 3 times · Linear regression (SLR & MLR)

Find VIF or % increase in standard error from predictor correlation

Read the passage below, then answer Q70
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.
Q70NAT1 Mark·Write the number
End Term · 22 Dec 2024 (AN)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 Q71
(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
Q71NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)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 Q72
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.
Q72NAT2 Marks·Write the number
End Term · 31 Aug 2025 (FN)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:

Type 15 · asked 3 times · Linear programming & duality

Count decision variables in the standard form of the primal LP

Read the passage below, then answer Q73
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.
Q73NAT1.5 Marks·Write the number
End Term · 22 Dec 2024 (AN)Key ↓
How many (count of) decision variables are present in the standard form of the primal?
Your answer:
Read the passage below, then answer Q74
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.
Q74NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
How many decision variables are present in the standard form of the primal linear Programming Problem?
Your answer:
Read the passage below, then answer Q75
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.
Q75NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)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:

Type 16 · asked 3 times · Linear programming & duality

Find objective value of the primal LP for a given production plan

Read the passage below, then answer Q76
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.
Q76NAT1 Mark·Write the number
End Term · 22 Dec 2024 (AN)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:
Read the passage below, then answer Q77
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.
Q77NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)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:
Read the passage below, then answer Q78
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.
Q78NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)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:

Type 17 · asked 3 times · Linear programming & duality

Count dual variables that are zero for a given production plan

Read the passage below, then answer Q79
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.
Q79NAT2 Marks·Write the number
End Term · 22 Dec 2024 (AN)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 Q80
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.
Q80NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)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:
Read the passage below, then answer Q81
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.
Q81NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)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:

Type 18 · asked 3 times · Data envelopment analysis (DEA)

Choose the objective function of the DEA LP for a sales office

Read the passage below, then answer Q82
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.
Q82MCQ1 Mark·Choose one option
End Term · 22 Dec 2024 (AN)Key ↓
What is the objective function?
1. A
2. B
3. C
4. D
5. E
Read the passage below, then answer Q83
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.
Q83MCQ2 Marks·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
What is the objective function?
1. A
2. B
3. C
4. D
5. E
Read the passage below, then answer Q84
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.
Q84MCQ1.5 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
What is the objective function?
1. A
2. B
3. C
4. D
5. E

Type 19 · asked 3 times · Data envelopment analysis (DEA)

Choose the normalising (type) constraint of the DEA LP

Read the passage below, then answer Q85
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.
Q85MCQ1 Mark·Choose one option
End Term · 22 Dec 2024 (AN)Key ↓
What is the type constraint?
1. A
2. B
3. C
4. D
Read the passage below, then answer Q86
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.
Q86MCQ2 Marks·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
What is the type constraint?
1. A
2. B
3. C
4. D
Read the passage below, then answer Q87
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.
Q87MCQ1.5 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
What is the type constraint?
1. A
2. B
3. C
4. D

Type 20 · asked 3 times · Data envelopment analysis (DEA)

Find which option is not a constraint of the DEA LP

Read the passage below, then answer Q88
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.
Q88MCQ1 Mark·Choose one option
End Term · 22 Dec 2024 (AN)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 Q89
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.
Q89MCQ2 Marks·Choose one option
End Term · 31 Aug 2025 (AN)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 Q90
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.
Q90MSQ1.5 Marks·Choose all correct options
End Term · 31 Aug 2025 (FN)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

Type 21 · asked 2 times · Probability, Bayes & distributions

Find total probability of an accident for a new policyholder

Read the passage below, then answer Q91
(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
Q91NAT1 Mark·Write the number
End Term · 13 Apr 2025 (FN)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:
Read the passage below, then answer Q92
(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 fixed 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.
Q92NAT1 Mark·Write the number
Quiz 1 · 26 Oct 2025 (AN)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 “1.235”, then enter it as “1.24”)
Your answer:

Type 22 · asked 2 times · Probability, Bayes & distributions

Pick which distributions are (not) symmetric

Q93MSQ1 Mark·Choose all correct options
End Term · 13 Apr 2025 (FN)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
Q94MSQ1 Mark·Choose all correct options
Quiz 1 · 26 Oct 2025 (AN)Key ↓
Which of the following distributions is/are Symmetric in nature (choose all that are applicable)?
1. AStandard Normal distribution
2. BStandard Binomial distribution
3. CUniform distribution
4. DPoisson distribution

Type 23 · asked 2 times · Chi-square goodness-of-fit tests

Find the mean from a frequency table for a goodness-of-fit test

Read the passage below, then answer Q95
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.
Q95NAT2 Marks·Write the number
End Term · 31 Aug 2025 (AN)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:
Read the passage below, then answer Q96
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.
Q96NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)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:

Type 24 · asked 2 times · Chi-square goodness-of-fit tests

Find the expected frequency in a bin for a goodness-of-fit test

Read the passage below, then answer Q97
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.
Q97NAT2 Marks·Write the number
End Term · 31 Aug 2025 (AN)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:
Read the passage below, then answer Q98
(The following is a partially imaginary scenario)
The BA discourse is often cluttered with queries / requests related to solutions for Past Year Question Papers (PYQP). The course instructor, Dr. Milo, had been informing that students need to put in effort to find solutions by searching the discourse. However, the results seem to be disappointing. Therefore, Dr. Milo wanted to do a few basic analytics on discourse behaviour of students. Past student data was collected for the analysis.
Past data was collected for the BA terms in Jan-2022, May-2022, Sep-2022, Jan-2023, May-2023 and Sep-2023. For each term, 150 randomly selected unique student IDs were sampled. Of the 150 student IDs, 75 were “Male” and the remaining were “Female”. The learners in the discourse have either “followed the instructions” or “not followed the instructions” or “have not accessed the discourse at all” (these three are referred to as access categories). Specifically, for the sample data in the different terms (in sequence of earliest term to later term i.e. Jan-2022 to Sep-2023) it was observed that
1. For the Male sample: 30, 20, 35, 35, 45 and 35 had not followed the instructions respectively in each term (i.e 30 male learners had not followed the instructions in Jan-2022 term and so on) 2. For the Male sample: 20, 10, 15, 15, 15 and 10 had not accessed discourse at all respectively in each term (i.e 20 male learners had not accessed discourse at all in Jan-2022 term and so on) 3. For the female sample: 15, 22, 33, 25, 20 and 20 had followed the instructions respectively in each term (i.e 15 female learners had followed the instructions in Jan-2022 term and so on) 4. For the female sample: 30, 20, 25, 25, 25 and 10 had not accessed discourse at all respectively in each term (i.e 30 female learners had not accessed discourse at all in Jan-2022 term and so on) Moreover, Dr. Milo assumes that all learners in the “followed the instructions” category are Uniformly distributed between 4 and 75. A total of 6 bins of equal area are created for performing the appropriate statistical test. Each term is a sample point.
Given this information, answer the sub questions.
Q98NAT1 Mark·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
What will be the expected frequency in Bin-2 when performing the hypothesis test to check if Dr. Milo’s assumption that all learners in the “followed the instructions” category are Uniformly distributed? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.235”, then enter it as “1.24”)
Your answer:

Type 25 · asked 2 times · Chi-square test of independence

Compute the chi-square test statistic for independence

Read the passage below, then answer Q99
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.
Q99NAT2 Marks·Write the number
End Term · 22 Dec 2024 (AN)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:
Read the passage below, then answer Q100
(The following is a purely imaginary scenario)
A company sells two products (A and B) in four different marketplaces. In the first marketplace, the sales are made at the Forenoon (FN). In the second marketplace, sales are made during the Afternoon (AN). In the third marketplace, sales are made during the Evening (E). In the fourth marketplace, sales are made during the Night (N). Table-2 provides the data on the sales in the four marketplaces for the two products in the first 5 days on January 2023. Using this data, answer the given subquestions.
Q100NAT3 Marks·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
The question of whether total sales in different marketplaces for product A and total sales in different marketplaces for product B are independent across the different days is being checked. Then what is the value of the computed test statistic? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.235”, then enter it as “1.24”)
Your answer:

Type 26 · asked 2 times · Linear regression (SLR & MLR)

Find R-square of a simple regression from the correlation

Read the passage below, then answer Q101
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.
Q101NAT1 Mark·Write the number
End Term · 22 Dec 2024 (AN)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:
Read the passage below, then answer Q102
(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
Q102NAT1 Mark·Write the number
End Term · 13 Apr 2025 (FN)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:

Type 27 · asked 2 times · Linear regression (SLR & MLR)

Find adjusted R-square of a simple regression from the correlation

Read the passage below, then answer Q103
(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
Q103NAT1 Mark·Write the number
End Term · 13 Apr 2025 (FN)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:
Read the passage below, then answer Q104
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.
Q104NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)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:

Type 28 · asked 2 times · Linear regression (SLR & MLR)

Find total variability (SST) in the dependent variable

Read the passage below, then answer Q105
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.
Q105NAT2 Marks·Write the number
End Term · 31 Aug 2025 (AN)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:
Read the passage below, then answer Q106
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.
Q106NAT2 Marks·Write the number
End Term · 31 Aug 2025 (FN)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:

Type 29 · asked 2 times · Demand response curves & pricing

Find elasticity of a linear demand curve at a given price

Read the passage below, then answer Q107
(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.
Q107NAT1.5 Marks·Write the number
End Term · 13 Apr 2025 (FN)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:
Read the passage below, then answer Q108
(The following is a purely imaginary scenario)
The demand for ice creams at different prices in the supermarket at IITM is specified in Table-1. Given this data, answer the subquestions (Note: For all the sub-questions, round your answer to two decimal places. Eg: If your answer is 10.256, then round it to 10.26)
Q108NAT1 Mark·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
What is the elasticity of the linear demand-response curve, when the price is Rs. 35? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.235”, then enter it as “1.24”)
Your answer:

Type 30 · asked 2 times · Demand response curves & pricing

Find market size of a linear demand curve

Read the passage below, then answer Q109
(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.
Q109NAT0.5 Marks·Write the number
End Term · 13 Apr 2025 (FN)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:
Read the passage below, then answer Q110
(The following is a purely imaginary scenario)
The demand for ice creams at different prices in the supermarket at IITM is specified in Table-1. Given this data, answer the subquestions (Note: For all the sub-questions, round your answer to two decimal places. Eg: If your answer is 10.256, then round it to 10.26)
Q110NAT1 Mark·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
If a linear demand-response curve is fit for the data in Table-1, what is the market size for ice creams? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.235”, then enter it as “1.24”)
Your answer:

Type 31 · asked 2 times · Demand response curves & pricing

Find satiating price of a linear demand curve

Read the passage below, then answer Q111
(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.
Q111NAT0.5 Marks·Write the number
End Term · 13 Apr 2025 (FN)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:
Read the passage below, then answer Q112
(The following is a purely imaginary scenario)
The demand for ice creams at different prices in the supermarket at IITM is specified in Table-1. Given this data, answer the subquestions (Note: For all the sub-questions, round your answer to two decimal places. Eg: If your answer is 10.256, then round it to 10.26)
Q112NAT1 Mark·Write the number
Quiz 1 · 26 Oct 2025 (AN)Key ↓
If a linear demand-response curve is fit for the data in Table-1, what is the satiating price for ice creams? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.235”, then enter it as “1.24”)
Your answer:

Type 32 · asked 2 times · Linear programming & duality

Count decision variables in the dual LP

Read the passage below, then answer Q113
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.
Q113NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)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:
Read the passage below, then answer Q114
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.
Q114NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)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:

Type 33 · asked 2 times · Linear programming & duality

Decide excess or deficit capacity for a given production plan

Read the passage below, then answer Q115
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.
Q115MSQ1 Mark·Choose all correct options
End Term · 31 Aug 2025 (AN)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 Q116
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.
Q116MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)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

Type 34 · asked 2 times · Data envelopment analysis (DEA)

Find DMUs on the efficient frontier from a DEA graph

Read the passage below, then answer Q117
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
Q117MCQ1 Mark·Choose one option
End Term · 22 Dec 2024 (AN)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)
Read the passage below, then answer Q118
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
Q118MCQ1 Mark·Choose one option
End Term · 13 Apr 2025 (FN)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)

Type 35 · asked 2 times · Conjoint analysis

Choose conjoint approach for continuous attributes with pairwise data

Q119MCQ1 Mark·Choose one option
End Term · 22 Dec 2024 (AN)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
Q120MSQ1.5 Marks·Choose all correct options
End Term · 13 Apr 2025 (FN)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

Type 36 · asked 2 times · Conjoint analysis

Find the part worth of upgrading one attribute level

Read the passage below, then answer Q121
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.
Q121NAT2 Marks·Write the number
End Term · 31 Aug 2025 (AN)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:
Read the passage below, then answer Q122
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.
Q122NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)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:

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q155 to 56

Q225

Q350

Q433.32 to 33.34

Q550

Q650 to 52

Q766.65 to 66.71

Q850

Q950

Q1025

Q1149.95 to 50.05

Q1249.95 to 50.05

Q1366 to 67

Q1487 to 89

Q1550

Q1666.65 to 66.71

Q177541 to 7542

Q1811.13 to 11.23

Q198061 to 8064

Q2010.5 to 11

Q217874 to 7876

Q2217.1 to 17.3

Q236915 to 6918

Q2427.5 to 27.9

Q25A, B

Q26A, B

Q27A, B, C

Q28A, B, C

Q29A, B, C

Q30A, B, C

Q3120.35 to 20.39

Q3225.9 to 25.96

Q3353.65 to 53.75

Q3420.35 to 20.39

Q3525.9 to 25.96

Q3653.65 to 53.75

Q372

Q384

Q391

Q402

Q415

Q422

Q431

Q441

Q451

Q4620

Q4746 to 47

Q4833.3 to 33.4

Q4960

Q5064 to 66

Q5157.1 to 57.2

Q5221 to 22

Q53589 to 592

Q545.2 to 5.5

Q5513.2 to 13.9

Q56C

Q57A

Q58B, D

Q59A

Q60B

Q61C

Q62B

Q63C

Q640.44 to 0.48

Q65C

Q660.44 to 0.48

Q6717 to 18

Q6820

Q69197 to 199

Q701.3 to 1.4

Q7118 to 20

Q7211 to 11.5

Q734

Q743

Q754

Q7620320 or -20320

Q77-1238000 or 1238000

Q7878125

Q792

Q801

Q810

Q82C

Q83C

Q84C

Q85A

Q86A

Q87A

Q88F

Q89F

Q90F

Q910.25 to 0.27

Q920.25 to 0.27

Q93D

Q94A, B, C

Q951.6 to 1.9

Q961.3 to 1.5

Q9718 to 19

Q981

Q9914.5 to 15

Q10031.5 to 33.5

Q10148.3 to 48.32

Q10225 to 27

Q10315 to 16

Q104-0.14 to -0.12

Q10518 to 21

Q1063900 to 3904

Q1070.02 to 0.05

Q1082.3 to 2.4

Q10939942

Q110200

Q1111352 to 1355

Q11250

Q115A, D, E

Q1214.82 to 4.84

Q1221.832 to 1.834

Detailed Answer Notes & Working

Q76Answer: 20320 or -20320: Official answer key accepts 20320 or -20320.
Q77Answer: -1238000 or 1238000: Official answer key accepts -1238000 or 1238000.

Questions and answer keys are reproduced from the official IIT Madras BS papers. Topics and repeated question types are BTechi’s own grouping. BTechi is not affiliated with IIT Madras.