The IIT Madras BS Business Analytics (Business Analytics) Quiz 2 paper sat on 16 Mar 2025, in the January 2025 term: 21 questions for 20 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.
The probability that a car battery functions for more than 10,000Kms is 0.8, the probability that it functions for more than 20,000kms is 0.4 and the probability that it functions for more than 30,000kms is 0.1. If a new car battery is still working after 10,000Kms, what is the probability that its total life will exceed 20,000Kms? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “0.235”, then enter it as “0.24”)
Correct answer: 0.50
The demand-response curve for a product is expected to be non-linear curve. It is noted that the demand was 1000 units at a price of Rs.80 and 2500 units at a price of Rs. 40. Then, at a price of Rs. 60, what is the expected demand? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “10.235”, then enter it as “10.24”)
Correct answer: 1462.5 (accepted within ±7.5)
Latent demand in a demand-response curve is the area obtained when?
Price is reduced below the identified optimal price
Price is increased beyond the identified optimal price
The optimal price is increased beyond the maximum available price
Quantity is reduced below the identified optimal quantity
Quantity is increased beyond the identified maximum quantity
Correct answer
Price is reduced below the identified optimal price
You solve the primal of a linear program with a maximization objective, three decision variables and two constraints of the less than or equal to type. Non-negativity restrictions apply to the decision variables. After solving the linear program, you find that the first constraint is not binding (LHS < RHS) and the second constraint is binding (LHS = RHS). Which of the following statements is/are correct?
There are three decision variables in the dual
The dual variable corresponding to the second constraint is zero
There are two decision variables in the dual formulation
The dual variable corresponding to the second constraint is non-zero
Correct answers
There are two decision variables in the dual formulation
The dual variable corresponding to the second constraint is non-zero
(The following comprehension is purely imaginary)
“FUNKY” is a compay that manufactures purses, shoes and backpacks. The construction of the three products requires leather and synthetic material, with leather being the limiting raw material. The production process uses two types of skilled labour: Sewing and Polishing. Table-2 gives the availability of the resources, the usage in the three products and the profits per unit.
| Resource | Resource requirements per unit | Daily availability of resource | ||
|---|---|---|---|---|
| Purse | Shoes | Backpacks | ||
| Leather (in feet) | 2 | 1 | 3 | 42 |
| Sewing (in Hours) | 2 | 1 | 2 | 40 |
| Polishing (in Hours) | 1 | 2 | 1 | 42 |
| Profit (in Rs./unit) | 24 | 22 | 45 | -- |
Table-2
Given the above information, formulate the problem as a linear program to maximize the profit and answer the subquestions.
How many (count of) decision variables are present in the standard form of the primal?
Correct answer: 3
(The following comprehension is purely imaginary)
“FUNKY” is a compay that manufactures purses, shoes and backpacks. The construction of the three products requires leather and synthetic material, with leather being the limiting raw material. The production process uses two types of skilled labour: Sewing and Polishing. Table-2 gives the availability of the resources, the usage in the three products and the profits per unit.
| Resource | Resource requirements per unit | Daily availability of resource | ||
|---|---|---|---|---|
| Purse | Shoes | Backpacks | ||
| Leather (in feet) | 2 | 1 | 3 | 42 |
| Sewing (in Hours) | 2 | 1 | 2 | 40 |
| Polishing (in Hours) | 1 | 2 | 1 | 42 |
| Profit (in Rs./unit) | 24 | 22 | 45 | -- |
Table-2
Given the above information, formulate the problem as a linear program to maximize the profit and answer the subquestions.
Excluding the non-negativity constraint, how many (count of) constraints are present in the standard form of the primal?
Correct answer: 3
(The following comprehension is purely imaginary)
“FUNKY” is a compay that manufactures purses, shoes and backpacks. The construction of the three products requires leather and synthetic material, with leather being the limiting raw material. The production process uses two types of skilled labour: Sewing and Polishing. Table-2 gives the availability of the resources, the usage in the three products and the profits per unit.
| Resource | Resource requirements per unit | Daily availability of resource | ||
|---|---|---|---|---|
| Purse | Shoes | Backpacks | ||
| Leather (in feet) | 2 | 1 | 3 | 42 |
| Sewing (in Hours) | 2 | 1 | 2 | 40 |
| Polishing (in Hours) | 1 | 2 | 1 | 42 |
| Profit (in Rs./unit) | 24 | 22 | 45 | -- |
Table-2
Given the above information, formulate the problem as a linear program to maximize the profit and answer the subquestions.
If you decide to make and sell 10 Purses, 15 Shoes and 2 Backpacks, then how many (count of) decision variables in the dual (which is developed based on the standard form of the primal) will have a value of “0”?
Correct answer: 2
(The following comprehension is purely imaginary)
“FUNKY” is a compay that manufactures purses, shoes and backpacks. The construction of the three products requires leather and synthetic material, with leather being the limiting raw material. The production process uses two types of skilled labour: Sewing and Polishing. Table-2 gives the availability of the resources, the usage in the three products and the profits per unit.
| Resource | Resource requirements per unit | Daily availability of resource | ||
|---|---|---|---|---|
| Purse | Shoes | Backpacks | ||
| Leather (in feet) | 2 | 1 | 3 | 42 |
| Sewing (in Hours) | 2 | 1 | 2 | 40 |
| Polishing (in Hours) | 1 | 2 | 1 | 42 |
| Profit (in Rs./unit) | 24 | 22 | 45 | -- |
Table-2
Given the above information, formulate the problem as a linear program to maximize the profit and answer the subquestions.
If you decide to make and sell 10 Purses, 15 Shoes and 2 Backpacks, then what is the primal objective function value?
Correct answer: 660
The estimated demand for a product follows the relationship: D(p) = 2570 - 4p. Where “p” is the selling price of the product. With this information answer the given subquestions.
If you intend to maximize the revenue, what is the best value for “p”? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “10.235”, then enter it as “10.24”)
Correct answer: 321.5 (accepted within ±0.5)
The estimated demand for a product follows the relationship: D(p) = 2570 - 4p. Where “p” is the selling price of the product. With this information answer the given subquestions.
It costs Rs. 250 to make the product. Then, if you intend to maximize the profit, what is the best value for “p”? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “10.235”, then enter it as “10.24”)
Correct answer: 446.5 (accepted within ±0.5)
To automatically detect a card’s suit a logistic regression model is developed. For a random sample of 600 cards, the performance of the model is captured by the confusion matrix in Table-1. Given this information, answer the subquestions.
What is the precision for predicting the “Hearts” class? (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”)
Correct answer: 71.5 (accepted within ±0.5)
To automatically detect a card’s suit a logistic regression model is developed. For a random sample of 600 cards, the performance of the model is captured by the confusion matrix in Table-1. Given this information, answer the subquestions.
What is the recall for predicting the “Spades” class? (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”)
Correct answer: 40 (accepted within ±0.1)
To automatically detect a card’s suit a logistic regression model is developed. For a random sample of 600 cards, the performance of the model is captured by the confusion matrix in Table-1. Given this information, answer the subquestions.
What is the sensitivity for predicting “Diamonds” class? (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”)
Correct answer: 81.5 (accepted within ±0.5)
To automatically detect a card’s suit a logistic regression model is developed. For a random sample of 600 cards, the performance of the model is captured by the confusion matrix in Table-1. Given this information, answer the subquestions.
What is the specificity for predicting “Clubs” class? (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”)
Correct answer: 85.5 (accepted within ±0.5)
To automatically detect a card’s suit a logistic regression model is developed. For a random sample of 600 cards, the performance of the model is captured by the confusion matrix in Table-1. Given this information, answer the subquestions.
What is the accuracy for 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”)
Correct answer: 63.3 (accepted within ±0.1)
The three figures below (Picture-1, Picture-2, Picture-3) provide the partial regression output from excel for three models (Model-1, Model-2 and Model-3) which were built on the same data (Hint: same dependent variable with same number of rows. However, the number of independent variable in each model is different).
Given this information, answer the subquestions.
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 3 | A1 | 59574.54 | 3177.885 | 5.44128E-10 |
| Residual | 6 | 112.4796 | 18.7466 | ||
| Total | 9 | 178836.1 |
Picture-1: Partial Results from Excel for Model-1
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 2 | 178723.4403 | 5552.402929 | 6.27476E-12 | |
| Residual | 112.6596987 | ||||
| Total | 9 |
| Coefficients | Standard Error | t Stat | |
|---|---|---|---|
| Intercept | 815.7547951 | 4.075009576 | |
| X Variable 1 | -3.952958885 | 0.03846985 | A2 |
| X Variable 2 | 3.664290745 | 0.791804173 |
Picture-2: Partial Results from Excel for Model-2
SUMMARY OUTPUT
| Regression Statistics | |
|---|---|
| Multiple R | 0.998720528 |
| R Square | 0.997442694 |
| Adjusted R Square | 0.99712303 |
| Standard Error | 7.560908499 |
| Observations | 10 |
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 1 | A3 | 3120.29158 | 1.17067E-11 | |
| Residual | 8 | A4 | |||
| Total | 9 | A5 |
Picture-3: Partial Results from Excel for Model-3
What is the value of “A1”? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Correct answer: 178723 (accepted within ±3)
The three figures below (Picture-1, Picture-2, Picture-3) provide the partial regression output from excel for three models (Model-1, Model-2 and Model-3) which were built on the same data (Hint: same dependent variable with same number of rows. However, the number of independent variable in each model is different).
Given this information, answer the subquestions.
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 3 | A1 | 59574.54 | 3177.885 | 5.44128E-10 |
| Residual | 6 | 112.4796 | 18.7466 | ||
| Total | 9 | 178836.1 |
Picture-1: Partial Results from Excel for Model-1
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 2 | 178723.4403 | 5552.402929 | 6.27476E-12 | |
| Residual | 112.6596987 | ||||
| Total | 9 |
| Coefficients | Standard Error | t Stat | |
|---|---|---|---|
| Intercept | 815.7547951 | 4.075009576 | |
| X Variable 1 | -3.952958885 | 0.03846985 | A2 |
| X Variable 2 | 3.664290745 | 0.791804173 |
Picture-2: Partial Results from Excel for Model-2
SUMMARY OUTPUT
| Regression Statistics | |
|---|---|
| Multiple R | 0.998720528 |
| R Square | 0.997442694 |
| Adjusted R Square | 0.99712303 |
| Standard Error | 7.560908499 |
| Observations | 10 |
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 1 | A3 | 3120.29158 | 1.17067E-11 | |
| Residual | 8 | A4 | |||
| Total | 9 | A5 |
Picture-3: Partial Results from Excel for Model-3
What is the value of “A2”? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Correct answer: -102 (accepted within ±1)
The three figures below (Picture-1, Picture-2, Picture-3) provide the partial regression output from excel for three models (Model-1, Model-2 and Model-3) which were built on the same data (Hint: same dependent variable with same number of rows. However, the number of independent variable in each model is different).
Given this information, answer the subquestions.
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 3 | A1 | 59574.54 | 3177.885 | 5.44128E-10 |
| Residual | 6 | 112.4796 | 18.7466 | ||
| Total | 9 | 178836.1 |
Picture-1: Partial Results from Excel for Model-1
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 2 | 178723.4403 | 5552.402929 | 6.27476E-12 | |
| Residual | 112.6596987 | ||||
| Total | 9 |
| Coefficients | Standard Error | t Stat | |
|---|---|---|---|
| Intercept | 815.7547951 | 4.075009576 | |
| X Variable 1 | -3.952958885 | 0.03846985 | A2 |
| X Variable 2 | 3.664290745 | 0.791804173 |
Picture-2: Partial Results from Excel for Model-2
SUMMARY OUTPUT
| Regression Statistics | |
|---|---|
| Multiple R | 0.998720528 |
| R Square | 0.997442694 |
| Adjusted R Square | 0.99712303 |
| Standard Error | 7.560908499 |
| Observations | 10 |
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 1 | A3 | 3120.29158 | 1.17067E-11 | |
| Residual | 8 | A4 | |||
| Total | 9 | A5 |
Picture-3: Partial Results from Excel for Model-3
What is the value of “A3”? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Correct answer: 178378 (accepted within ±5)
The three figures below (Picture-1, Picture-2, Picture-3) provide the partial regression output from excel for three models (Model-1, Model-2 and Model-3) which were built on the same data (Hint: same dependent variable with same number of rows. However, the number of independent variable in each model is different).
Given this information, answer the subquestions.
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 3 | A1 | 59574.54 | 3177.885 | 5.44128E-10 |
| Residual | 6 | 112.4796 | 18.7466 | ||
| Total | 9 | 178836.1 |
Picture-1: Partial Results from Excel for Model-1
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 2 | 178723.4403 | 5552.402929 | 6.27476E-12 | |
| Residual | 112.6596987 | ||||
| Total | 9 |
| Coefficients | Standard Error | t Stat | |
|---|---|---|---|
| Intercept | 815.7547951 | 4.075009576 | |
| X Variable 1 | -3.952958885 | 0.03846985 | A2 |
| X Variable 2 | 3.664290745 | 0.791804173 |
Picture-2: Partial Results from Excel for Model-2
SUMMARY OUTPUT
| Regression Statistics | |
|---|---|
| Multiple R | 0.998720528 |
| R Square | 0.997442694 |
| Adjusted R Square | 0.99712303 |
| Standard Error | 7.560908499 |
| Observations | 10 |
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 1 | A3 | 3120.29158 | 1.17067E-11 | |
| Residual | 8 | A4 | |||
| Total | 9 | A5 |
Picture-3: Partial Results from Excel for Model-3
What is the value of “A4”? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Correct answer: 457 (accepted within ±2)
The three figures below (Picture-1, Picture-2, Picture-3) provide the partial regression output from excel for three models (Model-1, Model-2 and Model-3) which were built on the same data (Hint: same dependent variable with same number of rows. However, the number of independent variable in each model is different).
Given this information, answer the subquestions.
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 3 | A1 | 59574.54 | 3177.885 | 5.44128E-10 |
| Residual | 6 | 112.4796 | 18.7466 | ||
| Total | 9 | 178836.1 |
Picture-1: Partial Results from Excel for Model-1
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 2 | 178723.4403 | 5552.402929 | 6.27476E-12 | |
| Residual | 112.6596987 | ||||
| Total | 9 |
| Coefficients | Standard Error | t Stat | |
|---|---|---|---|
| Intercept | 815.7547951 | 4.075009576 | |
| X Variable 1 | -3.952958885 | 0.03846985 | A2 |
| X Variable 2 | 3.664290745 | 0.791804173 |
Picture-2: Partial Results from Excel for Model-2
SUMMARY OUTPUT
| Regression Statistics | |
|---|---|
| Multiple R | 0.998720528 |
| R Square | 0.997442694 |
| Adjusted R Square | 0.99712303 |
| Standard Error | 7.560908499 |
| Observations | 10 |
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 1 | A3 | 3120.29158 | 1.17067E-11 | |
| Residual | 8 | A4 | |||
| Total | 9 | A5 |
Picture-3: Partial Results from Excel for Model-3
What is the value of “A5”? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Correct answer: 178836 (accepted within ±5)
The three figures below (Picture-1, Picture-2, Picture-3) provide the partial regression output from excel for three models (Model-1, Model-2 and Model-3) which were built on the same data (Hint: same dependent variable with same number of rows. However, the number of independent variable in each model is different).
Given this information, answer the subquestions.
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 3 | A1 | 59574.54 | 3177.885 | 5.44128E-10 |
| Residual | 6 | 112.4796 | 18.7466 | ||
| Total | 9 | 178836.1 |
Picture-1: Partial Results from Excel for Model-1
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 2 | 178723.4403 | 5552.402929 | 6.27476E-12 | |
| Residual | 112.6596987 | ||||
| Total | 9 |
| Coefficients | Standard Error | t Stat | |
|---|---|---|---|
| Intercept | 815.7547951 | 4.075009576 | |
| X Variable 1 | -3.952958885 | 0.03846985 | A2 |
| X Variable 2 | 3.664290745 | 0.791804173 |
Picture-2: Partial Results from Excel for Model-2
SUMMARY OUTPUT
| Regression Statistics | |
|---|---|
| Multiple R | 0.998720528 |
| R Square | 0.997442694 |
| Adjusted R Square | 0.99712303 |
| Standard Error | 7.560908499 |
| Observations | 10 |
ANOVA
| df | SS | MS | F | Significance F | |
|---|---|---|---|---|---|
| Regression | 1 | A3 | 3120.29158 | 1.17067E-11 | |
| Residual | 8 | A4 | |||
| Total | 9 | A5 |
Picture-3: Partial Results from Excel for Model-3
Which model is the best model for the provided data?
Model-1
Model-2
Model-3
Dr. Milo did not teach this, so none of the models are good (This is not the correct answer, please do not choose it. Just relax, think and answer the question)
Correct answer
Model-2
