Artificial Intelligence for Economics Nptel Week 2 Answers
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Nptel Artificial Intelligence for Economics Week 2 Answers (July-Dec 2025)
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Question 1. Which of the following statements are true regarding learning rate in optimization by gradient descent?
a) If learning rate is too high, the gradient descent may never converge
b) If learning rate is too low, then gradient descent will never converge
c) If learning rate is high, the gradient descent is more likely to converge to a global minima instead of local
d) There exists an optimal learning rate for which Gradient Descent is guaranteed to converge at a global minima
These are Nptel Artificial Intelligence for Economics Week 2 Answers
Question 2. What is the significance of the fundamental theorem of linear programming?
a) It tells us that we need to investigate only a few number of points in the feasible region to find the optima
b) It tells us whether or not the given linear problem is feasible
c) It provides us a closed-form expression to calculate the optimal solution
d) It tells us that each linear program has an unique solution
These are Nptel Artificial Intelligence for Economics Week 2 Answers
Question 3. I have a budget of 100. There are three projects, from where the expected returns are thrice, four times and twice the investments respectively. There is a rule that the investment I make to the most beneficial project cannot be more than twice the total investment to the others. How many slack variables are involved in the linear program? What is the maximum return that I can get?
a) 4, 367
b) 4, 334
c) 6, 334
d) 7, 367
Question 4. Consider functions f1, f2 defined over integers. I want to maximize f1(x) and minimize f2(x). We have f1(x) = 4x and f2(x) = 4 – x. Which of the following statements is false?
a) 2 dominates 1
b) 1 dominates 2
c) 3 dominates 2
d) There is no pareto-optimal solution
Question 5. What is the characteristic of barrier functions for interior point methods?
a) They take high values along and beyond the boundary of the feasible region
b) They take low values along and beyond the boundary of the feasible region
c) They take low values for all suboptimal solutions
d) They take high values for all suboptimal solutions
These are Nptel Artificial Intelligence for Economics Week 2 Answers
Question 6. Why are the multipliers increased in each iteration of exterior point methods, but decreased in interior point methods?
a) In case of exterior point methods, the constraints are initially not satisfied, but they are satisfied in case of interior point methods
b) In case of interior point methods, the convergence is usually quicker than exterior point methods
c) The nature of the augmented objective function are different for interior and exterior point methods
d) None of these
Question 7. In case of A algorithm, what do the functions f(n) and g(n) at node ‘n’ represent?*
a) f(n): possible shortest distance from node ‘n’ to goal, g(n): estimated distance from source to ‘n
b) f(n): estimated distance from node ‘n’ to goal, g(n): estimated shortest distance from source to ‘n
c) f(n): possible shortest distance from source to goal via node ‘n’, g(n): estimated distance from ‘n’ to goal
d) f(n): possible shortest distance from source to goal via node ‘n’, g(n): shortest distance from source to ‘n’
These are Nptel Artificial Intelligence for Economics Week 2 Answers
Question 8. What happens if the heuristic function for A search algorithm is not admissible?*
a) The algorithm is guaranteed to find the optimal path from source to some goal node
b) The algorithm fails to terminate and runs in loops
c) The algorithm eventually finds the optimal solution but becomes very inefficient
d) The algorithm terminates with a suboptimal path
Question 9. In the given game tree, A wants to minimize, B wants to maximize the leaf node value. Is there any chance that player A wins?
a) Yes, if A moves first
b) Yes, if B moves first
c) A will always win irrespective of who moves first
d) A cannot win irrespective of who moves first
These are Nptel Artificial Intelligence for Economics Week 2 Answers
Question 10. How can A-algorithm handle multicriteria optimization?*
a) f(n), g(n), h(n) become vector-valued to indicate the different criteria
b) by carrying out A* separately for each criterion and then comparing each discovered path with respect to all the criteria
c) by using the concept of pareto-domination in choosing which point to explore next
d) A* cannot handle multi-criteria
Question 11. Which of the following statements are true about agglomerative clustering?
a) Single-linkage criteria encourages bigger clusters
b) Multiple-linkage criteria encourages bigger clusters
c) The number of clusters formed is pre-specified
d) The number of clusters formed depends on a pre-specified threshold and choice of linkage
These are Nptel Artificial Intelligence for Economics Week 2 Answers
Question 12. Consider the following 1D observations: (-5.2, -4.3, -3.1, -1.8, -1.2, -0.7, 0.4, 2.8, 4.9, 5.2). Suppose they have been temporarily clustered as follows: {(-5.2, -4.3), (-3.1), (-1.8,-1.2,-0.7), (0.4), (2.8), (4.9, 5.2)}. In which of the following cases, will there be no further merging of these clusters?
a) Complete linkage with threshold 2
b) Complete linkage with threshold 3
c) Single linkage with threshold 1
d) Single linkage with threshold 2
These are Nptel Artificial Intelligence for Economics Week 2 Answers
Question 13. What is the objective function that is minimized in K-means algorithm iteratively?
a) It has no clearly defined objective function
b) Total inter-cluster distance between all pairs of cluster centers
c) Total inter-cluster distance between all pairs of points that are in different clusters
d) Average intra-cluster distance between all pairs of points that are in same clusters
Question 14. In the dataset below, there are 5 points (P1-P5), of whom the first two (P1, P2) are chosen as initial cluster centers. Which points will be new cluster centers after 1 round of iteration of Kmeans?
P1. (-1, -2), P2. (-2,-1), P3. (-1,0), P4. (0,1), P5. (2,1)
a) (-1,0) and (0,1)
b) (0.5,-0.5) and (-1,0)
c) (0,0) and (-2,2)
d) (-1,-2) and (2,1)
Question 15. In which of the following circumstances does K-means algorithm fail to converge at the desired clustering of the datapoints?
a) If the desired clusters are non-circular in shape
b) If the initially chosen cluster centers are too close to each other
c) If the desired clustering has too many clusters compared to the number of datapoints
d) If the desired clustering has too few clusters compared to the number of datapoints
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These are Nptel Artificial Intelligence for Economics Week 2 Answers