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Game Theory · Most repeated questions

72 questions · 93 marks · 4 papers · 26 question types

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Game Theory and Strategy

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 7 times · Shapley value, cost sharing, bankruptcy

Compute Shapley values from a coalition function

Read the passage below, then answer Q1–Q3
Calculate the Shapley value of the following game and answer the given subquestions.
Q1NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
S_1 = _____________
Your answer:
Q2NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
S_2 = _____________
Your answer:
Q3NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
S_3 = _____________
Your answer:
Read the passage below, then answer Q4–Q7
Calculate the Shapley value of the following game using the procedure for dissolving a partnership
Based on the above data, answer the given subquestions.
Q4NAT1.5 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
S_1 = ________________
Your answer:
Q5NAT1.5 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
S_2 = ________________
Your answer:
Q6NAT1.5 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
S_3 = ________________
Your answer:
Q7NAT1.5 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
S_4 = ________________
Your answer:

Type 2 · asked 6 times · Shapley value, cost sharing, bankruptcy

Split cable connection costs among three customers on a tree

Read the passage below, then answer Q8–Q10
A cable TV station wants to connect three new customers to its network. The connections to the network are described in the following tree graph:
Calculate the distribution of the costs among the three players if all three decide to connect to the network.
Based on the above data, answer the given subquestions.
Q8NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
The cost to be paid by player 1 will be _____________
Your answer:
Q9NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
The cost to be paid by player 2 will be ____________
Your answer:
Q10NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
The cost to be paid by player 3 will be ____________
Your answer:
Read the passage below, then answer Q11–Q13
A cable TV station wants to connect three new customers to its network. The connections to the network are described in the following tree graph:
Calculate the distribution of the costs among the three players if all three decide to connect to the network.
Based on the above data, answer the given subquestions.
Q11NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
The cost to be paid by player 1 will be ______________
Your answer:
Q12NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
The cost to be paid by player 2 will be _________________
Your answer:
Q13NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
The cost to be paid by player 3 will be ______________
Your answer:

Type 3 · asked 4 times · Best responses in continuous games

Find a player's best response in a continuous-action game

Read the passage below, then answer Q14
Each one of two political parties can choose to buy time on commercial radio shows to broadcast negative ad campaigns against their rival. These choices are made simultaneously. Due to government regulation, it is forbidden to buy more than 2 hours of negative campaign time, so that each party cannot choose an amount of negative campaigning above 2 hours. Given a pair of choices (a_1,a_2), the payoff of party i is given by the following function: v_i (a_1,a_2) = a_i − 2a_j + a_ia_j − (a_i)^2. Write the normal form representation of this game and answer the given sub-questions.
Q14MCQ1 Mark·Choose one option
Quiz 2 · 3 Aug 2025 (AN)Key ↓
If player 1 chooses 2 hours as his action, the best response of player 2 will be
1. A1.5
2. B1
3. C1.25
4. D0
Read the passage below, then answer Q15
Based on the above data, answer the given subquestions.
Q15NAT2 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Read the passage below, then answer Q16
Based on the above data, answer the given subquestions.
Q16NAT2 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
What is the best response of roommate 2 if roommate 1 chooses t_1 = 0? t_2 =________________
Your answer:
Read the passage below, then answer Q17
Q17MCQ2 Marks·Choose one option
Quiz 1 · 26 Oct 2025 (AN)Key ↓
1. A
2. B
3. C
4. D

Type 4 · asked 4 times · Information cascades & Bayes' rule

Posterior probability using Bayes' rule

Read the passage below, then answer Q18–Q19
Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 4 blue balls and 2 red ball or 4 red balls and 2 blue ball with equal probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority urn. We assume everyone hears what the previous individuals report and get their own private signal by randomly drawing one ball from the urn.
Based on the above data, answer the given subquestions.
Q18MCQ1 Mark·Choose one option
Quiz 2 · 3 Aug 2025 (AN)Key ↓
What is the probability that the urn is majority-red if the first student draws a blue ball?
1. A1/5
2. B4/5
3. C2/3
4. D1/3
Q19MCQ2 Marks·Choose one option
Quiz 2 · 3 Aug 2025 (AN)Key ↓
Now suppose, first three students draw the ball in the sequence (Blue, Blue, Red). What is the probability of urn being red-majority in this scenario?
1. A2/3
2. B1/25
3. C4/25
4. D1/3
Read the passage below, then answer Q20–Q21
Three machines, A, B, and C, produce respectively 50%, 30% and 20% of the total no. of items of a factory. The percentages of defective output of these machines are 3%, 4% and 5%.
Based on the above data, answer the given subquestions.
Q20NAT2 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Suppose an item is selected at random and found to be defective. The probability that the item was produced by machine A will be ____________
Your answer:
Q21NAT2 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Suppose an item is selected at random and found to be defective. The probability that the item was produced by machine A will be ______________
Your answer:

Type 5 · asked 4 times · Shapley value, cost sharing, bankruptcy

Divide an estate between two creditors by the contested garment rule

Read the passage below, then answer Q22–Q25
A man dies, leaving an estate worth 500 units. The deceased has two creditors; one’s claim is 400 units, and the other’s claim, 300 units. The division of the estate between them is carried out according to the contested garment principle.
Based on the above data, answer the given subquestions.
Q22NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Creditor 1 with claim 400 units gets
Your answer:
Q23NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Creditor 2 with claim 300 units gets
Your answer:
Q24NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Creditor 1 with claim 400 units gets
Your answer:
Q25NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Creditor 2 with claim 300 units gets
Your answer:

Type 6 · asked 4 times · Auctions & VCG pricing

VCG prices for two ad slots

Read the passage below, then answer Q26–Q27
Suppose a search engine has two ad slots that it can sell. Slot a has a clickthrough rate of 10 and slot b has a clickthrough rate of 5. There are three advertisers who are interested in these slots. Advertiser x values click at 3 per click, advertiser y values click at 2 per click, and advertiser z values click at 1 per click.
Based on the above data, answer the given subquestions.
Q26NAT2 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
VCG price for slot a will be ___________
Your answer:
Q27NAT2 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
VCG price for slot b will be __________
Your answer:
Read the passage below, then answer Q28–Q29
Suppose a search engine has two ad slots that it can sell. Slot a has a clickthrough rate of 10 and slot b has a clickthrough rate of 5. Three advertisers are interested in these slots. Advertiser x values click at 3 per click, advertiser y values click at 2 per click, and advertiser z values click at 1 per click.
Based on the above data, answer the given subquestions.
Q28NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
VCG price for slot a will be _________
Your answer:
Q29NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
VCG price for slot b will be _________
Your answer:

Type 7 · asked 3 times · Best responses in continuous games

Find the symmetric Nash equilibrium action in a continuous game

Read the passage below, then answer Q30
Each one of two political parties can choose to buy time on commercial radio shows to broadcast negative ad campaigns against their rival. These choices are made simultaneously. Due to government regulation, it is forbidden to buy more than 2 hours of negative campaign time, so that each party cannot choose an amount of negative campaigning above 2 hours. Given a pair of choices (a_1,a_2), the payoff of party i is given by the following function: v_i (a_1,a_2) = a_i − 2a_j + a_ia_j − (a_i)^2. Write the normal form representation of this game and answer the given sub-questions.
Q30MCQ1 Mark·Choose one option
Quiz 2 · 3 Aug 2025 (AN)Key ↓
How much negative campaign time will each player choose under a symmetric and unique Nash equilibrium?
1. A1.5
2. B1
3. C1.25
4. D0
Read the passage below, then answer Q31
Based on the above data, answer the given subquestions.
Q31NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Read the passage below, then answer Q32
Based on the above data, answer the given subquestions.
Q32NAT2 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 8 · asked 3 times · Information cascades & Bayes' rule

Probability of an observation via the law of total probability

Read the passage below, then answer Q33
Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 4 blue balls and 2 red ball or 4 red balls and 2 blue ball with equal probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority urn. We assume everyone hears what the previous individuals report and get their own private signal by randomly drawing one ball from the urn.
Based on the above data, answer the given subquestions.
Q33MCQ1 Mark·Choose one option
Quiz 2 · 3 Aug 2025 (AN)Key ↓
Now suppose, first three students draw the ball in the sequence (Blue, Blue, Red). What is the total probability of getting this sequence?
1. A1/25
2. B2/25
3. C1/9
4. D2/9
Read the passage below, then answer Q34–Q35
Three machines, A, B, and C, produce respectively 50%, 30% and 20% of the total no. of items of a factory. The percentages of defective output of these machines are 3%, 4% and 5%.
Based on the above data, answer the given subquestions.
Q34NAT2 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
If an item is selected at random, the probability that the item is defective is ______________
Your answer:
Q35NAT2 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
If an item is selected at random, the probability that the item is defective is _____________
Your answer:

Type 9 · asked 3 times · Coalition games & voting power

Identify the null player in a weighted majority game

Read the passage below, then answer Q36
Enter the coalition function for the game [61;40,40,30,10] and answer the given sub-questions:
Q36NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Which player is the null player in this game? ____________
Your answer:
Q37MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
In weighted majority game [7; 5, 1, 3, 4]
1. APlayer 1 is null player
2. BPlayer 2 is null player
3. CPlayer 3 is null player
4. DPlayer 4 is null player
Q38MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
In weighted majority game [7; 1, 4, 3, 5]
1. APlayer 1 is null player
2. BPlayer 2 is null player
3. CPlayer 3 is null player
4. DPlayer 4 is null player

Type 10 · asked 2 times · Bayesian & evolutionary games

Identify the Nash equilibria of a 2x2 game

Read the passage below, then answer Q39
Based on the above data, answer the given subquestions.
Q39MCQ1 Mark·Choose one option
Quiz 2 · 3 Aug 2025 (AN)Key ↓
Choose the correct alternative(s)
1. A(Slow, Slow) is an NE
2. B(Slow, Fast) is an NE
3. CBoth (Slow, Slow) is an NE & (Slow, Fast) is an NE
4. DNone
Read the passage below, then answer Q40
Consider the following normal form game and answer the given sub questions:
Q40MCQ2 Marks·Choose one option
Quiz 1 · 26 Oct 2025 (AN)Key ↓
This game has
1. AA unique Nash equilibrium in pure strategy
2. BA unique Nash equilibrium in mixed strategy
3. CBoth are true
4. DNone is true

Type 11 · asked 2 times · Best responses in continuous games

Equilibrium payoff/profit of each player

Read the passage below, then answer Q41
Each one of two political parties can choose to buy time on commercial radio shows to broadcast negative ad campaigns against their rival. These choices are made simultaneously. Due to government regulation, it is forbidden to buy more than 2 hours of negative campaign time, so that each party cannot choose an amount of negative campaigning above 2 hours. Given a pair of choices (a_1,a_2), the payoff of party i is given by the following function: v_i (a_1,a_2) = a_i − 2a_j + a_ia_j − (a_i)^2. Write the normal form representation of this game and answer the given sub-questions.
Q41MCQ1 Mark·Choose one option
Quiz 2 · 3 Aug 2025 (AN)Key ↓
Equilibrium payoff of each player will be
1. A-1.5
2. B1
3. C-1
4. D0
Read the passage below, then answer Q42
Based on the above data, answer the given subquestions.
Q42NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:

Type 12 · asked 2 times · Network goods & network effects

Network good: indifferent consumer theta-hat for price p and n^e

Read the passage below, then answer Q43
Based on the above data, answer the given subquestions.
Q43MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q44
Consider the market for a single network good as discussed in the lecture, and write a different consumer’s utility function for joining the network as U(θ)=θ(a+νn^e) capturing the idea that it may be more plausible that a user who has a higher value for the standalone component of a technology also assigns more importance to the size of its network (i.e., consumers differ in their valuation of both the standalone and the network benefits). Here, a is the standalone benefit, ν > 0 measures the network effect, n^e is the expected number of users joining the network and θ is uniformly distributed on the unit interval.
Based on the above data, answer the given subquestions.
Q44MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 13 · asked 2 times · Network goods & network effects

Network good: maximum price p at which there are buyers

Read the passage below, then answer Q45
Based on the above data, answer the given subquestions.
Q45MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
The maximum value of p to have buyers will be
1. A
2. B
3. C
4. D
Read the passage below, then answer Q46
Consider the market for a single network good as discussed in the lecture, and write a different consumer’s utility function for joining the network as U(θ)=θ(a+νn^e) capturing the idea that it may be more plausible that a user who has a higher value for the standalone component of a technology also assigns more importance to the size of its network (i.e., consumers differ in their valuation of both the standalone and the network benefits). Here, a is the standalone benefit, ν > 0 measures the network effect, n^e is the expected number of users joining the network and θ is uniformly distributed on the unit interval.
Based on the above data, answer the given subquestions.
Q46MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
The maximum value of p to have buyers will be
1. A
2. B
3. C
4. D

Type 14 · asked 2 times · Network goods & network effects

Network good: mass of buyers n as a function of theta-hat

Read the passage below, then answer Q47
Based on the above data, answer the given subquestions.
Q47MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q48
Consider the market for a single network good as discussed in the lecture, and write a different consumer’s utility function for joining the network as U(θ)=θ(a+νn^e) capturing the idea that it may be more plausible that a user who has a higher value for the standalone component of a technology also assigns more importance to the size of its network (i.e., consumers differ in their valuation of both the standalone and the network benefits). Here, a is the standalone benefit, ν > 0 measures the network effect, n^e is the expected number of users joining the network and θ is uniformly distributed on the unit interval.
Based on the above data, answer the given subquestions.
Q48MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 15 · asked 2 times · Network goods & network effects

Network good: willingness to pay p(n^e, n) for the nth unit

Read the passage below, then answer Q49
Based on the above data, answer the given subquestions.
Q49MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q50
Consider the market for a single network good as discussed in the lecture, and write a different consumer’s utility function for joining the network as U(θ)=θ(a+νn^e) capturing the idea that it may be more plausible that a user who has a higher value for the standalone component of a technology also assigns more importance to the size of its network (i.e., consumers differ in their valuation of both the standalone and the network benefits). Here, a is the standalone benefit, ν > 0 measures the network effect, n^e is the expected number of users joining the network and θ is uniformly distributed on the unit interval.
Based on the above data, answer the given subquestions.
Q50MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 16 · asked 2 times · Network goods & network effects

Network good: how p(n^e, n) varies with n and n^e

Read the passage below, then answer Q51
Based on the above data, answer the given subquestions.
Q51MSQ1 Mark·Choose all correct options
End Term · 31 Aug 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q52
Consider the market for a single network good as discussed in the lecture, and write a different consumer’s utility function for joining the network as U(θ)=θ(a+νn^e) capturing the idea that it may be more plausible that a user who has a higher value for the standalone component of a technology also assigns more importance to the size of its network (i.e., consumers differ in their valuation of both the standalone and the network benefits). Here, a is the standalone benefit, ν > 0 measures the network effect, n^e is the expected number of users joining the network and θ is uniformly distributed on the unit interval.
Based on the above data, answer the given subquestions.
Q52MSQ1 Mark·Choose all correct options
End Term · 31 Aug 2025 (FN)Key ↓
p(n^e,n) is _____________ (more than one options are correct)
1. Aincreasing function of n
2. Bdecreasing function of n
3. Cdecreasing function of n^e
4. Dincreasing function of n^e

Type 17 · asked 2 times · Network goods & network effects

Network good: fulfilled-expectations demand curve

Read the passage below, then answer Q53
Based on the above data, answer the given subquestions.
Q53MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
The fulfilled-expectations demand curve in this setting will be
1. A
2. B
3. C
4. D
Read the passage below, then answer Q54
Consider the market for a single network good as discussed in the lecture, and write a different consumer’s utility function for joining the network as U(θ)=θ(a+νn^e) capturing the idea that it may be more plausible that a user who has a higher value for the standalone component of a technology also assigns more importance to the size of its network (i.e., consumers differ in their valuation of both the standalone and the network benefits). Here, a is the standalone benefit, ν > 0 measures the network effect, n^e is the expected number of users joining the network and θ is uniformly distributed on the unit interval.
Based on the above data, answer the given subquestions.
Q54MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
The fulfilled-expectations demand curve in this setting will be
1. A
2. B
3. C
4. D

Type 18 · asked 2 times · Nash equilibrium, dominance & mixing

Market entry game: number of pure-strategy equilibria

Read the passage below, then answer Q55
Based on the above data, answer the given subquestions.
Q55NAT1 Mark·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
How many pure strategy equilibria are there in this game?
Your answer:
Read the passage below, then answer Q56
Based on the above data, answer the given subquestions.
Q56NAT2 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
How many pure strategy equilibria are there in this game?
Your answer:

Type 19 · asked 2 times · Nash equilibrium, dominance & mixing

Market entry game: do all three firms enter in some pure NE?

Read the passage below, then answer Q57
Based on the above data, answer the given subquestions.
Q57MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
In one of these pure NEs, all three players enter the market
1. ATRUE
2. BFALSE
Read the passage below, then answer Q58
Based on the above data, answer the given subquestions.
Q58MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
In one of these pure NEs, all three players enter the market
1. ATRUE
2. BFALSE

Type 20 · asked 2 times · Nash equilibrium, dominance & mixing

Market entry game: symmetric mixed-strategy entry probability

Read the passage below, then answer Q59
Based on the above data, answer the given subquestions.
Q59MCQ2 Marks·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
There is a symmetric mixed strategy equilibrium where all three players enter with the same probability (say p). Find the value of p
1. A1/5
2. B3/5
3. C4/5
4. D2/5
Read the passage below, then answer Q60
Based on the above data, answer the given subquestions.
Q60MCQ2 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
There is a symmetric mixed strategy equilibrium where all three players enter with the same probability (say p). Find the value of p
1. A1/5
2. B3/5
3. C4/5
4. D2/5

Type 21 · asked 2 times · Auctions & VCG pricing

Optimal bid in a first-price auction with uniform valuations

Read the passage below, then answer Q61–Q62
Five bidders with private valuations uniformly distributed between 0 and 1 participate in a sealed bid first price auction. Assuming that everyone is playing the symmetric equilibrium bidding strategy answer the given sub-questions:
Q61MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
Optimal bid for a bidder with valuation 0.6 will be
1. A0.4
2. B0.48
3. C0.5
4. D0.55
Q62MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
Optimal bid for a bidder with valuation 0.75 will be
1. A0.7
2. B0.6
3. C0.5
4. D0.75

Type 22 · asked 2 times · Auctions & VCG pricing

Seller's expected revenue in a first-price auction

Read the passage below, then answer Q63–Q64
Five bidders with private valuations uniformly distributed between 0 and 1 participate in a sealed bid first price auction. Assuming that everyone is playing the symmetric equilibrium bidding strategy answer the given sub-questions:
Q63MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
The expected revenue of the seller in this auction scenario will be
1. A4/5
2. B3/5
3. C2/3
4. D2/5
Q64MCQ2 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
The expected revenue of the seller in this auction scenario will be
1. A4/5
2. B3/5
3. C2/3
4. D2/5

Type 23 · asked 2 times · Auctions & VCG pricing

Expected value of the k-th order statistic of uniform draws

Q65MCQ2 Marks·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
Suppose 5 numbers are drawn independently from the uniform distribution on the interval [0, 1] and then sorted from smallest to largest. The expected value of the number in second position on the list is
1. A5/6
2. B2/3
3. C1/2
4. D1/3
Q66MCQ2 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
Suppose 5 numbers are drawn independently from the uniform distribution on the interval [0, 1] and then sorted from smallest to largest. The expected value of the number in second position on the list is
1. A5/6
2. B2/3
3. C1/2
4. D1/3

Type 24 · asked 2 times · Auctions & VCG pricing

Total valuation of the socially optimal ad-slot allocation

Read the passage below, then answer Q67
Suppose a search engine has two ad slots that it can sell. Slot a has a clickthrough rate of 10 and slot b has a clickthrough rate of 5. There are three advertisers who are interested in these slots. Advertiser x values click at 3 per click, advertiser y values click at 2 per click, and advertiser z values click at 1 per click.
Based on the above data, answer the given subquestions.
Q67NAT2 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Total valuation of socially optimal allocation will be ___________
Your answer:
Read the passage below, then answer Q68
Suppose a search engine has two ad slots that it can sell. Slot a has a clickthrough rate of 10 and slot b has a clickthrough rate of 5. Three advertisers are interested in these slots. Advertiser x values click at 3 per click, advertiser y values click at 2 per click, and advertiser z values click at 1 per click.
Based on the above data, answer the given subquestions.
Q68NAT1 Mark·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Total valuation of socially optimal allocation will be ____________
Your answer:

Type 25 · asked 2 times · Information cascades & Bayes' rule

Which statements about crowd wisdom and cascades are true

Q69MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
Consider following two statements: 1. Crowd can be never be wrong even if everyone in the crowd is rational and everyone takes the same action. 2. Aggregate behaviour of many people with limited information can never produce very accurate results. Which statement(s) is (are) true?
1. AOnly 1
2. BOnly 2
3. CBoth the Only 1 & Only 2
4. DNone
Q70MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
Consider following two statements: 1. Crowd can be wrong even if everyone in the crowd is rational and everyone takes the same action. 2. Aggregate behaviour of many people with limited information can sometimes produce very accurate results. Which statement(s) is (are) true?
1. AOnly 1
2. BOnly 2
3. CBoth 1 & 2
4. DNone

Type 26 · asked 2 times · Matching & Gale-Shapley

Choose the correct statement about stable matching

Q71MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
Choose the correct alternative
1. AA stable matching system is necessarily a system under which everyone is satisfied.
2. BA matching system is stable when an unmatched pair may find it beneficial to deviate from the matching and form their own match.
3. CBoth a stable matching system is necessarily a system under which everyone is satisfied & a matching system is stable when an unmatched pair may find it beneficial to deviate from the matching and form their own match.
4. DNone
Q72MCQ1 Mark·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
Choose the correct alternative
1. AA stable matching system is necessarily a system under which everyone is satisfied.
2. BA matching system is stable when an unmatched pair may find it beneficial to deviate from the matching and form their own match.
3. CBoth A stable matching system is necessarily a system under which everyone is satisfied & A matching system is stable when an unmatched pair may find it beneficial to deviate from the matching and form their own match.
4. DNone

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q15

Q25

Q30

Q474

Q530

Q662

Q774

Q86

Q930

Q1030

Q118

Q1230

Q1332

Q14A

Q1550

Q165

Q17C

Q18D

Q19D

Q200.4 to 0.405

Q210.4 to 0.405

Q22300

Q23200

Q24300

Q25200

Q2615

Q275

Q2815

Q295

Q30B

Q3166.5 to 67

Q3210

Q33C

Q340.035 to 0.04

Q350.035 to 0.04

Q364

Q37B

Q38A

Q39A

Q40B

Q41C

Q424444

Q43B

Q44B

Q45A

Q46A

Q47C

Q48C

Q49D

Q50D

Q51B, D

Q52B, D

Q53D

Q54D

Q553

Q563

Q57B

Q58B

Q59C

Q60C

Q61B

Q62B

Q63C

Q64C

Q65D

Q66D

Q6740

Q6840

Q69D

Q70C

Q71D

Q72D

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.