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Advanced Algorithms · Inclusion-exclusion counting

15 questions · 27 marks · 3 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Advanced Algorithms

Inclusion-exclusion counting

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
NAT: Numerical response. No negative marking.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

End Term · 31 Aug 2025 (FN)End Term

Read the passage below, then answer Q1–Q5
Based on the above data, answer the given subquestions.
Q1MCQ2 Marks·Choose one option
Asked 3 times Key ↓
1. A3^n
2. B2^n
3. Cn^3
4. Dn^2
Q2MCQ2 Marks·Choose one option
Asked 3 times Key ↓
1. A2^n
2. Bn
3. C1
4. D0
Q3MCQ2 Marks·Choose one option
Asked 3 times Key ↓
1. A3^n
2. B2^n
3. C1
4. D0
Q4NAT2 Marks·Write the number
Asked 6 times Key ↓
For n = 4, calculate the number of sequences of length 4 consisting only of numbers 0, 1, and 2 such that each number occurs at least once.
Your answer:
Q5NAT2 Marks·Write the number
Asked 6 times Key ↓
For n = 5, calculate the number of sequences of length 5 consisting only of numbers 0, 1, and 2 such that each number occurs at least once.
Your answer:

End Term · 31 Aug 2025 (AN)End Term

Read the passage below, then answer Q6–Q10
Based on the above data, answer the given subquestions.
Q6MCQ2 Marks·Choose one option
Asked 3 times Key ↓
1. A3^n
2. B2^n
3. Cn^3
4. Dn^2
Q7MCQ2 Marks·Choose one option
Asked 3 times Key ↓
1. A2^n
2. Bn
3. C1
4. D0
Q8MCQ2 Marks·Choose one option
Asked 3 times Key ↓
1. A3^n
2. B2^n
3. C1
4. D0
Q9NAT2 Marks·Write the number
Asked 6 times Key ↓
For n = 4, calculate the number of sequences of length 3 consisting only of numbers 0, 1, and 2 such that each number occurs at least once.
Your answer:
Q10NAT2 Marks·Write the number
Asked 6 times Key ↓
For n = 6, calculate the number of sequences of length 5 consisting only of numbers 0, 1, and 2 such that each number occurs at least once.
Your answer:

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Read the passage below, then answer Q11–Q15
Based on the above data, answer the given subquestions.
Q11MCQ1 Mark·Choose one option
Asked 3 times Key ↓
1. A
2. B
3. C
4. D
Q12MCQ1 Mark·Choose one option
Asked 3 times Key ↓
1. A
2. B
3. C
4. D
Q13MCQ1 Mark·Choose one option
Asked 3 times Key ↓
1. A
2. B
3. C
4. D
Q14NAT2 Marks·Write the number
Asked 6 times Key ↓
For n= 4, calculate the number of sequences of length 4 consisting only of numbers 0, 1, and 2 such that each number occurs at least once.
Your answer:
Q15NAT2 Marks·Write the number
Asked 6 times Key ↓
For n = 5, calculate the number of sequences of length 5 consisting only of numbers 0, 1, and 2 such that each number occurs at least once.
Your answer:

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q1B

Q2C

Q3D

Q436

Q5150

Q6B

Q7C

Q8D

Q96

Q10540

Q11B

Q12C

Q13D

Q1436

Q15150

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.