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DBMS · B+ trees, BSTs & multilevel index

13 questions · 34 marks · 6 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Database Management Systems

B+ trees, BSTs & multilevel index

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.

End Term · 31 Aug 2025 (FN)End Term

Q1MCQ2 Marks·Choose one option
Asked 3 times Key ↓
Consider a non-empty B+-tree of order 17. What are the maximum and minimum number of keys that can be placed in the root node?
1. Amax. number of keys = 16, min. number of keys = 1.
2. Bmax. number of keys = 17, min. number of keys = 1.
3. Cmax. number of keys = 16, min. number of keys = 8.
4. Dmax. number of keys = 17, min. number of keys = 8.
Q2MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. A2
2. B0
3. C1
4. D5
Q3NAT2 Marks·Write the number
Key ↓
Your answer:

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Q4MSQ4 Marks·Choose all correct options
Asked 2 times Key ↓
Construct a binary search tree by inserting the values in the following order 15,14, 30, 5, 13, 19, 26, 12, 1, 6. Which of the following statement(s) is/are correct? Note: Consider the root node at level 0.
1. AThe height of binary search tree is 6.
2. BThe sum of the leaf nodes of the binary search tree is 33
3. CThe nodes 12,1 and 6 are part of the left subtree of node 13.
4. DNode 19 is at level 2
Q5NAT4 Marks·Write the number
Key ↓
Consider a binary search tree consisting of 31 elements. Let m be the maximum height possible for a given binary search tree, and n be the minimum height possible for a given binary search tree. What will be the value of m − n?
Your answer:

End Term · 13 Apr 2025 (FN)End Term

Q6MCQ2 Marks·Choose one option
Asked 2 times Key ↓
1. A19
2. B20
3. C21
4. D22

End Term · 13 Apr 2025 (AN)End Term

Q7MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. A19
2. B20
3. C21
4. D22

End Term · 22 Dec 2024 (FN)End Term

Q8MCQ2 Marks·Choose one option
Asked 3 times Key ↓
Consider a non-empty B+-tree of order 13. What are the maximum and minimum number of keys that can be placed in the root node?
1. Amax. number of keys = 13, min. number of keys = 6.
2. Bmax. number of keys = 12, min. number of keys = 1.
3. Cmax. number of keys = 14, min. number of keys = 1.
4. Dmax. number of keys = 14, min. number of keys = 7.
Q9MCQ2 Marks·Choose one option
Asked 2 times Key ↓
Consider a multilevel index with five levels as L1, L2, L3, L4 and L5. Let L1 be the innermost and L5 be the outermost levels. Let the index blocking factor or the maximum number of entries held by a block be 50. If the number of blocks in level L1 is 62,50,000, then how many blocks are required at L2, L3, L4 and L5?
1. ANumber of blocks at L2 is 125000, Number of blocks at L3 is 2500, Number of blocks at L4 is 50, Number of blocks at L5 is 1
2. BNumber of blocks at L2 is 125000, Number of blocks at L3 is 2000, Number of blocks at L4 is 50, Number of blocks at L5 is 1
3. CNumber of blocks at L2 is 120000, Number of blocks at L3 is 2400, Number of blocks at L4 is 40, Number of blocks at L5 is 1
4. DNumber of blocks at L2 is 120000, Number of blocks at L3 is 3000, Number of blocks at L4 is 60, Number of blocks at L5 is 1
Q10MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. A5
2. B4
3. C6
4. D3

End Term · 22 Dec 2024 (AN)End Term

Q11MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. A5
2. B4
3. C6
4. D3
Q12MCQ2 Marks·Choose one option
Asked 3 times Key ↓
Consider a non-empty B+-tree of order 16. What are the maximum and minimum number of keys that can be placed in the root node?
1. Amax. number of keys = 15, min. number of keys = 8.
2. Bmax. number of keys = 15, min. number of keys = 1.
3. Cmax. number of keys = 16, min. number of keys = 1.
4. Dmax. number of keys = 16, min. number of keys = 8.
Q13MCQ2 Marks·Choose one option
Asked 2 times Key ↓
Consider a multilevel index with five levels as L1, L2, L3, L4 and L5. Let L1 be the innermost and L5 be the outermost levels. Let the index blocking factor or the maximum number of entries held by a block be 25. If the number of blocks in level L1 is 12,50,000, then how many blocks are required at L2, L3, L4 and L5?
1. ANumber of blocks at L2 is 50000, Number of blocks at L3 is 2000, Number of blocks at L4 is 80, Number of blocks at L5 is 4
2. BNumber of blocks at L2 is 125000, Number of blocks at L3 is 2000, Number of blocks at L4 is 80, Number of blocks at L5 is 1
3. CNumber of blocks at L2 is 50000, Number of blocks at L3 is 2000, Number of blocks at L4 is 80, Number of blocks at L5 is 1
4. DNumber of blocks at L2 is 125000, Number of blocks at L3 is 2500, Number of blocks at L4 is 80, Number of blocks at L5 is 4

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q1A

Q2C

Q35

Q4B, D

Q526

Q6B

Q7B

Q8B

Q9A

Q10A

Q11A

Q12B

Q13A

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