Complete K-Array Tree MCQ Quiz - Objective Question with Answer for Complete K-Array Tree - Download Free PDF
Last updated on Jun 12, 2025
Latest Complete K-Array Tree MCQ Objective Questions
Complete K-Array Tree Question 1:
The purpose of analysing an N-Ary association in databases is :
Answer (Detailed Solution Below)
Complete K-Array Tree Question 1 Detailed Solution
The correct answer is option 3: To deal with relationships that involve more than two tables
Key Points
- An N-ary association in a database refers to a relationship that involves N entities (or tables), where N ≥ 3.
- It is used when the relationship cannot be accurately or efficiently represented using just binary (2-table) associations.
- Commonly modeled using a relationship table that includes foreign keys referencing each of the N participating entities.
Additional Information
- Option 1: Parent-child relationships are typically represented using recursive relationships or 1:N binary associations.
- Option 2: One-to-many is a 2-entity (binary) relationship, not N-ary.
- Option 4: Inheritance is represented using generalization/specialization hierarchies, not N-ary associations.
Hence, the correct answer is: option 3: To deal with relationships that involve more than two tables
Complete K-Array Tree Question 2:
Non leaf nodes of B+ tree structure form a :
Answer (Detailed Solution Below)
Complete K-Array Tree Question 2 Detailed Solution
The correct answer is Multilevel sparse indices.
Key Points
- Non-leaf nodes of a B+ tree structure form multilevel sparse indices, which are crucial for its efficiency and performance.
- In a B+ tree, all the actual data records are stored in the leaf nodes, while the non-leaf nodes (or internal nodes) store the keys that act as pointers to guide the search process.
- The non-leaf nodes do not store every key, only enough to direct the search to the appropriate leaf node, making the indices sparse.
- This structure helps in reducing the height of the tree, thus speeding up the search, insert, and delete operations.
- Multilevel indexing means that the tree is structured in multiple levels (root, intermediate levels, and leaf nodes), where each level helps narrow down the search space progressively.
- The B+ tree is a balanced tree, meaning all the leaf nodes are at the same level, which ensures consistent and predictable performance.
Additional Information
- B+ trees are widely used in database indexing and file systems due to their efficiency in handling large amounts of data.
- They are an extension of B-trees, with the primary difference being that in B+ trees, all values are stored at the leaf level, and internal nodes only store keys.
- This structure ensures that sequential traversal of the data can be done efficiently by following the linked leaf nodes.
- Because of the multilevel sparse indexing, B+ trees are well-suited for range queries and ordered traversals.
- B+ trees maintain balance by splitting and merging nodes as necessary during insertions and deletions, ensuring that the tree remains balanced with minimal height.
Complete K-Array Tree Question 3:
Each node is having a successor node in _______.
Answer (Detailed Solution Below)
Complete K-Array Tree Question 3 Detailed Solution
The correct answer is: 2) Singly Circular Linked List
Explanation:
-
In a Singly Circular Linked List, each node has exactly one successor, and the last node’s next pointer points back to the first node, thus ensuring that every node has a successor.
-
In a Singly Linked List, the last node's next pointer is null, so it does not have a successor.
-
In a Doubly Linked List, nodes have both a successor and a predecessor, but again, the last node’s next is null, so not all nodes have a successor.
-
Hence, the only correct option where every node (including the last) has a successor is:
Complete K-Array Tree Question 4:
Of the following, which best approximates the ratio of the number of nonterminal nodes in the total number of nodes in a complex K-ary tree of depth N?
Answer (Detailed Solution Below)
Complete K-Array Tree Question 4 Detailed Solution
Concept -
Depth (N) |
Internal Nodes |
Total Nodes |
0 |
1 |
1 |
1 |
K |
KN+1 = K2 |
2 |
K2 |
K3 |
3 |
K3 |
K4 |
4 . . . n |
K4 . . . KN |
K5 . . . KN+1 |
No. of total internal nodes = 1 + K + K2 + K3 + … + KN = (KN -1)/ (K-1) - It constitutes geometric progression.
No. of total nodes = 1 + K + K2 + K3 + … + KN+1 = (KN+1 -1)/ (K-1)
\(\frac{{{\rm{No}}.{\rm{\;of\;total\;internal\;nodes\;}}}}{{{\rm{No}}.{\rm{\;of\;total\;nodes}}}}\tilde = \;\frac{1}{K}\)
Complete K-Array Tree Question 5:
A 5-ary tree is tree in which every internal node has exactly 5 children. The number of leaf nodes in such a tree with 8 internal nodes will be:
Answer (Detailed Solution Below)
Complete K-Array Tree Question 5 Detailed Solution
Formula:
L = I (n - 1) + 1
L =number of leaf nodes
I = number of internal nodes
n = n - ary tree
Calculation:
I = 8
n = 5
L = 8(5 - 1) + 1
L = 32 + 1 = 33
Number of leaf nodes = 33
Number of internal nodes = 8
Total number of nodes = 33 + 8 = 41Top Complete K-Array Tree MCQ Objective Questions
A 5-ary tree is tree in which every internal node has exactly 5 children. The number of leaf nodes in such a tree with 8 internal nodes will be:
Answer (Detailed Solution Below)
Complete K-Array Tree Question 6 Detailed Solution
Download Solution PDFFormula:
L = I (n - 1) + 1
L =number of leaf nodes
I = number of internal nodes
n = n - ary tree
Calculation:
I = 8
n = 5
L = 8(5 - 1) + 1
L = 32 + 1 = 33
Number of leaf nodes = 33
Number of internal nodes = 8
Total number of nodes = 33 + 8 = 41Of the following, which best approximates the ratio of the number of nonterminal nodes in the total number of nodes in a complex K-ary tree of depth N?
Answer (Detailed Solution Below)
Complete K-Array Tree Question 7 Detailed Solution
Download Solution PDFConcept -
Depth (N) |
Internal Nodes |
Total Nodes |
0 |
1 |
1 |
1 |
K |
KN+1 = K2 |
2 |
K2 |
K3 |
3 |
K3 |
K4 |
4 . . . n |
K4 . . . KN |
K5 . . . KN+1 |
No. of total internal nodes = 1 + K + K2 + K3 + … + KN = (KN -1)/ (K-1) - It constitutes geometric progression.
No. of total nodes = 1 + K + K2 + K3 + … + KN+1 = (KN+1 -1)/ (K-1)
\(\frac{{{\rm{No}}.{\rm{\;of\;total\;internal\;nodes\;}}}}{{{\rm{No}}.{\rm{\;of\;total\;nodes}}}}\tilde = \;\frac{1}{K}\)
Non leaf nodes of B+ tree structure form a :
Answer (Detailed Solution Below)
Complete K-Array Tree Question 8 Detailed Solution
Download Solution PDFThe correct answer is Multilevel sparse indices.
Key Points
- Non-leaf nodes of a B+ tree structure form multilevel sparse indices, which are crucial for its efficiency and performance.
- In a B+ tree, all the actual data records are stored in the leaf nodes, while the non-leaf nodes (or internal nodes) store the keys that act as pointers to guide the search process.
- The non-leaf nodes do not store every key, only enough to direct the search to the appropriate leaf node, making the indices sparse.
- This structure helps in reducing the height of the tree, thus speeding up the search, insert, and delete operations.
- Multilevel indexing means that the tree is structured in multiple levels (root, intermediate levels, and leaf nodes), where each level helps narrow down the search space progressively.
- The B+ tree is a balanced tree, meaning all the leaf nodes are at the same level, which ensures consistent and predictable performance.
Additional Information
- B+ trees are widely used in database indexing and file systems due to their efficiency in handling large amounts of data.
- They are an extension of B-trees, with the primary difference being that in B+ trees, all values are stored at the leaf level, and internal nodes only store keys.
- This structure ensures that sequential traversal of the data can be done efficiently by following the linked leaf nodes.
- Because of the multilevel sparse indexing, B+ trees are well-suited for range queries and ordered traversals.
- B+ trees maintain balance by splitting and merging nodes as necessary during insertions and deletions, ensuring that the tree remains balanced with minimal height.
Complete K-Array Tree Question 9:
A 5-ary tree is tree in which every internal node has exactly 5 children. The number of leaf nodes in such a tree with 8 internal nodes will be:
Answer (Detailed Solution Below)
Complete K-Array Tree Question 9 Detailed Solution
Formula:
L = I (n - 1) + 1
L =number of leaf nodes
I = number of internal nodes
n = n - ary tree
Calculation:
I = 8
n = 5
L = 8(5 - 1) + 1
L = 32 + 1 = 33
Number of leaf nodes = 33
Number of internal nodes = 8
Total number of nodes = 33 + 8 = 41Complete K-Array Tree Question 10:
Of the following, which best approximates the ratio of the number of nonterminal nodes in the total number of nodes in a complex K-ary tree of depth N?
Answer (Detailed Solution Below)
Complete K-Array Tree Question 10 Detailed Solution
Concept -
Depth (N) |
Internal Nodes |
Total Nodes |
0 |
1 |
1 |
1 |
K |
KN+1 = K2 |
2 |
K2 |
K3 |
3 |
K3 |
K4 |
4 . . . n |
K4 . . . KN |
K5 . . . KN+1 |
No. of total internal nodes = 1 + K + K2 + K3 + … + KN = (KN -1)/ (K-1) - It constitutes geometric progression.
No. of total nodes = 1 + K + K2 + K3 + … + KN+1 = (KN+1 -1)/ (K-1)
\(\frac{{{\rm{No}}.{\rm{\;of\;total\;internal\;nodes\;}}}}{{{\rm{No}}.{\rm{\;of\;total\;nodes}}}}\tilde = \;\frac{1}{K}\)
Complete K-Array Tree Question 11:
______ number of leaf nodes in a rooted tree of n nodes, where each node is having 0 or 3 children.
Answer (Detailed Solution Below)
Complete K-Array Tree Question 11 Detailed Solution
Consider an example:
n = 7
leaves = 5
Option 1:
\(\frac{n}{2} = \frac{7}{2} = 3.5\)
Option 2:
\(\frac{{\left( {2{\rm{n}}\: + \:1} \right)}}{3} = \frac{{2\: \times \:7\: + \:1}}{3} = 5\;\)
Option 3:
\(\frac{{\left( {n - 1} \right)}}{n} = \frac{{7 - 1}}{7} = \frac{6}{7}\)
Option 4:
\(n - 1 = 7 - 1 = 6\)
Complete K-Array Tree Question 12:
Each node is having a successor node in _______.
Answer (Detailed Solution Below)
Complete K-Array Tree Question 12 Detailed Solution
The correct answer is: 2) Singly Circular Linked List
Explanation:
-
In a Singly Circular Linked List, each node has exactly one successor, and the last node’s next pointer points back to the first node, thus ensuring that every node has a successor.
-
In a Singly Linked List, the last node's next pointer is null, so it does not have a successor.
-
In a Doubly Linked List, nodes have both a successor and a predecessor, but again, the last node’s next is null, so not all nodes have a successor.
-
Hence, the only correct option where every node (including the last) has a successor is:
Complete K-Array Tree Question 13:
Consider a complete k-ary tree. In the k-ary tree, every node has k or 0 children. The number of leaves in such a tree is 10. What is the relation between k and y if y is the number of internal node?
Answer (Detailed Solution Below)
Complete K-Array Tree Question 13 Detailed Solution
Data:
number of leaves = L = 10
Formula
If k- ary tree with y internal nodes, then number of leaves
L = (k – 1) × y + 1
Calculation
10 = (k – 1)y + 1
∴y = \(\frac{9}{k -1} \)
Verification
leaves = L = 5
5 = (k - 1)y + 1
y = 4 ÷ (k-1)
since k = 3
∴ y = 2
Complete K-Array Tree Question 14:
The purpose of analysing an N-Ary association in databases is :
Answer (Detailed Solution Below)
Complete K-Array Tree Question 14 Detailed Solution
The correct answer is option 3: To deal with relationships that involve more than two tables
Key Points
- An N-ary association in a database refers to a relationship that involves N entities (or tables), where N ≥ 3.
- It is used when the relationship cannot be accurately or efficiently represented using just binary (2-table) associations.
- Commonly modeled using a relationship table that includes foreign keys referencing each of the N participating entities.
Additional Information
- Option 1: Parent-child relationships are typically represented using recursive relationships or 1:N binary associations.
- Option 2: One-to-many is a 2-entity (binary) relationship, not N-ary.
- Option 4: Inheritance is represented using generalization/specialization hierarchies, not N-ary associations.
Hence, the correct answer is: option 3: To deal with relationships that involve more than two tables
Complete K-Array Tree Question 15:
Non leaf nodes of B+ tree structure form a :
Answer (Detailed Solution Below)
Complete K-Array Tree Question 15 Detailed Solution
The correct answer is Multilevel sparse indices.
Key Points
- Non-leaf nodes of a B+ tree structure form multilevel sparse indices, which are crucial for its efficiency and performance.
- In a B+ tree, all the actual data records are stored in the leaf nodes, while the non-leaf nodes (or internal nodes) store the keys that act as pointers to guide the search process.
- The non-leaf nodes do not store every key, only enough to direct the search to the appropriate leaf node, making the indices sparse.
- This structure helps in reducing the height of the tree, thus speeding up the search, insert, and delete operations.
- Multilevel indexing means that the tree is structured in multiple levels (root, intermediate levels, and leaf nodes), where each level helps narrow down the search space progressively.
- The B+ tree is a balanced tree, meaning all the leaf nodes are at the same level, which ensures consistent and predictable performance.
Additional Information
- B+ trees are widely used in database indexing and file systems due to their efficiency in handling large amounts of data.
- They are an extension of B-trees, with the primary difference being that in B+ trees, all values are stored at the leaf level, and internal nodes only store keys.
- This structure ensures that sequential traversal of the data can be done efficiently by following the linked leaf nodes.
- Because of the multilevel sparse indexing, B+ trees are well-suited for range queries and ordered traversals.
- B+ trees maintain balance by splitting and merging nodes as necessary during insertions and deletions, ensuring that the tree remains balanced with minimal height.