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 :

  1. To capture a parent-child relationship
  2. To deal with one to many relationships
  3. To deal with relationships that involve more than two tables
  4. To represent an inheritance relationship

Answer (Detailed Solution Below)

Option 3 : To deal with relationships that involve more than two tables

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 : 

  1. Multilevel sparse indices 
  2. Multilevel dense indices
  3. Sparse indices
  4. Multilevel clustered indices

Answer (Detailed Solution Below)

Option 1 : Multilevel sparse indices 

Complete K-Array Tree Question 2 Detailed Solution

B+ Tree Structure Explanation - guacandrollcantina.com

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 _______.

  1. Singly linked list
  2. Singly Circular Linked list 
  3. Doubly Linked list
  4. Not Possible in any linked list

Answer (Detailed Solution Below)

Option 2 : Singly Circular Linked list 

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?

  1. 1/N
  2. N-1/N
  3. 1/K
  4. K-1/K

Answer (Detailed Solution Below)

Option 3 : 1/K

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:

  1. 30
  2. 33
  3. 45
  4. 125

Answer (Detailed Solution Below)

Option 2 : 33

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 = 41

Top 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:

  1. 30
  2. 33
  3. 45
  4. 125

Answer (Detailed Solution Below)

Option 2 : 33

Complete K-Array Tree Question 6 Detailed Solution

Download Solution PDF

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 = 41

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?

  1. 1/N
  2. N-1/N
  3. 1/K
  4. K-1/K

Answer (Detailed Solution Below)

Option 3 : 1/K

Complete K-Array Tree Question 7 Detailed Solution

Download Solution PDF

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)

\(\frac{{{\rm{No}}.{\rm{\;of\;total\;internal\;nodes\;}}}}{{{\rm{No}}.{\rm{\;of\;total\;nodes}}}}\tilde = \;\frac{1}{K}\)

Non leaf nodes of B+ tree structure form a : 

  1. Multilevel sparse indices 
  2. Multilevel dense indices
  3. Sparse indices
  4. Multilevel clustered indices

Answer (Detailed Solution Below)

Option 1 : Multilevel sparse indices 

Complete K-Array Tree Question 8 Detailed Solution

Download Solution PDF
B+ Tree Structure Explanation - guacandrollcantina.com

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 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:

  1. 30
  2. 33
  3. 45
  4. 125

Answer (Detailed Solution Below)

Option 2 : 33

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 = 41

Complete 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?

  1. 1/N
  2. N-1/N
  3. 1/K
  4. K-1/K

Answer (Detailed Solution Below)

Option 3 : 1/K

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.

  1. \(\frac{n}{2}\)
  2. \(\frac{{\left( {2n + 1} \right)}}{3}\)
  3. \(\frac{{\left( {n - 1} \right)}}{n}\)
  4. (n - 1)

Answer (Detailed Solution Below)

Option 2 : \(\frac{{\left( {2n + 1} \right)}}{3}\)

Complete K-Array Tree Question 11 Detailed Solution

Consider an example:

F1 R.S M.P 30.07.19 D 19

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 _______.

  1. Singly linked list
  2. Singly Circular Linked list 
  3. Doubly Linked list
  4. Not Possible in any linked list

Answer (Detailed Solution Below)

Option 2 : Singly Circular Linked list 

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?

  1. \(\frac{9}{k -1} \)
  2. \(\frac{9}{k +1} \)
  3. \(\frac{10}{k -1} \)
  4. \(\frac{10}{k +1} \)

Answer (Detailed Solution Below)

Option 1 : \(\frac{9}{k -1} \)

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

F1 R.S M.P 30.07.19 D 19

 

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 :

  1. To capture a parent-child relationship
  2. To deal with one to many relationships
  3. To deal with relationships that involve more than two tables
  4. To represent an inheritance relationship

Answer (Detailed Solution Below)

Option 3 : To deal with relationships that involve more than two tables

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 : 

  1. Multilevel sparse indices 
  2. Multilevel dense indices
  3. Sparse indices
  4. Multilevel clustered indices

Answer (Detailed Solution Below)

Option 1 : Multilevel sparse indices 

Complete K-Array Tree Question 15 Detailed Solution

B+ Tree Structure Explanation - guacandrollcantina.com

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.
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