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# Discrete Mathematics | Binary Trees MCQs

**Discrete Mathematics | Binary Trees MCQs**: This section contains multiple-choice questions and answers on Binary Trees in Discrete Mathematics.

Submitted by Anushree Goswami, on October 23, 2022

**1. In a directed tree, a ____ tree is one in which every node has an outdegree less than or equal to two?**

- Non-binary
- Less binary
- Partial binary
- Binary

**Answer:** D) Binary

**Explanation:**

In a directed tree, a binary tree is one in which every node has an outdegree less than or equal to two.

**2. A binary tree consisting only of ____ (empty tree) is also a binary tree?**

- Edges
- Points
- Nodes
- Vertex

**Answer:** C) Nodes

**Explanation:**

A binary tree consisting only of nodes (empty tree) is also a binary tree.

**3. There is a unique node in a binary tree called its ____?**

- Parent
- Left child
- Right child
- Root

**Answer:** D) Root

**Explanation:**

There is a unique node in a binary tree called its root.

**4. There is a node to the ____ of the root called its left child?**

- Left
- Right
- Center
- None

**Answer:** A) Left

**Explanation:**

There is a node to the left of the root called its left child.

**5. Nodes that are ____ of a root are called its right children?**

- Center
- Left
- Right
- None

**Answer:** C) Right

**Explanation:**

Nodes that are right of a root are called its right children.

**6. Nodes that have ____ are called their parents?**

- Left Children
- Right Children
- Both left and right children
- All of the above

**Answer:** D) All of the above

**Explanation:**

Nodes that have left or right children or both are called their parents.

**7. It is called a sibling node when two nodes have the ____ parent?**

- Same
- Different
- Neighbour
- None

**Answer:** A) Same

**Explanation:**

It is called a sibling node when two nodes have the same parent.

**8. It is called a leaf if it has __ children?**

- One
- Two
- Multiple
- No

**Answer:** D) No

**Explanation:**

It is called a leaf if it has no children.

**9. There can be as few as ____ leaf (minimum) or as many as half the number of vertices (maximum) in a binary tree?**

- Zero
- One
- Two
- Three

**Answer:** B) One

**Explanation:**

There can be as few as one leaf (minimum) or as many as half the number of vertices (maximum) in a binary tree.

**10. When a node is the child of another node or a child of another descendant of another node, it is called a ____?**

- Ascendant
- Descendant
- Both A and B
- None of the above

**Answer:** B) Descendant

**Explanation:**

When a node is the child of another node or a child of another descendant of another node, it is called a descendant.

**11. In a tree, all nodes are descendants of the ___?**

- Leaf
- Root
- Stem
- Flower

**Answer:** B) Root

**Explanation:**

In a tree, all nodes are descendants of the root.

**12. Left subtrees are those whose roots are the ___ children of a node?**

- Left
- Right
- Middle
- None

**Answer:** A) Left

**Explanation:**

Left subtrees are those whose roots are the left children of a node.

**13. Right subtrees of nodes have their roots in the ____ child of that node?**

- Left
- Right
- Middle
- None

**Answer:** B) Right

**Explanation:**

Right subtrees of nodes have their roots in the right child of that node.

**14. A node's ____ is determined by its distance from the root?**

- Depth
- Level
- Quantity
- Quality

**Answer:** B) Level

**Explanation:**

A node's level is determined by its distance from the root.

**15. Root has a ____ level?**

- Zero
- One
- Two
- Three

**Answer:** A) Zero

**Explanation:**

Root has a zero level.

**16. Nodes beneath its parent have a level ____ than its own?**

- One Higher
- Two Higher
- Zero Higher
- One Lower

**Answer:** A) One Higher

**Explanation:**

Nodes beneath its parent have a level one higher than its own.

**17. Any level N can have a maximum of ___ nodes?**

- N
^{2} - 2
^{N} - 2
^{N-2} - 2
^{N-1}

**Answer:** B) 2^{N}

**Explanation:**

Any level N can have a maximum of 2^{N}nodes.

**18. An object's ____ refers to its maximum number of nodes in a branch?**

- Depth
- Height
- Both A and B
- None of the above

**Answer:** C) Both A and B

**Explanation:**

An object's depth or height refers to its maximum number of nodes in a branch.

**19. Binary trees of depth d can have a maximum number of nodes of ___, where d ≥1?**

- 2
^{d} - 2
^{d+1} - 2
^{d-1} - 2d-1

**Answer:** C) 2^{d-1}

**Explanation:**

Binary trees of depth d can have a maximum number of nodes of 2^{d-1}, where d ≥1.

**20. ____ nodes are nodes without children?**

- External
- Terminal
- Both A and B
- None of the above

**Answer:** C) Both A and B

**Explanation:**

External nodes or terminal nodes are nodes without children.

**21. A node that has one or more children is called a/an ____?**

- Internal
- Non-terminal
- Both A and B
- None of the above

**Answer:** C) Both A and B

**Explanation:**

A node that has one or more children is called an internal node or a non-terminal node.

**22. An ____ tree consists of a root containing the operator, a left subtree containing the left expression, and a right subtree containing the right expression?**

- Experience
- Expression
- Extravange
- Attribute

**Answer:** B) Expression

**Explanation:**

An expression tree consists of a root containing the operator, a left subtree containing the left expression, and a right subtree containing the right expression.

**23. Binary trees with the maximum number of possible nodes at every level, except perhaps the last, are considered ____?**

- Binary trees
- Incomplete binary trees
- Complete binary trees
- Partially complete binary trees

**Answer:** C) Complete binary trees

**Explanation:**

Binary trees with the maximum number of possible nodes at every level, except perhaps the last, are considered complete binary trees.

**24. Binary trees with full leaves and two children for non-leaf nodes are called ___ binary trees?**

- Half
- Full
- Non-empty
- Null

**Answer:** B) Full

**Explanation:**

Binary trees with full leaves and two children for non-leaf nodes are called full binary trees.

**25. Which of the following is TRUE about General Tree?**

- It is possible for the general tree to be empty.
- There are two types of children for a node: left children and right children.
- There is no distinction between a node that has children and a node that does not have children.
- None of the above

**Answer:** C) There is no distinction between a node that has children and a node that does not have children

**Explanation:**

There is no distinction between a node that has children and a node that does not have children.

**26. Which of the following is TRUE about Binary Tree?**

- There is no distinction between a node that has children and a node that does not have children.
- An empty binary tree or a tree with zero nodes does not exist.
- It is possible for the binary tree to be empty.
- There is only one type of children for a node: left children or right children.

**Answer:** C) It is possible for the binary tree to be empty

**Explanation:**

It is possible for the binary tree to be empty.

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