The argument of each recursive call is the content of a field of the original output. This definite characteristic belongs to which of the following function?

Generativity recursive function

Structurally recursive function

Generativity recursive function

Every recursive algorithm must have the problem of ________

collision of different function calls

overhead of repeated function calls

collision of different function calls

searching for all duplicate elements

28 + Mcqs in Induction and Recursion in Discrete Mathematics Page 1 McqOptions

1.	Let P(n) be the statement that postage of n cents can be formed using just 3-cents stamps and 5-cents stamps. Is the statements P(8) and P(10) are Correct?
A.	True
B.	False
C.	May be True or False
D.	Can't say
Answer» B. False

Discussion

2.	The argument of each recursive call is the content of a field of the original output. This definite characteristic belongs to which of the following function?
A.	Structurally recursive function
B.	Generativity recursive function
C.	General function
D.	Indirect recursive function
Answer» B. Generativity recursive function

Discussion

3.	Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) and P(2) is true; for all positive integers n, if P(n) and P(n+1) is true then P(n+2) is true.
A.	P(1)
B.	P(2)
C.	P(4)
D.	P(n)
Answer» E.

Discussion

4.	Every recursive algorithm must have the problem of ________
A.	overhead of repeated function calls
B.	collision of different function calls
C.	searching for all duplicate elements
D.	make only two recursive calls
Answer» B. collision of different function calls

Discussion

5.	Which of the following is contained in a recursive grammar?
A.	semantic rules
B.	production rules
C.	recursive language
D.	recursive function
Answer» C. recursive language

Discussion

6.	A polygon with 25 sides can be triangulated into _______
A.	23
B.	20
C.	22
D.	21
Answer» B. 20

Discussion

7.	How many types of self-referential recursive data are there in computer programs?
A.	6
B.	2
C.	10
D.	4
Answer» C. 10

Discussion

8.	________ is the consequence of dynamic programming.
A.	Bellman equation
B.	Frobenius equation
C.	Linear equation
D.	Boolean expression
Answer» B. Frobenius equation

Discussion

9.	A polygon with 7 sides can be triangulated into ________
A.	7
B.	14
C.	5
D.	10
Answer» D. 10

Discussion

10.	_______ recursion consists of multiple self-references.
A.	binary recursion
B.	single recursion
C.	multiple recursion
D.	coinductive recursion
Answer» D. coinductive recursion

Discussion

11.	A polygon with 12 sides can be triangulated into _______
A.	7
B.	10
C.	5
D.	12
Answer» C. 5

Discussion

12.	In which of the following problems recurrence relation holds?
A.	Optimal substructure
B.	Tower of Hanoi
C.	Hallmark substitution
D.	Longest common subsequence
Answer» C. Hallmark substitution

Discussion

13.	Which of the following functions generates new data at each step of a method?
A.	corecursive function
B.	structural recursive function
C.	unirecursive function
D.	indirect function
Answer» B. structural recursive function

Discussion

14.	Which amount of postage can be formed using just 4-cent and 11-cent stamps?
A.	2
B.	5
C.	30
D.	10
Answer» E.

Discussion

15.	Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n+2) is true.
A.	P(3)
B.	P(2)
C.	P(4)
D.	P(6)
Answer» B. P(2)

Discussion

16.	Which amount of postage can be formed using just 3-cent stamp and 10-cent stamps?
A.	27
B.	20
C.	11
D.	5
Answer» B. 20

Discussion

17.	The mutual recursion is also termed as ______
A.	indirect recursion
B.	constructive recursion
C.	generative recursion
D.	definitive recursion
Answer» B. constructive recursion

Discussion

18.	If the height of a binary tree is 54, how many null pointers are there as children?
A.	1267
B.	3⁵⁸
C.	56
D.	2⁵⁵
Answer» E.

Discussion

19.	What is the base case for the inequality 7ⁿ > n³, where n = 3?
A.	652 > 189
B.	42 < 132
C.	343 > 27
D.	42 <= 431
Answer» D. 42 <= 431

Discussion

20.	In the principle of mathematical induction, which of the following steps is mandatory?
A.	induction hypothesis
B.	inductive reference
C.	induction set assumption
D.	minimal set representation
Answer» B. inductive reference

Discussion

21.	For any integer m>=3, the series 2+4+6+…+(4m) can be equivalent to ________
A.	m²+3
B.	m+1
C.	mᵐ
D.	3m²+4
Answer» B. m+1

Discussion

22.	For m = 1, 2, …, 4m+2 is a multiple of ________
A.	3
B.	5
C.	6
D.	2
Answer» E.

Discussion

23.	For any positive integer m ______ is divisible by 4.
A.	5m² + 2
B.	3m + 1
C.	m² + 3
D.	m³ + 3m
Answer» E.

Discussion

24.	For every natural number k, which of the following is true?
A.	(mn)ᵏ = mᵏnᵏ
B.	m*k = n + 1
C.	(m+n)ᵏ = k + 1
D.	mᵏn = mnᵏ
Answer» B. m*k = n + 1

Discussion

25.	According to principle of mathematical induction, if P(k+1) = m⁽ᵏ⁺¹⁾ + 5 is true then _____ must be true.
A.	P(k) = 3m⁽ᵏ⁾
B.	P(k) = m⁽ᵏ⁾ + 5
C.	P(k) = m⁽ᵏ⁺²⁾ + 5
D.	P(k) = m⁽ᵏ⁾
Answer» C. P(k) = m⁽ᵏ⁺²⁾ + 5

Discussion

26.	By induction hypothesis, the series 1² + 2² + 3² + … + p² can be proved equivalent to ____________
A.	a
B.	b
C.	c
D.	d
Answer» C. c

Discussion

27.	What is the induction hypothesis assumption for the inequality m ! > 2ᵐ where m>=4?
A.	for m=k, k+1!>2ᵏ holds
B.	for m=k, k!>2ᵏ holds
C.	for m=k, k!>3ᵏ holds
D.	for m=k, k!>2ᵏ⁺¹ holds
Answer» C. for m=k, k!>3ᵏ holds

Discussion

28.	Which of the following is the base case for 4ⁿ⁺¹ > (n+1)² where n = 2?
A.	64 > 9
B.	16 > 2
C.	27 < 91
D.	54 > 8
Answer» B. 16 > 2

Discussion

Explore topic-wise MCQs in Discrete Mathematics.

Let P(n) be the statement that postage of n cents can be formed using just 3-cents stamps and 5-cents stamps. Is the statements P(8) and P(10) are Correct?

The argument of each recursive call is the content of a field of the original output. This definite characteristic belongs to which of the following function?

Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) and P(2) is true; for all positive integers n, if P(n) and P(n+1) is true then P(n+2) is true.

Every recursive algorithm must have the problem of ________

Which of the following is contained in a recursive grammar?

A polygon with 25 sides can be triangulated into _______

How many types of self-referential recursive data are there in computer programs?

________ is the consequence of dynamic programming.

A polygon with 7 sides can be triangulated into ________

_______ recursion consists of multiple self-references.

A polygon with 12 sides can be triangulated into _______

In which of the following problems recurrence relation holds?

Which of the following functions generates new data at each step of a method?

Which amount of postage can be formed using just 4-cent and 11-cent stamps?

Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) is true; for all positive integers n, if P(n) is true then P(n+2) is true.

Which amount of postage can be formed using just 3-cent stamp and 10-cent stamps?

The mutual recursion is also termed as ______

If the height of a binary tree is 54, how many null pointers are there as children?

What is the base case for the inequality 7ⁿ > n³, where n = 3?

In the principle of mathematical induction, which of the following steps is mandatory?

For any integer m>=3, the series 2+4+6+…+(4m) can be equivalent to ________

For m = 1, 2, …, 4m+2 is a multiple of ________

For any positive integer m ______ is divisible by 4.

For every natural number k, which of the following is true?

According to principle of mathematical induction, if P(k+1) = m⁽ᵏ⁺¹⁾ + 5 is true then _____ must be true.

By induction hypothesis, the series 1² + 2² + 3² + … + p² can be proved equivalent to ____________

What is the induction hypothesis assumption for the inequality m ! > 2ᵐ where m>=4?

Which of the following is the base case for 4ⁿ⁺¹ > (n+1)² where n = 2?