MCQs of Number Theory

Q1: Which of the following is a prime number?

(A) 51
(B) 37
(C) 55
(D) 49

Answer: (B) 37

Q2: The greatest common divisor (GCD) of 36 and 60 is:

(A) 6
(B) 12
(C) 18
(D) 24

Answer: (B) 12

Q3: Which of the following is a perfect square?

(A) 30
(B) 64
(C) 72
(D) 90

Answer: (B) 64

Q4: The least common multiple (LCM) of 8 and 12 is:

(A) 24
(B) 48
(C) 36
(D) 72

Answer: (A) 24

Q5: The number of divisors of 36 is:

(A) 6
(B) 8
(C) 9
(D) 12

Answer: (B) 9

Q6: The number of prime factors of 210 is:

(A) 2
(B) 3
(C) 4
(D) 5

Answer: (C) 4

Q7: The remainder when 128 is divided by 7 is:

(A) 3
(B) 4
(C) 2
(D) 1

Answer: (B) 4

Q8: Which of the following is a solution to the equation 3x≡1 (mod 7)3x≡1 (mod 7)?

(A) 2
(B) 4
(C) 5
(D) 3

Answer: (A) 2

Q9: Which of the following is true about the number 1?

(A) It is neither prime nor composite.
(B) It is prime.
(C) It is composite.
(D) It is a perfect number.

Answer: (A) It is neither prime nor composite.

Q10: What is the value of 54mod  654mod6?

(A) 1
(B) 2
(C) 3
(D) 4

Answer: (A) 1

1. What is the number of elements in this set {{a, b}, c}?
A. 1
B. 3
C. 4
D. 0

2. What is the order of the power set n?
A. n2
B. 2n
C. n
D. None of these

3. If this is a bijective function [f: A —>] then f -1 off =?
A. IA(Identity map of the set A)
B. f -1
C. f
D. f o f -1

4. What is the identity element in the group (R*, *) If * is defined on R* as a * b = (ab/2)?
A. 1/2
B. 1/3
C. 1
D. 2

5. If {1, – 1, I,- i } is a group then what is the inverse of – i in the multiplicative group?
A. -1
B. -i
C. i
D. 1

6. What is the value of (a-1 b)-1 in the group (G, .)?
A. b-1a
B. ab-1
C. ba-1
D. a-1b

7. What is the inverse of a if (Z,*) is a group with a*b = a+b+1 ∀ a,b ∈ Z?
A. a-2
B. -a-2
C. 0
D. -2

8. Which one of the following statement is TRUE?
A. Set of all matrices forms a group under multiplication
B. Set of all rational negative numbers forms a group under multiplication
C. Set of all non-singular matrices forms a group under multiplication
D. Both (b) and (c)

9. Which one of the statement is FALSE?
A. The set of rational integers is an abelian group under addition
B. The set of rational numbers form an abelian group under multiplication
C. The set of rational numbers is an abelian group under addition
D. None of these

10. G = {2, 4, 6, 8) is a group under multiplication modulo 10 then what is the identity element?
A. 8
B. 6
C. 10
D. 0