MCQs of Number Theory

MCQs of Number Theory

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

Answer - Click Here:
C

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

Answer - Click Here:
B

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

Answer - Click Here:
A

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

Answer - Click Here:
D

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

Answer - Click Here:
C

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

Answer - Click Here:
A

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

Answer - Click Here:
B

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)

Answer - Click Here:
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

Answer - Click Here:
D

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

Answer - Click Here:
B