## 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

**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