ECAT Mathematics Chapter 23 With Answers

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ECAT Mathematics Chapter 23

Sr. # Questions Answers Choice
1 The set Q Forms a group under addition Does not form a group Contains no additive indentity Contains no additive inverse
2 The statement that a group can have more than one identity elements is True False Fallacious Some times true
3 The set of all positive even integers is Not a group A group w.r.t subtraction A group w.r.t division A group w.r.t multiplication
4 The set {1,-1, i, -i} form a group under Addition Multiplication Subtraction None
5 The multiplicative inverse of -1 in the set {1-,1} is 1 -1 ±1 0 Does not exist
6 The set of complex numbers forms a group under the binary operation of Addition none of these Division Subtraction
7 The set of the first elements of the ordered pairs forming a relation is called its Function on B Range Domain A into B
8 The set {{a,b}} is Infinite set Singleton set Two points set None
9 Which of the following is the subset of all sets Φ {1,2,3} {Φ} {0}
10 The multiplicative inverse of x such that x = 0 is -x Does not exist 1/x ±1
11 The complement of set A relative to universal set U is the set {x / x∈ A∧ x∈ U} {x / x∉ A∧ x ∈ U} {x / x∈ A and x ∉ U} A-U
12 Let A,B, and C be any sets such that A∪B = A∪C and A∩B = A∩C then A≠ C B = C A = B A≠ B
13 Given X,Y are any two sets such that number of elements in set X = 28, number of elements in set Y = 28, and number of elements in set X∪Y = 54, then number of elements in set X ∩ Y = 4 3 2 1
14 For any set X, X∪X is X X' Φ Universal Set
15 G = {e, a, b, c} is an Abelian group with e as identity element The order of the other elements are 2,2,2 3,3,3 2,2,4 2,3,4
16 Z is the set of integers (Z.*) is a group with a * b = a +b +1, a,b ∈ G.then inverse of a is -a a +1 -1-a None of these
17 Which of the following has the same value as i113 i -1 -i 1
18 If z1 = 2 + 6i and z2 = 3 + 7i then which expression defines the product of z1 and z2 36 +(-32)i -36+32i 6+(-11)i 0, +(-12)i
19 Under multiplication, solution set of is Groupoid Abelian group Semi group All of these
20 Identity w.r.t intersection in a power set of any set is ∅ Set itself Singleton set {0}
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