ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 2 (Set Function and Groups)

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
• a + 1 B
• -2 -a C
• None of these D

The number of proper subset of A ={a.b.c.d} is

• 3 A
• 6 B
• 8 C
• 15 D

The set {{a,b}} is

• Infinite set A
• Singleton set B
• Two points set C
• None D

A = B iff

• All elements of A also the elements of B A
• A and B should be singleton B
• A and B have the same number of elements C
• If both have the same element D

The set Q

• Forms a group under addition A
• Does not form a group B
• Contains no additive indentity C
• Contains no additive inverse D

The sets {1, 2, 4} and {4, 6, 8, 10} are

• Equal sets A
• Equivalent sets B
• Disjoint sets C
• Over lapping sets D

The set of real numbers is a subset of

• The set of natural numbers A
• The set of rational numbers B
• The set of integers C
• The set of complex numbers D

In a school, there are 150 students. Out of these 80 students enrolled for mathematics class, 50 enrolled for English class, and 60 enrolled for Physics class. The students enrolled for English cannot any other class, but the students of mathematics and Physics can take two courses at a time. Find the number of students who have taken both physics and mathematics

• 40 A
• 30 B
• 50 C
• 20 D

A∪(A∪B)= --------------------

• B A
• A B
• A∪B C
• None of these D

A conjunction of two statement p and q is true only if

• p is true A
• q is true B
• Both p and q are true C
• both p and q are false D

• A onto B A
• both a & c B
• A into B C
• none of these D

A set having only one element is called

• An empty set A
• Universal set B
• A singleton set C
• A power set D

If B ={x/x€ Z ^ - 3 < x < 6}, then n (B) =

• 5 A
• {-3,-2,-1,0,1,2,3,4,5,6} B
• 8 C
• 9 D

Power set of X i.e P(X) _______ under the binary operation of union U

• Forms a group A
• Does not form a group B
• Has no identity element C
• Infinite set although X is infinite D

What is the number of elements of the power set of { }

• 0 A
• 1 B
• 2 C
• 3 D

• 
  A
• 
  B
• 
  C
• none of these D

Given X.Y are any two sets such that number of elements in X = 18, number of elements in set Y = 24,and number of elements in set X∪ Y =40,then number of elements in set x∩ Y =

• 3 A
• 1 B
• 2 C
• 4 D

Additive inverse of -a -b is

• a A
• -a + b B
• a - b C
• a + b D

The set of the first elements of the ordered pairs forming a relation is called its

• Function on B A
• Range B
• Domain C
• A into B D

Φ set is the _______ of all sets

• Subset A
• Union B
• Universal C
• Intersection D

Given X, Y are many two sets such that number of elements in X = 18, number of elements in set Y = 24, and number of elements in set X ∪ Y = 40, then number of elements in set X + Y =

• 3 A
• 1 B
• 2 C
• 4 D

The set {-1, 1} is

• Group under the multiplication A
• Group under addition B
• Does not form a group C
• Contains no identity element D

The set {{a,b}} is

• Infinite set A
• Singleton set B
• Two points set C
• None D

• 
  A
• 
  B
• 
  C
• 
  D

What is the number of elements of the power set of {0, 1}

• 1 A
• 2 B
• 3 C
• 4 D

If A and B are two sets then intersection of A and B is denoted by

• 
  A
• 
  B
• 
  C
• 
  D

The multiplicative inverse of -1 in the set {1-, 1} is

• 1 A
• -1 B
• 0 C
• Does not exist D

• 
  A
• 
  B
• 
  C
• None of these D

If a set S contains "n" elements then P (S) has ...... number of elements

• 2ⁿ A
• 2²ⁿ B
• 2 . n C
• n² D

The set of all positive even integers is

• Not a group A
• A group w.r.t. subtraction B
• A group w.r.t. division C
• A group w.r.t. multiplication D