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

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

A function whose range is just one element is called

• One-one function A
• Constant function B
• Onto function C
• Identity function 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

The set of integers is a subset of

• The set of natural numbers A
• The set of whole numbers B
• The set of prime numbers C
• The set of rational numbers D

Z is a

• Infinite set A
• Finite set B
• Singleton set C
• Set of all integers D

The function whose range consists of just one element is called

• One-One Function A
• Identity Function B
• Onto Function C
• Constant Function 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

If n(A) = n then n(P(A)) is

• 2n A
• n² B
• n/2 C
• 2ⁿ D

Z is a group under

• Subtraction A
• Multiplication B
• Addition C
• None of these D

A statement which is either true or false is called

• Induction A
• Deduction B
• Propositicon C
• Logic D

• An empty set A
• Universal set B
• A singleton set C
• None of these D

The set {-1, 1} is closed under the binary operation of

• Addition A
• Multiplication B
• Subtraction C
• Division D

To each element of a group there corresponds ______ inverse element

• Two A
• One B
• No C
• Three D

Every set is an improper subset of

• Empty set A
• Equivalent set B
• Itself C
• Singleton set D

The set of complex numbers forms

• Commutative group w.r.t addition A
• Commutative group w.r.t multiplication B
• Commutative group w.r.t division C
• Non commutative group w.r.t addition D

• An empty set A
• Universal set B
• A singleton set C
• None of these D

Which of the following statement is true?

• A set is a collection of non-empty object A
• A set is a collection of only numbers B
• a set is any collection of things C
• a set is well-defined collection of objects D

If B-A≠φ , then n(B-A) is equal to

• n(a)+n(c) A
• n(c)-n(a) B
• n(a)-n(c) C
• None of these 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

The set R is ........w.r.t subtraction

• Not a group A
• A group B
• No conclusion drawn C
• Non commutative group D

If f:A→B is an injective function and second elements of no two of its ordered pairs are equal, then f is called

• 1-1 and onto A
• Bijective B
• 1-1 and into C
• None of these D

The set of whole numbers is subset of

• The set on integers A
• The set of natural numbers B
• {1, 3, 5, 7, ....} C
• The set of prime numbers D

The complement of set A relative to universal set U is the set

• {x / x∈ A∧ x∈ U} A
• {x / x∉ A∧ x ∈ U} B
• {x / x∈ A and x ∉ U} C
• A-U 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

The set of integer is

• Finite group A
• A group w.r.t addition B
• A group w.r.t multiplication C
• Not a group D

• A = C A
• A = B B
• B = C C
• None of these D

If x = 1/x for x ∈ R then the value of x is

• ±1 A
• 0 B
• 2 C
• 4 D

A disjunction of two statement p and q is true

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

If A⊆ B, and B is a finite set, then

• n (a) < n(B) A
• n(B)<(A) B
• n(A)≤ n (B) C
• n(A)≥ n(B) D

A conditional is regarded as false only when the antecedent is true and consequent is

• True A
• False B
• Known C
• Unknown D