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

The set which has no proper subset is

• {0} A
• {} B
• {∅} C
• None of these D

For any set X, X∪X is

• X A
• X' B
• Φ C
• Universal Set D

The set of complex numbers forms a group under the binary operation of

• Addition A
• Multiplication B
• Division C
• Subtraction 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

Φ set is the _______ of all sets

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

The contra positive of p → q is

• q → p A
• ~q→~q B
• ~p→~q C
• None of these D

If a 1-1 correspondence can be established b/w two sets A and B, then they are called

• Equal sets A
• Equivalent sets B
• Over lapping sets C
• None of these D

The number of different ways of describing a set is

• One A
• Two B
• Three C
• Four D

0 is a symbol of

• singleton set A
• Empty set B
• Equivalent set C
• Infinite set 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

If E = { } , then P(E)

• ∅ A
• { } B
• {(2),(4),(6)....} C
• (∅) D

• A A
• B B
• A' C
• None of these D

Group of none-singular matrices under multiplication is

• None-Abelian group A
• Semi group B
• Abelian group C
• None of these D

If A and B are two sets then any subset R of B x A is called

• relation on A A
• relation on B B
• relation from A to B C
• relation from B to A D

Onto function is also called

• Binjective function A
• Injective function B
• Surjechive function C
• None of these D

If A = {x/x is a positive integer and 4≤x<23}, then A=

• {1,2,3,4,5,6,7} A
• {4,5,6...........22} B
• {1,2,3,.........23} C
• {1,2,3,4,5} D

The set { {a,b} } is

• Infinite set A
• Singleton set B
• Two points set C
• Empty set D

If p and q are two statements then their conjunction is denoted by

• 
  A
• 
  B
• 
  C
• 
  D

The identity element of a set X with respect to intersection in P(x) is

• X A
• Does not exist B
• ∅ C
• None of these D

The total number of subsets that can be formed out of the set {a, b, c} is

• 1 A
• 4 B
• 8 C
• 12 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

If A∩B=B, then n(A∩B) is equal to

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

A conditional "if p then q" is denoted by

• 
  A
• 
  B
• 
  C
• 
  D

Identity w.r.t intersection in a power set of any set is

• ∅ A
• Set itself B
• Singleton set C
• {0} D

The set (Z, +) forms a group

• Forms a group w.r.t addition A
• Forms a group w.r.t multiplication B
• Non commutative group w.r.t multiplication C
• Doesn't form a group D

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 function {f(x,y)|y = ax2 +bx +c} is

• One-one function A
• Constant function B
• Onto function C
• Quadratic function D

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

• domain A
• range B
• relation C
• function 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

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