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
• -1-a C
• None of these 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

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 A
• 3 B
• 2 C
• 1 D

If a = {2m/2m < 9 ,m€ p} , the (n A) =

• {2,3,4,5,6,7,8} A
• {2,4,6,8............16} B
• { 4, 6} C
• {2,3,5,7} 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

Two sets A and B are said to be disjoint if

• 
  A
• 
  B
• 
  C
• 
  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
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• none of these D

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

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

The set { {a, b} } is

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

The set (Z,+) forms a group

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

If p and q are two statements then their biconditional 'p if q' is denoted by

• 
  A
• 
  B
• 
  C
• 
  D

The set which has no proper subset is

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

If A is a subset of B and B contains at least one element which is not an element of A, then A is said to be

• Improper subset of B A
• Super set of B B
• Proper subset of B C
• None of these D

• A A
• B B
• U C
• None of these D

For any set X, X∪X is

• X A
• X' B
• Φ C
• Universal Set D

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

• 1 A
• -1 B
• ±1 C
• 0 D
• Does not exist E

Which of the following is the definition of singleton

• The objects in a set A
• A set having no element B
• A set having no subset C
• None of these D

• Addition A
• Multiplication B
• Division C
• Both addition and multiplication D

Empty set is

• Not subset of every set A
• Finite set B
• Infinite set C
• Not the member of real numbers D

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

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

• A A
• B B
• U C
• None of these D

The set {1, -1, i, -i}

• Form a group w.r.t addition A
• Form a group w.r.t multiplication B
• Does not form a group w.r.t multiplication C
• Not closed under multiplication 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 {Z\ {0} } is group w.r.t

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

• 1 A
• 12 B
• 5 C
• 29 D

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

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

The set {Z\{0}} is group w.r.t

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

• 
  A
• 
  B
• 
  C
• 
  D