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
• 
  B
• 
  C
• 
  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

Let A,B and C be any sets such that A∪B = A∪C and A∩ B = A∩ C then

• A = B A
• B = C B
• A≠ C C
• A ≠ B D

The multiplicative inverse of x such that x = 0 is

• -x A
• Does not exist B
• 1/x C
• ±1 D

The set R is ______ w.r.t subtraction

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

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

• 
  A
• 
  B
• 
  C
• none of these D

A monoid (G, *) is said to be group if

• have identity element A
• is commutative B
• have inverse of each element C
• None of these D

Φ set is the _______ of all sets

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

If n(X) = 18, n(X∩Y) = 7, n(X∪ Y) = 40 then n(Y) =

• 1 A
• 12 B
• 5 C
• 29 D

• A = C A
• A = B B
• B = C 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

{0} is a

• Empty set A
• Singleton set B
• Zero set C
• Null Set D

• 
  A
• 
  B
• 
  C
• 
  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
• -1-a C
• None of these D

Z is a group under

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

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

Which of the following has the same value as i113

• i A
• -1 B
• -i C
• 1 D

Which symbolic notation represent unary operation ?

• - A
• ∨ B
• ∧ C
• ⇔ D

The graph of a quadratic function is

• Circle A
• Ellipse B
• Parabola C
• Hexagon D

• A A
• B B
• A'B' C
• B'A D

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

• 
  A
• 
  B
• 
  C
• 
  D

Multiplicative inverse of "1" is

• +- 1 A
• 0 B
• 1 C
• None of these D

• A A
• B B
• A' C
• None of these D

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

• Addition A
• none of these B
• Division C
• Subtraction D

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

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

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

A set having only one element is called

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