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

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

• 
  A
• 
  B
• 
  C
• 
  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

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

For any set X, X∪X is

• X A
• X' B
• Φ C
• Universal Set 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

• 
  A
• 
  B
• 
  C
• 
  D

In a country, 55% of the male population has houses in cities while 30% have houses both in cities and in village. Find the percentage of the population that has house only in villages.

• 45 A
• 30 B
• 25 C
• 50 D

The set of natural is a semi group w.r.t

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

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

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

Z is a

• Infinite set A
• Finite set B
• Singleton set C
• Set of all integers 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 n(X) = 18, n(X∩Y) = 7, n(X∪ Y) = 40 then n(Y) =

• 1 A
• 12 B
• 5 C
• 29 D

• A A
• A' B
• U C
• None of these D

• Biconditional A
• Implication B
• Antecedent C
• Hypothesis D

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

• 1 A
• 2 B
• 3 C
• 4 D

Multiplicative inverse of 0 is

• 0 A
• 1 B
• +-1 C
• Does not exist D

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

• 2n A
• n² B
• n/2 C
• 2ⁿ 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

A = B if

• 
  A
• 
  B
• 
  C
• A is equivalent to B D

The statement that a group can have more than one identity elements is

• True A
• False B
• Ambiguous C
• Some times true D

Φset is the ______ of all sets?

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

A set having only one element is called

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

• 
  A
• 
  B
• 
  C
• 
  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 contra positive of p → q is

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

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

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

• 
  A
• A B
• A' C
• U D

• 
  A
• 
  B
• 
  C
• 
  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