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

Every set is an improper subset of

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

• 
  A
• 
  B
• 
  C
• 
  D

{1, 2, 3, 4,.....} is set of ______

• Natural numbers A
• Whole numbers B
• Integers C
• Rational numbers D

In set builder notation the set {0, 1, 2, ............, 100} can be written as

• 
  A
• 
  B
• 
  C
• 
  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

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

• True A
• False B
• Fallacious C
• Some times true 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

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

0 is a symbol of

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

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

• 
  A
• 
  B
• 
  C
• 
  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

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

If P = {x/x = p/q where p,q∈ Z and q≠ 0}, then P is the set of

• Irrational numbers A
• Even numbers B
• Rational numbers C
• Whole numbers D

The number of subsets of B = {1,2,3,4,5}

• 10 A
• 32 B
• 16 C
• 5 D

Which of the following sets is finite

• The set of natural numbers between 3 and 10 A
• The set of rational numbers between 3 and 10 B
• The set of real numbers between 0 and 1 C
• The set of rational numbers between 0 and 1 D

If z1 = 2 + 6i and z2 = 3 + 7i then which expression defines the product of z1 and z2

• 36 +(-32)i A
• -36+32i B
• 6+(-11)i C
• 0, +(-12)i D

For a set A, A∪Ac= ---------------------

• A A
• ∅ B
• Ac C
• U 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

• 
  A
• 
  B
• 
  C
• 
  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

If B⊆ A, then complement of B in A is = -----------------------

• A-B A
• A∩B B
• B-A C
• A∪B D

• square root function A
• identity function B
• linear function C
• quadratic function D

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

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

• Addition A
• Multiplication B
• Division C
• Subtraction 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

Every subset of a finite set is

• Disjoint A
• Null B
• Finite C
• Infinite D

The set which has no proper subset is

• {0} A
• {} B
• {∅} 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