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

Given X.Y are any 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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

If x = 1/x for x ∈ R then the value of x is

• ±1 A
• 0 B
• 2 C
• 4 D

For any set B,B∪B' is

• Is set B A
• Set B' B
• Universal set C

0 is a symbol of

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

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

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

Which of the following sets in infinite

• The set of students of your class A
• The set of all schools in Pakistan B
• The set of natural numbers between 3 and 10 C
• The set of rational numbers between 3 and 10 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

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

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

The set (Q, .)

• Forms a group A
• Does not form a group B
• Contains no additive identity C
• Contains no additive inverse 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

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

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

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

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

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

Which symbolic notation represent unary operation ?

• - A
• ∨ B
• ∧ C
• ⇔ D

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

• 1 A
• 12 B
• 5 C
• 29 D

If A⊆ B, and B is a finite set, then

• n (a) < n(B) A
• n(B)<(A) B
• n(A)≤ n (B) C
• n(A)≥ n(B) D

If A ⊆ B then A ∪ B is

• A A
• B B
• A' C
• A ∩B D

Which of the following statement is true?

• A set is a collection of non-empty object A
• A set is a collection of only numbers B
• a set is any collection of things C
• a set is well-defined collection of objects 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

• 
  A
• 
  B
• 
  C
• 
  D

Multiplicative inverse of "1" is

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

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

G = {e, a, b, c} is an Abelian group with e as identity element. The order of the other elements are

• 2, 2, 2 A
• 3, 3, 3 B
• 2, 2, 4 C
• 2, 3, 4 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