ECAT Mathematics
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ECAT Mathematics
Chapter 1: Number System
97 Questions
90 Minutes
Pass: 60%+
ECAT Prep
0
Which of the following is NOT a real number?
A
√2
B
π
C
√(-1)
D
0
1
Natural numbers are denoted by:
A
Z
B
N
C
Q
D
R
2
Which property states a+b = b+a?
A
Associative
B
Commutative
C
Distributive
D
Identity
3
The additive identity is:
A
0
B
1
C
-1
D
∞
4
The multiplicative identity is:
A
0
B
1
C
-1
D
1/a
5
Every rational number is of the form:
A
p/q where q≠0
B
p/q where q=0
C
non-terminating irrational
D
complex number
6
Which is irrational?
A
0.333...
B
0.5
C
√3
D
3/4
7
The absolute value of -7 is:
A
−7
B
7
C
1/7
D
49
8
If |x| = 5, then x =
A
5 only
B
−5 only
C
5 or −5
D
25
9
Integers include:
A
Only positive numbers
B
Positive, negative whole numbers and zero
C
All fractions
D
All real numbers
10
a(b+c) = ab+ac is the:
A
Commutative
B
Associative
C
Distributive
D
Closure
11
The reciprocal of a non-zero a is:
A
a
B
−a
C
1/a
D
a²
12
Which set has infinitely many elements?
A
Empty set
B
Vowels
C
Natural numbers
D
Days in week
13
1/3 = 0.333... is:
A
Terminating
B
Non-terminating repeating
C
Non-terminating non-repeating
D
Finite
14
Zero is:
A
Positive
B
Negative
C
Neither positive nor negative
D
Imaginary
15
If a<b and b<c then:
A
a>c
B
a<c
C
a=c
D
c<a
16
Complex numbers C contains:
A
Only reals
B
Only imaginary
C
Real and imaginary numbers
D
Only integers
17
Conjugate of z = a+bi is:
A
a−bi
B
−a+bi
C
−a−bi
D
a+bi
18
Modulus of 3+4i is:
A
7
B
5
C
1
D
25
19
Which is complex?
A
5
B
√2
C
2+3i
D
7/3
20
Real part of 5−3i is:
A
5
B
−3
C
3
D
−5
21
Imaginary part of 2+7i is:
A
2
B
7
C
−7
D
i
22
i² =
A
1
B
−1
C
i
D
−i
23
i⁴ =
A
−1
B
1
C
i
D
−i
24
(a+bi)+(a−bi) =
A
0
B
2a
C
2bi
D
|z|²
25
N ⊂ Z ⊂ Q ⊂ R means:
A
Naturals ⊂ Integers ⊂ Rationals ⊂ Reals
B
Reals ⊂ Rationals ⊂ Integers ⊂ Naturals
C
Integers ⊂ Naturals ⊂ Q ⊂ R
D
Q ⊂ Z ⊂ N ⊂ R
26
(a+bi)(a−bi) =
A
Imaginary
B
Real (a²+b²)
C
Zero
D
Negative real
27
An irrational number between 1 and 2:
A
1.5
B
√2
C
4/3
D
7/5
28
(2+3i)+(1−i) =
A
3+2i
B
3+4i
C
1+4i
D
3−2i
29
Additive inverse of −5 is:
A
5
B
−5
C
1/5
D
−1/5
30
Integers closed under addition: example:
A
3+(−3)=0 (integer)
B
3+1/2=3.5
C
√2+1=irrational
D
none
31
i³ =
A
−i
B
i
C
−1
D
1
32
A number both rational and irrational:
A
Exists
B
Does not exist
C
Is zero
D
Is ∞
33
{x∈N : x<1} =
A
{}
B
{{0}}
C
{1}
D
{0,1}
34
|x−3|<2 means x ∈:
A
(1,5)
B
(5,1)
C
[−1,5]
D
(0,6)
35
Non-distributivity is:
A
A property
B
Not a property of reals
C
The same as associativity
D
True for some reals
36
π is:
A
Rational
B
Integer
C
Irrational
D
Imaginary
37
√2 × √3 =
A
√6
B
√5
C
6
D
2√3
38
Rationals ∪ Irrationals =
A
Naturals
B
Integers
C
Real numbers
D
Complex numbers
39
|ab| =
A
|a|+|b|
B
|a|×|b|
C
|a|−|b|
D
|a|/|b|
40
5 is both integer and:
A
Whole number
B
Natural number
C
Rational number
D
All of the above
41
(a+b)+c = a+(b+c) is:
A
Commutative
B
Associative
C
Distributive
D
Identity
42
i²+1 =
A
0
B
1
C
−2
D
2
43
(2+i)⁻¹ =
A
(2−i)/5
B
(2−i)/3
C
(2+i)/5
D
1/(2+i)
44
[−3,7) represents:
A
−3<x<7
B
−3≤x<7
C
−3≤x≤7
D
−3<x≤7
45
Integers between −2 and 3 exclusive:
A
4
B
5
C
6
D
3
46
a⁰ = (a≠0):
A
0
B
1
C
a
D
undefined
47
Whole numbers start from:
A
1
B
0
C
−1
D
2
48
a>0, b>0 → a/b is:
A
Irrational
B
Always positive
C
Always negative
D
Zero
49
√4 =
A
Irrational
B
Imaginary
C
Rational (=2)
D
Complex only
50
−2x>6 is equivalent to:
A
x>−3
B
x<−3
C
x>3
D
x<3
51
Q−Z contains:
A
All integers
B
Non-integer fractions
C
Irrationals
D
Complex numbers
52
i¹⁰⁰ =
A
1
B
−1
C
i
D
−i
53
Real number line contains:
A
Only positive
B
All integers
C
All real numbers
D
Only rationals
54
|a|=|b| implies:
A
a=b only
B
a=−b only
C
a=b or a=−b
D
a=b=0
55
Conjugate of real a is:
A
a
B
−a
C
ai
D
1/a
56
De Moivre's theorem relates complex numbers to:
A
Polynomials
B
Trigonometry
C
Matrices
D
Series
57
−√5 is:
A
Rational
B
Natural
C
Irrational
D
Imaginary
58
Every real number is complex with imaginary part:
A
1
B
−1
C
0
D
undefined
59
Even integers closed under:
A
Addition and multiplication
B
Division
C
Subtraction only
D
None
60
0.121212... is:
A
Irrational
B
Rational
C
Imaginary
D
Neither
61
|2x−1|=3 gives x=
A
x=2 or x=−1
B
x=1 or x=−1
C
x=2 or x=1
D
x=3 or x=−3
62
Z⁺ denotes:
A
All integers
B
Positive integers
C
Non-negative integers
D
Whole numbers
63
For z=r(cosθ+i sinθ), |z|=
A
θ
B
r²
C
r
D
cosθ
64
Archimedean property: for any real x, ∃ n∈N with:
A
n<x
B
n>x
C
n=x
D
n≤x
65
1 radian ≈
A
57.3°
B
45°
C
90°
D
180°
66
(a+bi)(a−bi) =
A
a²−b²
B
a²+b²
C
2ab
D
0
67
{x∈R: x²=−1} =
A
{}
B
{i,−i}
C
{1,−1}
D
{0}
68
If c<0, then a<b implies:
A
ac<bc
B
ac>bc
C
ac=bc
D
ac≤bc
69
22/7 is:
A
Equal to π
B
Rational
C
Irrational
D
Imaginary
70
Between any two reals there are:
A
No numbers
B
Exactly one
C
Infinitely many
D
At most two
71
Principal √16 =
A
−4
B
±4
C
4
D
8
72
z+z̄ = 2a means:
A
Twice imaginary part
B
Twice real part
C
Zero
D
Imaginary
73
Distance between a and b on number line:
A
a+b
B
a−b
C
|a−b|
D
|a+b|
74
N is NOT a field because:
A
No inverses for multiplication
B
No additive inverses
C
No closure
D
No identity
75
|3−4i|² =
A
7
B
25
C
12
D
−7
76
√2+√3 is:
A
Rational
B
Irrational
C
Integer
D
Complex
77
Empty set {} is subset of:
A
No set
B
Every set
C
Universal set only
D
Singleton sets
78
(a+b)² =
A
a²+b²
B
a²+2ab+b²
C
a²−2ab+b²
D
2a+2b
79
Integers closed under subtraction:
A
Yes, a−b∈Z
B
No, may be fractional
C
Only for positives
D
Only for naturals
80
0 is:
A
Positive
B
Negative
C
Neither
D
Imaginary
81
−(−a) =
A
−a
B
a
C
0
D
2a
82
Polar (modulus-argument) form: r(cosθ+i sinθ) is also called:
A
Cartesian
B
Polar
C
Algebraic
D
Standard
83
Natural numbers also called:
A
Whole numbers
B
Counting numbers
C
Integers
D
Rationals
84
∈ means:
A
Subset of
B
Element of
C
Equal to
D
Greater than
85
|x|<3 means:
A
(−3,3)
B
(−∞,−3)∪(3,∞)
C
[−3,3]
D
(3,∞)
86
1 is:
A
Prime
B
Composite
C
Neither prime nor composite
D
Even
87
√(−9) =
A
3
B
−3
C
3i
D
−3i
88
Real part of (3+4i)/(1+i) is:
A
3.5
B
1.5
C
3
D
4
89
Number of real cube roots of −8:
A
1
B
2
C
3
D
0
90
Integers strictly between 1 and 2:
A
0
B
1
C
2
D
None
91
|a+b| ≤ |a|+|b| is:
A
De Morgan law
B
Triangle inequality
C
Cauchy-Schwarz
D
AM-GM
92
0.25 =
A
1/4
B
1/3
C
2/5
D
3/8
93
Algebraic number is a root of:
A
Any equation
B
Polynomial with rational coefficients
C
Transcendental equation
D
Trigonometric equation
94
Complex numbers with b=0 are:
A
Empty set
B
Real numbers
C
Imaginary
D
Natural numbers
95
If a+b√2=0 with a,b rational, then:
A
a=√2, b=0
B
a=0 and b=0
C
a=b
D
a=2b
96
|x| is always:
A
Negative
B
Non-negative
C
Positive
D
Zero
0
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