This document contains a summary of Chapter 1 from the textbook "Algebra and Trigonometry Class XI" along with 43 multiple choice questions related to the chapter. The chapter discusses number systems including real numbers, rational numbers, integers, complex numbers, and their properties. The questions cover topics like conjugate complex numbers, addition and multiplication of complex numbers, properties of real and complex numbers, and finding real and imaginary parts of complex numbers.

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MCQs – Ch # 1: F.Sc Part 1
Text Book of Algebra and Trigonometry Class XI
Available online at http://www.mathcity.org, Version: 1.0.0
Chapter 1: NUMBER SYSTEMS
1)
A)
B)
C)
D)
2)
6)
3 is
The conjugate of – 6 + 3i
A) – 6 – 3i
B) – 6 + 3i
C) 6 + 3i
D) 6 – 3i
7)
The solution set of 5x + 8 = 0 when x ∈ N is
Rational
Irrational
Integer
Prime
Product
− 2 × − 2 is equal to
A) non empty set
A)
B)
C)
D)
3)
–2
2
0
4
B)
C)
8)
A) Z1 Z 2
B) Z1 + Z 2
4)
5)
9)
x>z
x<z
x=z
none of these
10)
A) = Z1 + Z 2
11)
C) ≤ Z1 + Z 2
6)
(- i )5 is
A)
B)
C)
D)
i
–1
1
–i
12)
x – iy
x + iy
– x – iy
{x/x2 + y2, - y /x2 + y2}
The conjugate of a complex number 5i
–5
5i
– 5i
5
The property used in this equation 3 x 7 = 7 x 3 is
called
A)
B)
C)
D)
D) = Z1 × Z 2
Commutative property under multiplication
Associative under multiplication
Distributive under multiplication
Commutative under addition
The additive inverse of a complex number x + yi
A)
B)
C)
D)
Z1 + Z 2 is
B) > Z1 + Z 2
For all x, y, z ∈ R, if (x y ) z = x (yz) then this
property is called
A)
B)
C)
D)
If x < y, y < z then
A)
B)
C)
D)
8
5
A)
B)
C)
D)
C) Z1 − Z 2
Z1
Z2
8
5
D) empty set
Z1 Z 2 =
D)
−
Closure law
Commutative law for addition
Commutative property w.r.t multiplication
Identity
The additive inverse of (-x, -y) is
A)
B)
C)
D)
(-x, -y)
(x, y)
(-x, 0)
(x, -y)

2. MCQs – Ch # 1: F.Sc Part 1
13)
called
The property used in the equation 8 + 0 = 8 is
A)
B)
C)
D)
2
20)
Commutative
Associative
Additive Identity
Additive Inverse
If Z1, Z2 be complex numbers then Z1 + Z 2 =
A) Z1 − Z 2
B) Z1 + Z 2
C) Z1 + Z 2
14)
For all a, b, c ∈ R, if (a + b) + c = a + (b + c) then
the property is called
A)
B)
C)
D)
15)
D) Z1 − Z 2
21)
Commutative under addition
Associative w.r.t addition
Distributive under addition
None of these
A) (a, - b)
B) (-a , b)
 a
2
2
a +b
 −a
D)  2
2
a +b
C) 
The inverse of an element ‘a’ under addition is
A)
1
a
If z = (a, b), then z –1 =
22)
A) a2 – b2
B) a2 + b2
The additive identity is
C)
a 2 − b2
D)
a 2 + b2
A)
B)
C)
D)
17)
23)
A)
B)
C)
D)
A) < z1 + z 2
B) ≤ z1 + z 2
C) > z1 + z 2
D) ≥ z1 + z 2
24)
1
5
¾
5/3
(- i )15 =
A)
B)
C)
D)
Real number
Irrational number
Complex number
Natural number
1 + 2i
=
2−i
If z1 and z2 are any two complex numbers then
z1 − z 2
Real number
Complex number
Irrational number
Natural number
The sum of two conjugate complex numbers is
always a
A)
B)
C)
D)
19)
0
–1
1
none of these
The product of two conjugate complex numbers is
always a
A)
B)
C)
D)
18)
2
If z = a + bi, then z =
B) - a
C) 1
D) 0
16)
−b 

a + b2 
b 
, 2

a + b2 
,
25)
If z1 = (a, b) and z2 = (c, d) then z1z2 =
A)
B)
C)
D)
26)
1
–1
i
–i
(ac – bd,
(ac + bd,
(ad + bc,
(ad – bd,
ad + bc)
cd – bc)
ac – bd)
ac + bd)
2x2 + 3y2 =
A) (2x + 3iy) (2x – 3iy)
B) ( 2 x + 3iy )( 2 x −
C) (2x – 3y) (2x + 3y)
D) ( 2 x +
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3iy )
3 y )( 2 x − 3 yi )
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3. MCQs – Ch # 1: F.Sc Part 1
27)
π ∈ _________
A) N
B) Q
C) Q/
D) none
28)
The magnitude of
37)
If x = 0, then multiplicative inverse of x is _______
A)
1
x
B) – x
C) 1
D) 0
E) none
38)
The real & imaginary part of
The complex No. (a + ib) can be written as ______
A)
5
,
8
5
B) ,
8
8
C) ,
5
The imaginary part of the complex Nos. (b, a) is
______
A) ia
B) b
C) a
D) none
32)
39)
If Z = I then Z = _________
If Z = − Z then Z is _________
40)
35)
i = _________
A) – 1
B) 1
C) 0
D) i
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If the area f triangle is 16, formed by the points Z,
Z+iZ
and
iZ
in
a
complex
plane,
then Z = ______
A) 16
If Z = −1 − i then Z = ________
A) (-1, -1)
B) (-1, 1)
C) (1, -1)
D) none
The value of in = _______ where n is an odd No.
A) – i
B) + i
C) ± i
D) None
A) real
B) imaginary
C) neither type
34)
2
5
−2
5
2
5
D) none
A) i
B) – i
C) ±1
D) none
33)
1
3
+
is
2+i 2−i
_____
A) (a, ib)
B) {a, b}
C) (a, b)
D) [a, b]
31)
1 + 2i
is _________
2 −i
A) 5 + 2i
B) – 1
C) 1
D) none
Every recurring ∈′ terminating decimal represents
A) Q
B) Q/
C) R
D) none
30)
36)
∀x ∈ R, x = x is called _______ property.
A) symmetric
B) reflexive
C) transitive
D) none
29)
3
B) 5 3
C) 4 2
D) none
41)
if x + iy = 5 – 6i
_______
2k
, then imaginary part (y) =
A) – 6
B) 6
C) 0
D) None
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4. MCQs – Ch # 1: F.Sc Part 1
42)
4
43)
is
A real number is always
The property used in the equation 7.8 + (- 7.8) = 0
A)
B)
C)
D)
A) A natural no
B) Positive integer
C) Rational number
D) Complex number
Commutative
Associative
Additive Identity
Additive inverse
****************************************************************************************
Written by NAUMAN IDREES
(nomi255@yahoo.com)
FSc (Session: 2007-09)
ICMS College System Hayatabad, Peshawar
Written by NAUMAN IDREES (nomi255@yahoo.com)
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