Download chap # 1 number systems

Chapter 1
1)
NUMBER SYSTEMS
Answer:
Z1 Z 2
B)
Z1  Z 2
C)
Z1  Z 2
D)
Z1
Z2
A)
B)
C)
D)
10)
x>z
x<z
x=z
none of these
B
Answer:
11)
Z1  Z 2 is
 Z1  Z 2
B)
 Z1  Z 2
Answer:
C)
 Z1  Z 2
12)
D)
 Z1  Z 2
Answer.
(- i )5 is
A)
B)
C)
D)
i
–1
1
–i
Answer:
D
6)
The conjugate of – 6 + 3i
A) – 6 – 3i
B) – 6 + 3i
C) 6 + 3i
D) 6 – 3i
Answer:
A
The property used in this equation 3 x 7 = 7 x 3 is
called
Answer:
13)
Closure law
Commutative law for addition
Commutative property w.r.t multiplication
Identity
C
The additive inverse of (-x, -y) is
A)
B)
C)
D)
C
–5
5i
– 5i
5
C
A)
B)
C)
D)
A)
x – iy
x + iy
– x – iy
{x/x2 + y2, - y /x2 + y2}
C
The conjugate of a complex number 5i
A)
B)
C)
D)
If x < y, y < z then
Commutative property under multiplication
Associative under multiplication
Distributive under multiplication
Commutative under addition
B
The additive inverse of a complex number x + yi
Answer:
A
8
5
For all x, y, z  R, if (x y ) z = x (yz) then this property
is called
A)
B)
C)
D)
9)
8
5
D) empty set
D
Answer:
A)
Answer:
6)
Answer:
8)
Z1Z 2 
A)
B)
C)
D)
5)
C)
A
Answer:
4)
 2   2 is equal to
–2
2
0
4
Answer:
3)
B) 
Rational
Irrational
Integer
Prime
B
Product
A)
B)
C)
D)
The solution set of 5x + 8 = 0 when x  N is
A) non empty set
3 is
A)
B)
C)
D)
2)
7)
(-x, -y)
(x, y)
(-x, 0)
(x, -y)
B
The property used in the equation 8 + 0 = 8 is called
A) Commutative
B) Associative
C) Additive Identity
D) Additive Inverse
Answer:
C
14)
For all a, b, c  R, if (a + b) + c = a + (b + c) then the
property is called
A)
B)
C)
D)
Answer:
15)
21)
If z = (a, b), then z –1 =
A) (a, - b)
B) (-a , b)
Commutative under addition
Associative w.r.t addition
Distributive under addition
None of these
B
 a
2
2
a b
 a
D)  2
2
a b
C) 
The inverse of an element ‘a’ under addition is
Answer:
A)
1
a
22)
B) - a
C) 1
D) 0
Answer:
16)
The additive identity is
Answer:
17)
Answer:
18)
Answer:
Real number
Irrational number
Complex number
Natural number
A
1  2i

2i
A)
B)
C)
D)
Answer:
Real number
Complex number
Irrational number
Natural number
A
The sum of two conjugate complex numbers is always a
A)
B)
C)
D)
19)
0
–1
1
none of these
A
C
If z = a + bi, then
1
5
¾
5/3
23)
z
a 2  b2
D)
a 2  b2
D
If z1 and z2 are any two complex numbers then
z1  z2
A)
 z1  z2
B)
 z1  z2
C)
 z1  z2
D)
 z1  z2
Answer:
24)
B
(- i )15 =
A)
B)
C)
D)
1
–1
i
–i
Answer:
25)
C
If z1 = (a, b) and z2 = (c, d) then z1z2 =
A)
B)
C)
D)
Answer:
A
C)
Answer:
The product of two conjugate complex numbers is always a
A)
B)
C)
D)
2
A) a2 – b2
B) a2 + b2
B
A)
B)
C)
D)
b 

a  b2 
b 
, 2

a  b2 
,
26)
(ac – bd,
(ac + bd,
(ad + bc,
(ad – bd,
A
ad + bc)
cd – bc)
ac – bd)
ac + bd)
2x2 + 3y2 =
A) (2x + 3iy) (2x – 3iy)
20)
If Z1, Z2 be complex numbers then Z1  Z 2 
A) Z1  Z 2
B) Z1  Z 2
C) Z1  Z 2
D) Z1  Z 2
Answer:
B
B) ( 2 x  3iy )( 2 x 
C) (2x – 3y) (2x + 3y)
D) ( 2 x 
Answer:
B
27)
3 y )( 2 x  3 yi )
  _________
A) N
3iy )
B) Q
C) Q/
D) none
Answer:
28)
B) 1
C) 0
D) i
C
x  R, x  x is called _______ property.
A) symmetric
B) reflexive
C) transitive
D) none
Answer:
A
29)
Every recurring  terminating decimal represents
Answer:
36)
37)
30)
The complex No. (a + ib) can be written as ______
Answer:
38)
D
The real & imaginary part of
5
,
8
5
B) ,
8
8
C) ,
5
The imaginary part of the complex Nos. (b, a) is ______
A)
A) ia
B) b
C) a
D) none
32)
1
x
B) – x
C) 1
D) 0
E) none
A
Answer:
C
If Z  I then Z  _________
Answer:
33)
D) none
39)
C
The value of in = _______ where n is an odd No.
A) – i
B) + i
C) ± i
D) none
A
If Z   Z then Z is _________
1
3

is _____
2i 2i
2
5
2
5
2
5
Answer:
A) i
B) – i
C) ±1
D) none
1  2i
is _________
2i
If x = 0, then multiplicative inverse of x is _______
A)
A) (a, ib)
B) {a, b}
C) (a, b)
D) [a, b]
Answer:
C
31)
The magnitude of
A) 5 + 2i
B) – 1
C) 1
D) none
Answer:
C
A) Q
B) Q/
C) R
D) none
Answer:
B
Answer:
D
A) real
B) imaginary
C) neither type
40)
34)
If Z  1  i then Z  ________
A) (-1, -1)
B) (-1, 1)
C) (1, -1)
D) none
Answer:
B
35)
i  _________
A) – 1
If the area f triangle is 16, formed by the points Z, Z+iZ
and iZ in a complex plane, then
Z  ______
A) 16
B)
5 3
C) 4 2
D) none
Answer:
41)
C
if x + iy = 5 – 6i 2k, then imaginary part (y) = _______
A) – 6
B) 6
C) 0
D) none
Answer:
42)
C
A real number is always
A) a natural no
B) positive integer
C) Rational number
D) complex number
Answer:
C
43)
The property used in the equation 7.8 + (- 7.8) = 0 is
A)
B)
C)
D)
Answer:
Commutative
Associative
Additive Identity
Additive inverse
D