Chapter 1: Number System Notes
1)
A real number system contains
a)
Positive numbers
b)
Negative numbers
c) Zero d)
(option a, b and c)
2)
Rational number is a number which can be written
as a terminating decimal fraction or a
a)
Non-terminating decimal fraction
b)
Non-recurring
c)
Recurring decimal fraction
d)
a, b and c
3)
There is no element common in
a)
N and W b)
E and W
c) N and O d)
Q and Q
4)
The decimal fraction in which we have finite
number of digits in its decimal part is called a
a)
Recuring decimal fraction b) Non terminating fraction
c) Non recurring fraction d)
Terminating decimal fraction
5)
It is not possible to find the exact value
of
b)
9
c) 3 27
d)
1
6)
Sum of two real numbers is also a real number,
this property is called:
a)
Commutative property w.r.t addition
b)
Closure property w.r.t. addition
c)
Associative property w.r.t. addition
d)
Distributive property w.r.t addition
1
7)
If a x = 1 then this property is called a
a)
Multiplicative identity b)
Multiplicative inverse
c) Additive identity d)
Associative property
8)
1 is not a
a)
Real number
b)
Natural number
c) Prime number d) Whole
number
10)
There exist no rational number x, such that
a)
x2 = 4 b)
x = 9
c) x2 = 2
11)
If P is a whole number greater than 1, which has
only P and I are factors. Then P is called
a)
Whole number
b)
Prime number
c) Even numbers d)
Odd number
12)
24 can be written as a product of
a)
Odd factors
b)
Even factors
c) Whole factors d)
Prime factors
13)
Which of the following, has closure property
w.r.t. addition
a)
{1} b)
{1, 2}
c) {0} d)
{1, 1}
14)
If a < b, and c < 0, then
a)
ac = bc b)
ac = 0
c) a > b d)
a < b
15)
If 0 < a < b, then
a)
b = 0 b)
a + b = 0
c) 1
1 c)
1 1 a b a b
16)
If a < b, and c < 0, then
a)
ac = bc b)
ac
bc
c) ac
bc d)
ac > bc
17)
For any a
R
a)
a2 > 0 b)
a2 < 0
c) a2 0 d)
a2 0
18)
For all a, b, c,
R and a = b ac = bc ca = cb. This property is
called
a)
Multiplicative inverse b)
symmetric property
c) Multiplicative property d)
Identity element
19)
For all a, b
R, and a = b
b = a, this property is called
a)
Reflexive property b)
Multiplicative property
c) Additive property d)
Symmetric property
20)
Any real number can be written in the form of
a
a)
Natural number
b)
Complex number
c) Rational number d) Irrational
number
21)
In a complex number x + iy, y is called
a)
real number b)
imaginary number
c) even number d)
odd number
22)
Any real number x =
a)
(0,x) b)
(0 + xi)
c) (x, 0)
d)
(x + i)
23)
In the algebra of real numbers we can replace-1
with
a)
i b)
i2
c) |1|
d)
1
24)
The multiplicative identity for the set of a
complex number is
a)
(0, 1) b)
(1, 0)
c) (1 , 1)
d)
(,
0)
25)
If z1 = x1 + iy1,
and z2 = x2 + iy2, then z1z2
=
a)
(x1x2 – y1y2,
x1y2 + y1x2) b) (a1
+ a2 b1 + b2)
c) (a1a2 – b1b2)
d)
(x1y2 b1b2)
26)
If z = (x
, 0) and z lies on OX
where x > 0 then
=
a)
b)
2
c) d)
2
27)
Product of a complex number with its own
conjugate is a
a)
Prime number b)
Imaginary number
c)
real number d)
real and imaginary numbe r
28)
Which of the following has the same value as i63.
a)
1
b)
1 c)
i d)
i
29)
I
i2
a)
I b)
i
c) I
d)
0
34)
The equation |z + I| = 2, represents a
a)
triangle b)
ellipse
c) square
d)
circle
38)
One of the factor of 9x2 + 25y2
over the complex number is
a)
3x + 5y b)
5x – 5y
c) 3x + 5i
d)
3x + 5iy
39)
Argument of a complex number is
a)
unique quantity
b)
not a unique quantity
c) real number d)
a rational number
40)
r is called the
a)
amplitude b)
argument
c) modulus
d)
radian
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