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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