1) If 
is a root of the equation 
then the other root is
a) 
b) 
c) 
/5
d) none of these
2) If 
are the real roots of 
and 
are
the roots of 
then the equation 
has always
a) two real roots
b) two negative roots
c) two positive roots
d) none of these
3) If a,b,c are rational and no two of them are equal then the equations
and
a) have rational roots
b) will be such that at least one has rational roots
c) have exactly one root common
d) both a and c
4) The equations 
and 
have
one and only one root common. Then
a) a-b=0
b) a-b+2=0
c) 
d) All the above
5) If 
has no real roots and p, q,r are real such that 
then
a) p-q+r<0
b) p-q+r>0
c) p+r=q
d) all of these
6) For the equation 
a) roots are rational
b) 
c) roots are irrational
d) None of the above
7) 
is a factor of 
if
a) 
b) 
c) 
d) All the above
8) If a, b are the real roots 
and c, d are the real roots of 
then (a-c)(b-c)(a+d)(b+d) is divisible by
a) a+b+c+d
b) a+b-c-d
c) a-b+c-d
d) Both a and b
9) A quadratic equation whose roots are 
and 
,
where 
are the roots of 
,
is
a) 
b) 
c) 
d) none of these
10)
If z1 and z2 are
non zero complex numbers such that | z1 + z2 |
= | z1 | + | z 2 |; then Arg z1
– Arg z
a)
– p
b)
-( p/2 )
c) 0
d)
p/2
11) 
a) -1
b) 0
c) -i
d) i
12) 
a) A Circle
b) A Straight Line
c) An Ellipse
d) None of the given
13) 
a) |z| = 1
b) |z| > 1
c) |z| < 1
d) None of the given
14)
The equation of the right bisector of the line
joining z1 and z2 is
a) 
b) 
c) 
d) None of the given
15) 
a) n – 1
b) n
c) -1
d) 1
16) 
a) 1
b) 2
c) 3
d) 4
17) 
a) a = 2, b = -1
b) a = 1, b = 0
c) a = 0, b = 1
d) a = – 1 , b = 2
18) 
a) -3
b) -2
c) -1
d) 0
19) If the area of the triangle on the complex plane formed by the points z , z + iz and iz is 50, then | z | is
a) 1
b) 5
c) 10
d) None of the given
20) 
a) 1
b) 2
c) < 1
d) > 1
21) 
a) a
b) b
c) c
d) d
22) 
a) Zero
b) real and positive
c) real and negative
d) purely imaginary
23) 
a) 4 , 7
b) -4, -7
c) -4, 7
d) 4, -7
24) 
a) 
b) 
c) 
d) 
25) The inequality | z – 2 | < | z - 4 | represents the half plane
a) 
b) Re (z) = 3
c) 
d) None of the given
26)
If n is a positive integer greater than unity,
and z is a complex number satisfying the equation zn = ( z + 1
)n , then
a) Re (z) < 0
b) Re (z) > 0
c) Re (z) = 0
d) None of the given
27) 
a) all roots real and distinct
b) two real and two imaginary roots
c) three roots real and one imaginary
d) one roots real and three imaginary
28) 
represent points P,Q on the locus 
and the line segment PQ subtends an angle 
at the point z=1 then 
is equal to
(i)  |
(ii)  |
(iii)  |
(iv)  |
a) i and iii
b) ii and iii
c) iii and iv
d) none of these
29) If 
then the equation
has
a) one positive root and one negative root
b) both roots positive
c) both roots negative
d) nonreal roots
30) 
a) a circle of radius 1
b) 
c) a line through the origin
d) a circle on the line joining 1 and -i as diameter
31) If 
has equal integral roots then
a) b and c are integers
b) b and c are even integers
c) b is an even integer and c is a perfect square of a positive integer
d) none of these
32) If z = 1 + I, then the multiplicative inverse of 
is
a) 1 – i
b) 
c) -i/2
d) 2 i
33) 
a) a right angled triangle
b) an equilateral triangle
c) isosceles triangle
d) scalene triangle
34) The inequality 
represents
the half plane
a) 
b) Re(z)>3
c) Re(z)=3
d) none of these
35) If 2a+3b+6c=0, then at least one root of the equation 
a) (0,1)
b) (1,2)
c) (2,3)
d) none of these
36) 
all
are real, then the quadratic equation 
a) at least one root in (0,1)
b) one root in (1,2) and the other in (3,4)
c) one root in (-1,1) and the other in (-5,-2)
d) both roots imaginary
37) If 
then the number of values of x is
a) 2
b) 4
c) 1
d) none of these
38) If a>1, roots
of the equation 
are
a) non positive and one negative
b) both negative
c) both positive
d) both nonreal complex
39) Let a, b, c be three real numbers such that 2a+3b+6c=0.
Then the quadratic equation 
has
a) imaginary roots
b) at least one root in (0, 1)
c) at least one root in (-1, 0)
d) both roots in (1,2)
40)
If a and b
are the roots of x2 + px + q= 0 , then the equation has
a) two real roots
b) two positive roots
c) two negative roots
d) one positive and one negative roots
41)
If the quadratic equation ax2+2cx+b=0
and ax2 + 2bx + c = 0 (b ¦ c)
have a common root, then a+ 4b+4c is equal to
a) 0
b) 1
c) 2
d) -1
42)
If Cos a, Sin a
be the roots of the equations ax2+bx+c = 0,á then
a)
a2-b2+2ac =
0
b)
(a+c)2 = b2+c2
c)
a2+b2-2 ac =
0
d)
(a-c)2=b2+c2
43)
If the difference of the corresponding roots of
the equationá x2+px+q = 0 and x2+qx+p=0
be the same then
a) p+q+4=0
b) p+q-4=0
c) p-q-4=0
d) None of the given
44)
If a, b, c Î R ,
then the roots of the quadratic equation a (x-b) (x-c) + b (x-a) (x-c) + c
(x-a) (x-b) = 0 are
a) real
b) imaginary
c) in determinate
d) none of these
45)
The sum of the roots of the quadratic equation
ax2+bx+c = 0 is equal to the sum of the squares of their
reciprocals, then a/c , b/a , c/b are in
a) AP
b) GP
c) HP
d) None of the given
46)
If the equation (3X)2 +
(27 x
31/p – 15) X + 4 = 0 has equal roots, then p is
equal
a) -1/2
b) 1/2
c) -1/3
d) 1/3
47) If a, b, c are real and a + b + c=0, then the quadratic equation 4ax+3bx+2c = 0 has
a) one positive and one negative root
b) imaginary roots
c) two real roots
d) None of the given
48)
If the roots of the equation á x2-2ax+a2+a-3=0
are real and less than 3, then
a) a < 2
b)
2 ú
a ú
c)
3 <
a ú 4
d) a > 4
49)
If one root of the equation ax2+
bx + c = 0 is reciprocal of the one root of the equation a1x2+
b1x +c1 = 0, then
a)
(cc1– aa1)2 =
(ba1 – b1c) (ab1-c1b)
b)
(ab1– a1b)2 =
(bc1-b1c) (ca1-c1a)
c)
(bc1– b1c)2
= (ca1– a1c) (ab1– a1b)
d) None of the given
50)
If the ratio of the roots of the equation
x2+px+q=0 be equal to the ratio of the roots of x2+lx+m=0,
then
a)
p2m = q2 l
b)
pm2 = q2 l
c)
p2 l = q2m
d)
p2m = l2 q
51) 
a) a > 0
b)
b2 < 4 ac
c) c > 0
d) a and b are of opposite signs
Answers