**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 z_{1} and z_{2} are

non zero complex numbers such that | z_{1} + z_{2} |

= | z_{1} | + | z_{ 2} |; then Arg z_{1}

– 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 z_{1} and z_{2} 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 z^{n} = ( 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 x ^{2} + 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 ax^{2}+2cx+b=0

and ax^{2} + 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 ax^{2}+bx+c = 0,á then

**a)**

a^{2}-b^{2}+2ac =

0

**b)**

(a+c)^{2} = b^{2}+c^{2}

**c)**

a^{2}+b^{2}-2 ac =

0

**d)**

(a-c)^{2}=b^{2}+c^{2}

**43) **

If the difference of the corresponding roots of

the equationá x^{2}+px+q = 0 and x^{2}+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

ax^{2}+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
3^{1/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 x^{2}-2ax+a^{2}+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 ax^{2}+

bx + c = 0 is reciprocal of the one root of the equation a_{1}x^{2}+

b_{1}x +c_{1} = 0, then

**a)**

(cc_{1}– aa_{1})^{2} =

(ba_{1} – b_{1}c) (ab_{1}-c_{1}b)

**b)**

(ab_{1}– a_{1}b)^{2} =

(bc_{1}-b_{1}c) (ca_{1}-c_{1}a)

**c)**

(bc_{1}– b_{1}c)^{2}

= (ca_{1}– a_{1}c) (ab_{1}– a_{1}b)

**d)** None of the given

**50) **

If the ratio of the roots of the equation

x^{2}+px+q=0 be equal to the ratio of the roots of x^{2}+lx+m=0,

then

**a)**

p^{2}m = q^{2 }l

**b)**

pm^{2} = q^{2 }l

**c)**

p^{2 }l = q^{2}m

**d)**

p^{2}m = l^{2 }q

**51) ****a)** a > 0**b)**

b^{2} < 4 ac

**c)** c > 0**d)** a and b are of opposite signs

Answers