**1) 1+i ^{2}+i^{4}+i^{6}+……+i^{2n} is**

**a)**+ve

**b)**-ve

**c)**0

**d)**cannot be found

**2) i ^{2}+i^{4}+i^{6}+…..(2 n+1) terms =**

**a)**i

**b)**-i

**c)**1

**d)**-1

**3) If x + iy =****a)** **b)** **c)** **d)**

**4) If (a + ib) (c + id) (e + if) (g + ih)=A+ iB, then (a ^{2 }+ b^{2})(c^{2
}+ d^{2})(e^{2 }+ f^{2})(g^{2 }+ h^{2})**

=

**a)**

^{}

**b)**

^{}

**c)**

^{}

**d)**

^{}

**5) z ^{2} + (p + iq) z+ r + is=0 where p, q, r, s are non-zero has real
roots, then**

**a)**

^{}

**b)**

^{}

**c)**

^{}

**d)**

^{}

**6) If the amplitude of z -2 -3i=,
then the locus of z is**

**a)**x-y=2

**b)**x+y=0

**c)**x+y=1

**d)**x-y+1=0

**7) If is a cube root of unity
and (1+) ^{7}= A+B
then A and **

**a)**0,1

**b)**1,1

**c)**1,0

**d)**-1,1

**8) Let z and be two non-zero complex
numbers such that and Arg z + Arg
=
then z equals**

**a)**

**b)**

**c)**

**d)**

**9) The argument of the complex number
+ i is**

**a)**

**b)**

**c)**

**d)**

**10) If
then the locus of z is**

**a)**

**b)**

**c)**

**d)**none of these

**11) Let be two complex numbers
such that Then**

**a)**

**b)**

**c)**

**d)**none of these

**12) If are two pairs of conjugate
complex numbers, then arg equals**

**a)**0

**b)**

**c)**

**d)**

**13) If m, n, p, q are consecutive integers, then the value of
is**

**a)**1

**b)**4

**c)**0

**d)**none of these

**14) If then the value of
is**

**a)**-27

**b)**27

**c)**3

**d)**0

**15) Value of arg x when x < 0 is ****a)** 0**b)** **c)** **d)** none of these

**16) The value of is****a)** 1**b)** -1**c)** i**d)** -i

**17) If is a purely imaginary number,
then is equal to**

**a)**0

**b)**1

**c)**2

**d)**none of these

**18) If is an imaginary cube root
of unity, then the value of is**

**a)**-2

**b)**-1

**c)**1

**d)**0

**19) If , then the value of
is**

**a)**n

**b)**

**c)**0

**d)**none of these

**20) If for complex numbers is
equal to**

**a)**

**b)**

**c)**

**d)**0

**21) If ****a)** C + iS**b)** C – iS**c)** S + iC**d)** S – i C

**22) The number of solutions of the system of equations Re
is**

**a)**4

**b)**3

**c)**2

**d)**1

**23) The closest distance of the origin from a curve given as
is (a is a complex number)**

**a)**1

**b)**

**c)**

**d)**

**24) ****a)** an equilateral triangle**b)** a right angled triangle**c)** an isosceles triangle**d)** none of these

**25) If and locus of 5z – 1 is
the circle having radius a and
then **

**a)**a : 1

**b)**2a : 1

**c)**a : 10

**d)**none of these

**26) If and m and n be the least
and greatest values of and K be
the least value of on the interval
then K =**

**a)**n

**b)**m

**c)**n+m

**d)**none of these

**27) If is an imaginary cube root
of unity, then the value of **

**a)**

**b)**

**c)**

**d)**

**28) Common roots of the equations z ^{3}+2z^{2}+2z+1=0 and z^{1985
}+ z^{100} +1=0 are**

**a)**

**b)**

**c)**

**d)**none of these

**29) The value of is****a)** -1**b)** -2**c)** -3**d)** -4

**30) If are four complex numbers
represented by the vertices of a quadrilateral taken in this order such that
Then the quadrilateral is**

**a)**a square

**b)**a rectangle

**c)**rhombus

**d)**a cyclic quadrilateral

**31) If are three distinct complex
numbers and a, b, c are three +ve real numbers such that
then**

**a)**

**b)**

**c)**

**d)**none of these

**32) Consider which of the following
hold(s) good**

**a)**

**b)**

**c)**

**d)**

**33) ****a)** **b)** **c)** **d)** none of these

**34) If n > 1, then the roots of
lie on a**

**a)**circle

**b)**straight line

**c)**parabola

**d)**none of these

**35) For complex number where
then the angle between the roots of the equation
is**

**a)**

**b)**

**c)**

**d)**none of these

**36) If , where a, b, c are real
and is a non-real cube root of unity,
then**

**a)**

**b)**abc + bcd + and + acd = 4

**c)**a + b + c + d = -2a

**d)**

**37) If ****a)** **b)** **c)** **d)**

**38) If ****a)** 0**b)** **c)** **d)** none of these

**39) If is equal to****a)** **b)** 4**c)** **d)** none of these

**40) If ****a)** **b)** **c)** 1**d)** none of these

**41) If are conjugate complex numbers
and are also conjugate, then **

**a)**

**b)**

**c)**

**d)**

**42) If , then the locus of z is****a)** an ellipse**b)** a circle**c)** a parabola**d)** a st. line

**43) The complex number which satisfies the equation
is**

**a)**2+i

**b)**-2+i

**c)**-2-i

**d)**2-i

**44) For any complex number x + iy, put
Then which one of the following is true **

**a)**

**b)**a>b

**c)**

**d)**a = b + 2

**45) If and ,
then K =**

**a)**3

**b)**4

**c)**2

**d)**none of these

**46) If , then
is equal to**

**a)**

**b)**

**c)**

**d)**none of these

**47) is equal to****a)** **b)** **c)** **d)** none of these

**48) is equal to****a)** **b)** **c)** **d)** none of these

**49) If are two complex numbers such
that and
where then the angle between
and is**

**a)**

**b)**

**c)**

**d)**

**50) If at least one value of the complex number z = x + iy satisfy the condition
and the inequality ,
then**

**a)**a>2

**b)**a=2

**c)**a<2

**d)**none of these

**51) Given z is a complex number with modulus 1. Then the equation
has**

**a)**all roots, real and distinct

**b)**two roots real and two imaginary

**c)**three roots real and one imaginary

**d)**one root real and three imaginary

**52) **

**The locus of the complex number z in an argand plane satisfying the inequality
is**

(where )

**a)**a circle

**b)**an interior of a circle

**c)**the exterior of the circle

**d)**none of these

**53) If are the nth roots of unity,
then is equal to**

**a)**

**b)**

**c)**

**d)**none of these

**54) If p, q are two real numbers lying between 0 and 1 such that
and form an equilateral triangle,
then (p, q) =**

**a)**

**b)**

**c)**

**d)**none of these

**55) The origin and the roots of the equation
form an equilateral triangle if**

**a)**

**b)**

**c)**

**d)**

**56) Let z be a complex number such that
and arg , then z is equal to**

**a)**

**b)**

**c)**

**d)**

**57) Let 3-i and 2+i be affixes of two points A and B in the Argand plane and
P represents the complex number z = x + iy such that
Then the locus of P is**

**a)**a circle on AB as diameter

**b)**the line AB

**c)**the perpendicular bisector of AB

**d)**none of these

**58) The locus of the points representing the complex number z for which
is**

**a)**a circle with centre at the origin

**b)**a st. line passing through the origin

**c)**the single point (0.-2)

**d)**none of these

**59) Let z be a complex number (not lying on x-axis) of maximum modulus such
that . Then**

**a)**Im(z)=0

**b)**Re(z)=0

**c)**

**d)**none of these

**60) The value of a so that the sum of the squares of the roots of
the equation
assume
the least value, is**

**a)**2

**b)**0

**c)**3

**d)**1

**61) The number of values of a for which
is an identity in x is**

**a)**0

**b)**2

**c)**1

**d)**infinite

**62) The number of values of the pair (a, b) for which
is an identity in x is**

**a)**0

**b)**1

**c)**2

**d)**infinite

**63) The number of values of the triplet (a, b, c) for which
is satisfied by all real x is**

**a)**0

**b)**2

**c)**3

**d)**infinite

**64) The polynomial
has**

**a)**four real zeros

**b)**at least two real zeros

**c)**at most two real zeros

**d)**no real zeros

**65) The number of real solutions of the equation
is**

**a)**one

**b)**two

**c)**four

**d)**infinite

**66) The sum of the real roots of the equation
is**

**a)**4

**b)**0

**c)**-1

**d)**none of these

**67) The number of real solutions of the equation
is**

**a)**0

**b)**1

**c)**2

**d)**infinitely many

**68) The number of real solutions of
is**

**a)**0

**b)**1

**c)**2

**d)**4

**69) The equation
has **

**a)**one real solution

**b)**no real solution

**c)**infinitely many real solution

**d)**none of these

**70) The product of all the solutions of the equation
is**

**a)**2

**b)**-4

**c)**0

**d)**none of these

**71) The number of real solutions of the equation
is**

**a)**two

**b)**one

**c)**zero

**d)**none of these

**72) The number of real solutions of
is**

**a)**one

**b)**two

**c)**three

**d)**none of these

**73) If x is an integer satisfying
and
then the number of possible values of x is**

**a)**3

**b)**4

**c)**6

**d)**none of these

**74) If a , b, c are nonzero, unequal**

rational numbers then the roots of the equation

are

**a)**rational

**b)**imaginary

**c)**irrational

**d)**none of these

**75) If l, m, n are real and
then the roots of the equation
are **

**a)**real and equal

**b)**nonreal complex

**c)**real and unequal

**d)**none of these

**76) If a, b, c , d are four consecutive
terms of an increasing AP then the
roots of the equation (x-a)(x-c)+2(x-b)(x-d)
= 0 are**

**a)**real and distinct

**b)**nonreal complex

**c)**real and equal

**d)**integers

**77) If a, b, c are three distinct positive
real numbers then the number of real
roots of
is **

**a)**4

**b)**2

**c)**0

**d)**none of these

**78) The equation
has **

**a)**

**b)**

**c)**

**d)**

**79) The roots of ,
where
and coefficients are real, are nonreal complex and a + c < b. Then **

**a)**4a+c>2b

**b)**4a+c<2b

**c)**4a+c=2b

**d)**none of these

**80) If the roots
of the equation
are less than
3 then **

**a)**a<2

**b)**

**c)**

**d)**a>4

**81) If one root of the equation
is reciprocal of the other then k has the value **

**a)**

**b)**

**c)**1

**d)**both (a) and (b)

**82) If the ratio of the roots of
is equal to the ratio of the roots of
then
are in **

**a)**AP

**b)**GP

**c)**HP

**d)**none of these

**83) p, q, r and s are integers. If the AM of the roots
of
and GM of the roots of
are equal then **

**a)**q is an odd integer

**b)**r is an even integer

**c)**p is an even integer

**d)**s is an odd integer

**84) If
are roots of the equation
then the roots of the equation
are**

**a)**a, c

**b)**b, c

**c)**a, b

**d)**a+c, b+c

**85) If the roots of
differ by unity then the negative value of k is **

**a)**3

**b)**

**c)**

**d)**none of these

**86) If the product of the roots of the equation
is 8 then
is **

**a)**

**b)**

**c)**3

**d)**none of these

**87) If the roots of
are ,
and those of
are
such that
then **

**a)**

**b)**

**c)**

**d)**none of these

**88) If
are the roots of
then the equation
in y has the roots**

**a)**

**b)**

**c)**

**d)**

**89) If the roots of
change by the same quantity then the expression in a, b, c that
does not change is **

**a)**

**b)**

**c)**

**d)**none of these

**90) If
are the roots of
then the product of the roots of the quadratic equation
whose roots are
and
is **

**a)**

**b)**

**c)**

**d)**none of these

**91) If the sum of the roots of the quadratic equation
is equal to the sum of the squares of their reciprocals then
is equal to **

**a)**2

**b)**-2

**c)**1

**d)**-1

**92) If the absolute value of the difference of roots of the equation
exceeds **

** then ****a)** p<-1 or p>4**b)** p>4**c)** -1

**d)**

**93) If
are roots of
and
are the roots of
then
is equal to
**

**a)**q+r

**b)**q-r

**c)**-(q+r)

**d)**-(p+q+r)

**94) If
are roots of
and
then
is **

**a)**

**b)**

**c)**

**d)**none of these

**95) If a and b are rational and b is not a perfect square
then the quadratic equation with rational coefficients
whose one root is
is **

**a)**

**b)**

**c)**

**d)**none of these

**96) If
is a root of
, where a, b**

*are real, then*

**a)**a=25, b=-8

**b)**a=25, b=16

**c)**a=5, b=4

**d)**none of these

**97) If
be the roots of the equation
then the value of
is **

**a)**3

**b)**

**c)**

**d)**none of these

**98) The quadratic equations
and
have **

**a)**

**b)**

**c)**

**d)**none of these

**99) If
are three quadratic equations of which each pair has exactly
one root common then the number of solutions of the triplet
is**

**a)**2

**b)**1

**c)**9

**d)**27

**100) The set of possible values of
for which **

** has roots whose sum and product are both less than 1
is **

**a)**

**b)**(1, 4)

**c)**

**d)**none of these

**Answers**