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CBSE Questions for Class 11 Engineering Maths Complex Numbers And Quadratic Equations Quiz 10 - MCQExams.com

(x2+1)2x2=0 has
  • four real roots
  • two real roots
  • no real roots
  • one real root
The argument of the complex number sin6π5+i(1+cos6π5) is
  • 6π5
  • 5π6
  • 9π10
  • 2π5
The equation 3x2+x+5=x3, where x is real, has 
  • no solution.
  • exactly one solution.
  • exactly two solutions.
  • exactly four solutions.
If z0=1i2,  then (1+z0)(1+z210)(1+z220)..........(1+z2n0)  must be
  • (1i)(1+122n) for n>1
  • (1i)(1122n) for n>1
  • 1+i2 for n>1
  • (1i)(1122n+1) for n>1
The number of solutions of log15log12(|z|2+4|z|+3)<0 is/are?
  • 0
  • 2
  • 4
  • infinite
Let α, β be real and z be a complex number. If z2+αz+β=0 has two distinct roots on the line Re(z)=1, then it is necessary that: 

  • β(0,1)
  • β(1,0)
  • |β|=1
  • β(1,)
Let z be a complex number and c be a real number  1 such that z + c|z+1|+i=0, then c belongs to 
  • [2,3]
  • (3,4)
  • [1,2]
  • None of these
lf logtan30(2|Z|2+2|Z|3|z|+1)<2 then
  • |z|<32
  • |z|>32
  • |z|>2
  • |z|<2
If x=2+5i(where 1i=1) and 2(11!9!+13!7!)+15!5!=2ab! then x35x2+33x10=
  • a+b
  • ba
  • ab
  • ab
  • (ab)(a+b)
If x=9139199127.....,y=4134194127...., and z=r=1(1+i)r, then arg(x+yz) is equal to
  • 0
  • tan1(23)
  • tan1(23)
  • tan1(23)
If |log3|z|2|z|+12+|z||<2, then
  • |z|<13
  • |z|=1
  • |z|=5
  • 1<|z|<5
Given z is a complex number with modulus 1. Then the equation in a, (1+ia1ia)4=z has
  • all roots real and distinct.
  • two real and two imaginary.
  • three roots real and one imaginary.
  • one root real and three imaginary.
Find the value of x such that (x+α)2(x+β)2α+β=sin2θsin2θ. when α and β are the roots of t22t+2=0
  • x=icotθ1
  • x=(icotθ+1)
  • x=icotθ
  • x=itanθ1
The complex numbers sinx+icos2x  and  cosxisin2x are conjugate to each other, for
  • x=nπ
  • x=(n+12)π
  • x=0
  • No value of x
If z1,z2 be two non zero complex numbers satisfying the equation |z1+z2z1z2|=1 then z1z2+(z1z2) is
  • zero
  • 1
  • purely imaginary
  • 2
Interpret the following equations geometrically on the Argand plane.
1<|z23i|<4
  • Annular
  • Straight line
  • A point
  • Ring
If n is a natural number 2, such that zn=(z+1)n, then
  • Roots of equation lie on a straight line parallel to the yaxis
  • Roots of equation lie on a straight line parallel to the xaxis
  • Sum of the real parts of the roots is [(n1)/2]
  • None of these
Dividing f(z) by zi, we obtain the remainder i and dividing it by z+i, we get the remainder 1+i, then remainder upon the division of f(z) by z2+1 is
  • 12(z+1)+i
  • 12(iz+1)+i
  • 12(iz1)+i
  • 12(z+i)+1
If b1b2=2(c1+c2), then at least one of the equations x2+b1x+c1=0 and x2+b2x+c2=0 has
  • imaginary roots
  • real roots
  • purely imaginary roots
  • none of these
Find the regions of the z-plane for which |zaz+¯a|<1,=1 or >1. when the real part of a is positive.
  • The required regions are the right half of the z-pane, the imaginary axis and the left half of the z-plane respectively.
  • The required regions are the left half of the z-pane, the imaginary axis and the right half of the z-plane respectively.
  • The required regions are the right half of the z-pane the real axis and the left half of the z-plane respectively.
  • The required regions are the left half of the z-pane the real axis and the right half of the z-plane respectively.
If α,β are the roots of equation (k+1)x2(20k+14)x+91k+40=0;(α<β), k>0, then 
The nature of the roots of this equation is
  • imaginary
  • real and distinct
  • equal real roots
  • None of these
If z be a complex number satisfying z4+z3+2z2+z+1=0 then  |z| is 
  •  12
  •  34
  •  1
  • None of these
Find the range of real number α for which the equation z+α|z1|+2i=0;z=x+iy has a solution. Find the solution.
  • x=5/2,y=2
  • x=2,y=5/2
  • x=5/2,y=2
  • x=2,y=5/2
(3+i2)6+(i32)6=
  • 2
  • 2
  • 1
  • 1
Let  z1=a+ib,z2=p+iq be two unimodular complex numbers such that  Im(z1z2)=1. If ω1=a+ip,ω2=b+iq then
  •  Re(ω1ω2)=1
  •  Im(ω1ω2)=1
  •  Rm(ω1ω2)=0
  •  Im(ω1¯ω2)=0
Find all complex numbers satisfying the equation 2|z|2+z25+i3=0
  • ±(62+12i);±(16+32i)
  • ±(6212i);±(2632i)
  • ±(6213i);±(1632i)
  • ±(6212i);±(1632i)
Let z=1+ib=(a,b)  be any complex number, a,b,ϵR and 1=i. Let z0+0i,argz=tan1(ImzRez) where π<argzπ 

arg(ˉz)+arg(z)={π,ifarg(z)<0π,ifarg(z)>0

Let z & w be non-zero complex numbers such that they have equal modulus values and argzargˉw=π, then z equals

  • w
  • w
  • ˉw
  • ˉw
The root of (x+a)(x+b)8k=(k2)2 are real and equal, when a,b,c ϵ R, then
  • a+b=0
  • a=b
  • k=3
  • k=0
If z=x+iy and w=(1iz)(zi), then |w|=1 implies that, in the complex plane
  • z lies on the imaginary axis
  • z lies on the real axis
  • z lies on the unit circle
  • None of these
If a,b,c are real distinct numbers satisfying the condition a+b+c=0, then the roots of the quadratic equation 3ax2+5bx+7c=0 are
  • positive
  • negative
  • real and distinct
  • imaginary
Find the modulus, argument and the principal argument of the complex numbers.
z=1+cos10π9+isin(10π9)
  • Principal Arg z=4π9;|z|=2cos4π9;Argz=2kπ4π9kϵl
  • Principal Arg z=10π9;|z|=2cos10π9;Argz=2kπ10π9kϵl
  • Principal Arg z=10π9;|z|=2cos10π9;Argz=2kπ4π9kϵl
  • Principal Arg z=4π9;|z|=2cos4π9;Argz=2kπ4π9kϵl
Find the modulus, argument and the principal argument of the complex numbers.
(tan1i)2
  • Modulus=sec21,Arg(z)=2nπ+(2π),Principal Arg(z)=(2π)
  • Modulus=cosec21,Arg(z)=2nπ(2π),Principal Arg(z)=(2π)
  • Modulus=sec21,Arg(z)=2nπ(2π),Principal Arg(z)=(2π)
  • Modulus=cosec21,Arg(z)=2nπ+(2π),Principal Arg(z)=(2π)
The set of all real values of p for which the equation x+1=px has exactly one root is
  • {0}
  • {4}
  • {0, 4}
  • {0,2}
If z1,z2,...,zn lie on |z|=r and Re(nj=1nk=1zjzk)=0, then
  • nj=1zj=0
  • |nj=1zj|=0
  • nj=11zj=0
  • None of these
Given that i=1, find the multiplicative inverse of 5i.
  • 5+i
  • 5+i26
  • 15+i
  • 5+i24
  • 5i24
Write the complete number 22i in polar form.
  • 2(cosπ4+isinπ4)
  • 2(cosπ4isinπ4)
  • 22(cos3π4+isin3π4)
  • 22(cos7π4+isin7π4)
  • 22(cos5π4+isin5π4)
If a>0 and discriminant of ax2+2bx+c is -ve then
|abax+bbcbx+cax+bbx+c0| is equal to
  • +ve
  • (acb2)(ax2+2bx+c)
  • -ve
  • 0
If (cosθ+isinθ)(cos2θ+isinθ) ....
(cosnθ+isinnθ)=1, then the value of θ is
  • 2mπn(n+1)
  • 4mπ
  • 4mπn(n+1)
  • mπn(n+1)
Add and express in the form of a complex number a+bi
(2+3i)+(4+5i)(93i)3
  • 4+9i
  • 5+9i
  • 2+9i
  • 5+8i
If z is a complex number such that |z|2 then the minimum value of |z+12| is
  • Is strictly greater than 52
  • Is strictly greater than 32 but less than 52
  • Is equal to 52
  • Lies in the interval (1,2)
If α and β are two different complex numbers with |β|=1, then |βα1ˉαβ| is equal to.
  • 0
  • 1
  • 12
  • 1
If the equation 4x2+x(p+1)+1=0  has exactly two equal roots , then one of the value of p is
  • 5
  • 3
  • 0
  • 3
Evaluate in standard form: (23i)(22i), where i2=1.
  • 54i4
  • 54+i4
  • 54i4
  • 54+i4
If z1,z2,..zn lie on the circle |z|=2 then the value of |z1,z2,..zn|4|1z1+1z2++1zn|=
  • 0
  • n
  • n
  • 1
Let z1 = 18 + 83i, z2 = 18 + 39i, ana z3= 78 + 99i. where i = 1. Let z be a unique comlpex number with the properties that z3z1z2z1 zz2zz3 is a real number and the imaginary part of the size z is the greatest possible.
  • Re(z)=56
  • Re(z)=61
  • Re(z)=54
  • Re(z)=59
If z=20i21+21+20i, then the principal value of arg 'z' can be 
  • π4
  • 3π4
  • 3π4
  • π4
What is i1000+i1001+i1002+i1003 equal to (where i=1)?
  • 0
  • i
  • i
  • 1
If Z1,Z2 are two complex numbers satisfying |Z13Z23Z1Z2|=1|z1|3 then |z2|=
  • 1
  • 2
  • 3
  • 4
A complex number z is said to be unimodular if |z|=. Suppose z1 and z2 are complex numbers such that z12z22z1¯z2 is unimolecolar and z2 is not unimodular. Then the point z1 lies on a:
  • straight line parallel to y-axis
  • circle of radius 2.
  • Circle of radius 2.
  • Staright line parallel to x-axis.
If z1+z2+z3=0 and |z1|=|z2|=|z3|=1, then area of triangle whose vertices are z1,z2 and z3 is:
  • 334
  • 34
  • 1
  • 2
0:0:2


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