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CBSE Questions for Class 11 Engineering Maths Complex Numbers And Quadratic Equations Quiz 1 - MCQExams.com

Express 1(1cosθ+2isinθ) in the form x+iy
  • (15+3cosθ)+(2cotθ/25+3cosθ)i
  • (153cosθ)+(2cotθ/253cosθ)i
  • (15+3cosθ)+(2cotθ/25+3cosθ)i
  • (153cosθ)+(2cotθ/253cosθ)i
If z=x+iy and ω=(1iz)(zi), then |ω|=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 and c are real numbers then the roots of the equation (xa)(xb)+(xb)(xc)+(xc)(xa)=0 are always
  • Real
  • Imaginary
  • Positive
  • Negative
If (x+iy)(23i)=4+i then (x, y) =
  • (1,113)
  • (513,1413)
  • (513,1413)
  • (513,1413)
If z=3+5i, then z3+z+198=
  • 315i
  • 315i
  • 3+15i
  • 3+15i
If z=23i then z24z+13=
  • 0
  • 1
  • 2
  • 3
The complex number 1+2i1i lies in the quadrant :
  • I
  • II
  • III
  • IV
375=
  • 15
  • 15i
  • 15
  • 15i
The sum of two complex numbers a+ib and c+id is a real number if
  • a+c=0
  • b+d=0
  • a+b=0
  • b+c=0
The locus of complex number z such that z is purely real and real part is equal to - 2 is
  • Negative y-axis
  • Negative x-axis
  • The point (-2, 0)
  • The point (2, 0)
1i1+1i+1 is
  • positive rational number
  • purely imaginary
  • positive Integer
  • negative integer
The argument of every complex number is
  • Double valued
  • Single valued
  • Many valued
  • Triple valued
The sum of two complex numbers a+ib and c+id is purely imaginary if
  • a+c=0
  • a+d=0
  • b+d=0
  • b+c=0
For a<0, arg (ia)= 
  • π2
  • π2
  • π
  • π
The principal value of the argument of 3+i is :
  • π6
  • 3π6
  • 5π6
  • 7π6
Amplitude of 1+i1i is :
  • 0
  • π
  • π2
  • π
Which of the following equations has two distinct real roots ?
  • 2x232x+94=0
  • x2+x5=0
  • x2+3x+22=0
  • 5x23x+1=0
A quadratic equation ax2+bx+c=0 has two distinct real roots, if 
  • a=0
  • b24ac=0
  • b24ac<0
  • b24ac>0
For a>0, arg (ia)=
  • π2
  • π2
  • π
  • π
The modulus of 2i2i is:
  • 2
  • 2
  • 0
  • 22
The roots of the equation 3x24x+3=0 are :
  • real and unequal
  • real and equal
  • imaginary
  • none of these
For a<0,  arg a=
  • π2
  • π2
  • π
  • π
If the square of (a+ib) is real, then ab=
  • 0
  • 1
  • 1
  • 2
Find the argument of 1i3
  • θ=2π/3
  • θ=2π/3
  • θ=4π/3
  • θ=4π/3
The roots of x2x+1=0 are:
  • Real and equal
  • Real and not equal
  • Imaginary
  • Reciprocals
Nature of the roots of the quadratic equation 2x226x+3=0 is:
  • Real, irrational, unequal
  • Real, rational, equal
  • Real, rational, unequal
  • Complex
Determine the nature of roots of the equation x2+2x3+3=0.
  • Real and distinct
  • Non-real and distinct
  • Real and equal
  • Non-real and equal
Find the value of x of the equation (1i)x=2x 
  • 1
  • 2
  • 0
  • none of these
If the discriminant of a quadratic equation is negative, then its roots are:
  • unequal
  • equal
  • inverse
  • imaginary
Solve (1i)x+(1+i)y=13i,
  • x=1,y=2.
  • x=2,y=1.
  • x=2,y=1.
  • x=1,y=2.
The roots of 4x22x+8=0 are:
  • Real and equal
  • Rational and not equal
  • Irrational
  • Not real
Evaluate :
 25+34+29
  • 17i
  • 5i
  • 17i
  • 6i
If x22px+8p15=0 has equal roots, then p=
  • 3 or 5
  • 3 or 5
  • 3 or 5
  • 3 or 5
Determine the values of p for which the quadratic equation 2x2+px+8=0 has equal roots.
  • p=±64
  • p=±8
  • p=±4
  • p=±16
Find the values of k for the following quadratic equation, so that they have two real and equal roots:
2x2+kx+3=0
  • k=±23
  • k=±26
  • k=±6
  • k=±3
i4n+3+(i)8n3(i)12n1i216n,nεN is equal to
  • 1 + i
  • 2i
  • -2i
  • -1 - i
1+i2+i4+i6+........+i2n is
  • Positive
  • Negative
  • Zero
  • Cannot be determined
Find the modulus and the principal value of the argument of the number 1i
  • 2,π/4
  • 2,π/4
  • 2,π/3
  • 2,3π/4
If i2=1, then the value of 200n=1in is
  • 50
  • -50
  • 0
  • 100
If i = 1,then1+i2+i3i6+i8 is equal to -
  • 2- i
  • 1
  • -3
  • -1
Check whether 2x23x+5=0 has real roots or no.
  • The equation has real roots.
  • The equation has no real roots.
  • Data insufficient
  • None of these
(i10+1)(i9+1)(i8+1).......(i+1)  equal to 
  • -1
  • 1
  • 0
  • i
If i2 =1, then find the odd one out of the following expressions.
  • i2
  • (i)2
  • i4
  • (i)4
  • i6
When (32i) is subtracted from (4+7i), then the result is
  • 1+5i
  • 1+9i
  • 7+5i
  • 7+9i
The value of k for which polynomial x2kx+4 has equal zeroes is
  • 4
  • 2
  • 4
  • 2
If the discriminant of a quadratic equation is negative, then its roots are
  • Unequal
  • Equal
  • Inverses
  • Imaginary
If the equation (1+m2)x2+2mcx+(c2a2)=0 has equal roots, then c2= 
  • a2(1+m2)
  • a(1+m2)
  • a4(1m2)
  • a2(1m2)
Amplitude of 1+3i3+iis
  • π3
  • π2
  • 0
  • π6
For i=1, what is the sum (7+3i)+(8+9i)?
  • 1+12i
  • 16i
  • 15+12i
  • 156i
If the equation x2bx+1=0 does not possess real roots then
  • 3<b<3
  • 2<b<2
  • b>2
  • b<2
0:0:1


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