MCQ Questions For Class 11 Complex Numbers and Quadratic Equations with Answers

Students can refer to the following Complex Numbers and Quadratic Equations MCQ Questions for Class 11 Maths with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here a collection of multiple choice questions for Complex Numbers and Quadratic Equations Class 11 covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

Complex Numbers and Quadratic Equations MCQ Questions for Class 11 Maths with Answers

We have provided below Complex Numbers and Quadratic Equations MCQ Questions for Class 11 Maths with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As Complex Numbers and Quadratic Equations MCQs in Class 11 Mathematics pdf download can be really scoring for students, you should go through all problems provided below so that you are able to get more marks in your exams.

Question. The val ues of ( ) / 16 1 4 are
(a) ±2, ± 2 i
(b) ±4 , ± 4 i
(c) ±1, ± i
(d) None of these

Question: 

(a) (0, – 2)
(b) (-2, 0)
(c) (0, 2)
(d) (2, 0) 

Question:

Question: The real value of a for which the expression

Question: The value of 1 + i² + i⁴ + i⁶ +… + i²ⁿ is
(a) positive
(b) negative
(c) zero
(d) cannot be determined 

Question:

Question: The value of sum

(a) i
(b) i – 1
(c) – i
(d) 0 

Question: The real value of q for which the expression

Question:  If(1+i)²/2-i=X+iY,  then the value of x+y is equal to
(a) 5/2
(b) – 2/5
(c)2/5
(d) – 5/2 

Question: Given z=q+ir/1+P,, then p+iq/1+r=1+iz/1-iz, if
(a) p²+ q²+ r²=1
(b) p²+q²+r²=2 
(c) p₂+ q²-r²=1
(d) None of these 

Question: Two students while solving a quadratic equation in x, one copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term coefficient of x² correctly as -6 and 1 respectively the correct roots are
(a) 3,- 2 
(b) – 3, 2
(c) -6, 1
(d) 6, -1 

Question: If the roots of the given equation

Question: The coefficient of x in the equation x2+px+q=0 was taken as 17 in place of 13 its roots were found to be – 2and -15. The roots of the original equation are
(a) 3, 10,
(b) – 3 -10 ,
(c) – 5- 8 ,
(d) None of these 

Question: If P (x)= ax²+bx+c and Q(x) = – ax²+dx+c,where ac ≠0, then P(x) Q (x) = 0 has atleast
(a) four real roots
(b) two real roots
(c) four imaginary roots
(d) None of these 

Question: If the roots of (a²+b²)x²-2(bc+ad)x+c²+d²=0 are equal, then
(a) a/b=c/d 
(b) a/c+b/d=0
(c) a/d=b/c
(d) a+ b= c +d   

Question: If α,β,y are the roots of x³+2x²-3x-=0,then α-²+β^-2+y^-2 is equal to
(a) 12
(b) 13
(c) 14
(d) 15   

Question: If sin α sin β and cos α are in GP, then roots of x²+2x cot β+1=0  are always
(a) real
(b) real and negative
(c) greater than one
(d) non-real   

Question: If sin and cos a a are the roots of the equation ax²+bx+c=0, then
(a) a²-b²+2ac=0
(b) (a-c)²=b²+c²)
(c) a2+b²-2ac=0 
(d) a²+b²+2ac=0 

Question: If one root of equation x²+ax+12=0  is 4 while the equation x²+ax+b=0 has equal roots, then the value of b is
(a) 4/49
(b) 49/4
(c) 7/4
(d) 4/7 

Question: The solution set of the equation

Question: Let f (x)= x²+ax+b;a,b ∈R.If f (1)+f(2)+f (3)=0, then the roots of the equation f (x) = 0
(a) are imaginary
(b) are real and equal
(c) are from the set {1, 2, 3}
(d) real and distinct 

Question: If the product of the roots of the equation (a+1)x²+(2a+3)x+(3a+4)=0 is 2,, then the sum of roots is
(a) 1
(b) -1
(c) 2
(d) -2   

Question: If the roots of the equation ax²+bx+c=0 of the form 

Question:The system y^(x2+7x+12)=1 andx+y=6,y>0 has
(a) no solution
(b) one solution
(c) two solutions
(d) more than 2 solutions 

Question:

Question: If [x]²= [x+2],  where [x]= the greatest integer less than or equal to x, then x must be such that
(a) x = 2, 1, 
(b) [-1,0) ∪ [2 , 3)
(c) x ∈-[-1, 0)
(d) None of these   

Question: If(1+i/1-i)^x =1,then
(a) x = 2n + 1
(b) x = 4n
(c) x = 2n
(d) x = 4n + 1, where n ∈ N 

Question: The conjugate of

Question: If z-1/z+1is a purely imaginary number ( z≠ – 1), then the value of |z| is 
(a) –1
(b) 1
(c) 2
(d) –2 

Question: sin x+i cos 2x and cos x – i sin 2x are conjugate to each other for 
(a) x= nπ
(b) x =(n+1/2) π/2
(c) x = 0
(d) No value of x 

Question: If z = x + iy lies in the third quadrant, then 

also lies in the third quadrant, if 
(a) x > y > 0
(b) x < y < 0
(c) y < x < 0
(d) y > x > 0 

Question:

(a) 0
(b) 1/2
(c) 1
(d) 2   

Question: The value of ( z + 3)( ¯z + 3) is equivalent to
(a) | z + 3 |²
(b) | z – 3 |
(c) z² + 3
(d) None of these 

Question: If |z + 1|= z + 2 (1 + i), then the value of z is
(a)1/2- 2i
(b)1/2+ 2i
(c)1/2- 3i
(d)1/3- 2i   

Question:

Question:|z₁+z₂ |=|z₁ |+|z₂ | is possible, if 
(a) z2 ¯z₁ =
(b) z₂ =1/z₁
(c) arg (z₁) = arg (z₂)
(d) | z₁ | | z₂ |     

Question: If| z – 2|= min {|z – 1|,|z – 5|} , where z is a complex number, then
(a) Re (z) = 3/2
(b) Re (z) = 7/2
(c) Re (z ) ∈{3/2,7/2}
(d) None of these 

Question: If z is a comp lex num ber, then ( z-1)( z) is equal to
(a) 1
(b) -1
(c) 0
(d) None of these   

Question: If the points z₁,z₂ and z₃ and are the verti ces of anequilateral triangle in the complex plane, then the value of

Question: In the argand plane the complex number z = 4 – 3 i is
turned in the clockwise sense through 180° and stretched three times. The com plex num ber rep re sented by the new num ber is
(a) 12 + 9i
(b) 12 – 9i
(c) -12 – 9i
(d) -12 + 9i 

Question: In a given parallelogram, if the points P₁ and P₂ represent two complex numbers z₁ and z₂,then the point P₃ represents the num ber
(a) z₁+ z₂ 
(b) z₁– z₂ 
(c) z₁x z₂ 
(d) z₁÷ z₂ 

Question: The points rep re sented by the com plex num bers 1 + i, -2 +3 i and 5/3 i on the ar gand di a gram are
(a) vertices of an equilateral triangle
(b) vertices of an isosceles triangle
(c) collinear
(d) None of the above 

Question: Let z₁ and z₂ be the non-real roots of the equa tion 3z²+ 3z+b=0. If the ori gin to gether with the points rep re sented by z₁ and z₂ form an equi lat eral tri an gle, then the value of b is
(a) 1
(b) 2
(c) 3
(d) None of these

Question:

Question: If the comp lex num bers iz, z and z + iz rep re sent the three ver ti ces of a triangle, then the area of the triangle is

Question:

(a) 2
(b) 3
(c) 4
(d) 6 

Question: The area of the triangle whose Vertices are represented by the complex numbers 

Question: If the real part of

is 4, then the locus of the point representing z in the complex plane is
(a) a circle
(b) a parabola
(c) a hyperbola
(d) an ellipse 

Question:

Question: When z+ i/z+2 is purely imaginary, the locus described by the point z in the argand diagram is a
(a) circle of radius√5/2
(b) circle of radius 5/4
(c) straight line
(d) parabola

Question:

(a) 8
(b) 10
(c) 12
(d) None of these 

Question: The equation of a circle whose radius and centre are r and z₀ respectively, is

Question: If iz³+ z²– z +i =0,then |z| is equal to 
(a) 1
(b) i
(c) -1
(d) – i 

Question: The centre of the circle

Question:

(a) a straight line
(b) a circle
(c) a parabola
(d) an ellipse

Question: The maximum distance from the origin of coordinates to the point z satisfying the equation

Question: The value of  x⁴+9x³+35x²-x+4  for
x = – 5 + 2√-4 is
(a) 0
(b) –160
(c) 160
(d) –164 

Question: Let z₁,z₂ and  z₃ be the affixes of the vertices of a triangle having the circumcenter at the origin. If z is the affix of it’s orthocenter then z is equal to
(a)z₁+ z₂+ z₃
(b)z₁+ z₂+ z₃/2
(c) z₁+ z₂+ z₃ 
(d) None of these 

Question:

Question:

Question: The num ber of non-zero integral solutions of the equation |1 – i|^x = 2^x is
(a) infinite
(b) 1
(c) 2
(d) None of these 

Question:

Question: Given that the equation z²+(p+iq) z+ r+ is =0 where p, q, rand s are real and non-zero roots, then
(a) pqr = r² + p²s
(b) prs = q² + r²p
(c) qrs = p² + s²q
(d) pqs = s² + q²r 

Question:

Question. If x = a + b, y = aa + bb and z = ab + ba, where a and b are complex cube roots of unity, then xyz is equal to
(a) a² + b²
(b) a³ + b³
(c) a³b³
(d) a³ – b³

Question. If w( ¹ 1) is a cube root of unity and (1 ) , + w 7 = A + Bw then A and B are re spec tively
(a) 0 , 1
(b) 1, 1
(c) 1, 0
(d) -1, 1

Question. If w is a com plex cube root of unity, then for pos i tive in te gral value of n, the prod uct of w× w2 × w3 w ….. n will be 
(a) 1-i√3/2
(b) 1-I√3/2
(c) 1 
(d) Both (b) and (c)

Question. Com mon roots of the equa tions z₃+z₂ + 2z + 1 = 0 and  z¹⁹⁸⁵ + z¹⁰⁰ = 0 are
(a) ω, ω²
(b) ω, ω³
(c) ω² ω³ ,
(d) None of these

Question. If a₁ , a₂ , …, a_{n -1} are n roots of unity, then the value of (1- a₁ ) (1- a₂) (1- a₃) . . . (1- a_n-1) is equal to
(a) 3
(b) 1/2
(c) n
(d) 0

Question. If Im (z-1/2z+1) = -4, then lo cus of z is
(a) an ellipse
(b) a parabola
(c) a straight line
(d) a circle

Question. In the ar gand plane the com plex num ber z = 4 – 3 i is turned in the clock wise sense through 180° and stretched three times. The com plex num ber rep re sented by the new num ber is
(a) 12 + 9i
(b) 12 – 9i
(c) -12 – 9i
(d) -12 + 9i

Question. If the com plex num bers z z 1 2 and and the origin from an equilateral triangle, then z₁² + z₂² is equal to
(a) z₁z₂
(b) z₁z₂
(c) z₂z₁
(d) |z₁|² = |z₂|²

Question. In a given parallelogram, if the points P₁ and P₂ represent two complex numbers z₁ and z₂,then the point P₃ represents the number

(a) z₁ + z₂ 
(b) z₁ – z₂ 
(c) z₁ x z₂ 
(d) z₁ + z₂

Question. Let z1 and z2 be the non-real roots of the equa tion 3z2 + 3z + b = . If the ori gin to gether with thepoints  rep re sented by z1 and z2 and form an equi lat eral tri an gle, then the value of b is
(a) 1
(b) 2
(c) 3
(d) None of these

Question. Locus of z, if arg (z-1/z+1) = π/2 , is
(a) a circle
(b) a semi-circle
(c) a straight line
(d) None of these

Question. The lo cus of the points z which sat isfy the con di tion arg (z-1/z+1) = π/3 , is
(a) a straight line
(b) a circle
(c) a parabola
(d) None of these

Question. Let z be a complex number and a be a real parameter such that z₂ + ax + a₂ = 0, then
(a) locus of z is a pair of straight lines
(b) locus of z is a circle
(c) arg (z) = ± 5π/3
(d) |z | = – 2|a |

Question. If z₁ , z₂ , z₃  and z₄ are the af fixes of four points in the ar gand plane and z is the af fix of a point, such that
|z – z₁|=|z – z₂|=|z – z₃|=|z – z₄|, then and are
(a) concyclic
(b) vertices of a parallelogram
(c) vertices of a rhombus
(d) in a straight line

Question. Let z and ω be com plex num bers such that z + iw = 0 and arg ( zω) = p. Then, arg (z̄) is equal to
(a) π /4
(b) π /2
(c) 3π /4
(d) 5π /2

Question. If |z₂ – | |z|2 + 1 = + 1 then z lies on 
(a) the real axis
(b) the imaginary axis
(c) a circle
(d) an ellipse

Question. The points rep re sented by the com plex num bers 1 + i, -2 + 3i and 5/3 on the ar gand di a gram are 
(a) vertices of an equilateral triangle
(b) vertices of an isosceles triangle
(c) collinear
(d) None of the above

Question. If the area of the triangle on the complex plane formed by the points z, z + iz and iz is 200, then the value of |3 z| must be equal to
(a) 20
(b) 40
(c) 60
(d) 80

Question. Re( z ) 2 = 1 is rep re sented by
(a) the circle x² + y²  = 1
(b) the hyperbola x² – y² = 1
(c) parabola or a circle
(d) All of these

Question. If the comp lex num bers iz, z and z + iz rep re sent the three ver ti ces of a tri an gle, then the area of the tri an gle is
(a) 1/2|z|²
(b) |z|²
(c) 1/2|z – 1|
(d) |z – 1|²

Question. The area of the tri an gle whose ver ti ces are rep re sented by the com plex num bers 0, z zei , a,(0 < a < p) is equal to
(a) 1/2|z|² cosα
(b) 1/2|z|² sinα
(c) 1/2|z|² sinαcosα
(d) 1/2|z|²

Question.|z-2/z+2| =π/6 , then the lo cus of z is
(a) a straight line
(b) a circle
(c) a parabola
(d) an ellipse

Question. If z1 and z2 are two non-zero com plex num bers such that |z1 + z2| = |z2| |z1| + |z2|  then arg ( z2 ) arg is equal to
(a) -π/2
(b) 0
(c) -π
(d) π/2 

Question. If z and w are two non-zero com plex num bers such that |zw|= 1 and arg ( z) – arg (w) = , π/2 then z̄w is equal to
(a) 1
(b) -1
(c) i
(d) – i

Question. If the real part of z̄+2/z̄-1 is 4, then the lo cus of the point representing z in the com plex plane is
(a) a circle
(b) a parabola
(c) a hyperbola
(d) an ellipse

Question. The equa tion of a cir cle whose ra dius and centre are r and z0 respectively, is
(a) zz̄ – zz̄₀ – z̄z₀ + z₀z̄₀ = r²
(b) zz̄ + zz̄₀ – z̄z₀ + z₀z̄₀ = r²
(c) zz̄ – zz̄₀ + z̄z₀ – z₀z̄₀ = r²
(d) None of the above

Question. If z³ + z² – z + i = 0, then |z| is equal to
(a) 1
(b) i
(c) -1
(d) – i

Question. The centre of the circle
zz̄ – (2 + 3i) z – (2 – 3i)z̄ + 9 = 0 is
(a) (2, – 3)
(b) (2, 3)
(c) (-2, – 3)
(d) (-2, 3)

Question. The num ber of non-zero in te gral so lu tions of the equa tion |1 – i|x = 2x is 
(a) infinite
(b) 1
(c) 2
(d) None of these

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