MCQ Questions Chapter 5 Complex Numbers and Quadratic Equations Class 11 Mathematics

Please refer to MCQ Questions Chapter 5 Complex Numbers and Quadratic Equations Class 11 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 11 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 11 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 5 Complex Numbers and Quadratic Equations in Class 11 Mathematics provided below to get more marks in exams.

Chapter 5 Complex Numbers and Quadratic Equations MCQ Questions

Please refer to the following Chapter 5 Complex Numbers and Quadratic Equations MCQ Questions Class 11 Mathematics with solutions for all important topics in the chapter.

MCQ Questions Answers for Chapter 5 Complex Numbers and Quadratic Equations Class 11 Mathematics

Question. If in polar form z₁ = (1, α), z₂= (1, β), z₃ = (1, γ) and z₁ + z₂ + z₃ = 0, then z̄₁ + z₂ + z₃  is equal to
(a) 1
(b) 0
(c) –1
(d) None of these

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

Question. If α = cos (2π/7) + isin(2π/7) then the qua dratic equa tion whose roots are α = a +a2 + a4 and β = a3 + a5 + a6  is
(a) x² – x + 2 = 0
(b) x² + x – 2 = 0
(c) x² – x – 2 = 0
(d) x² + x + 2 = 0

Question. Given that the equa tion 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. If |z – iRe ( z)|=|z – Im ( z)| (where i = √-1), then z lies on
(a) Re (z) = 2
(b) Im (z) = 2
(c) Re (z) + Im (z) = 2
(d) None of the above

Question. If z₁ z₂ and be complex numbers such that z₁ ≠ z₂ and|z₁| = |z₂| If z1 has positive real part and z₂ has negative imaginary part, then [( z₁ + z₂ )/( z₁ – z₂ )]may be
(a) purely imaginary
(b) real and positive
(c) real and negative
(d) None of the above

Question. If |z₁| |z₂| = , arg (z₁ /z₂ ) = p, then z₁ + z₂ is equal to
(a) 0
(b) purely imaginary
(c) purely real
(d) None of these

Question. If |z|<√2 – 1, then |z₂ + 2zcosα | is
(a) less than 1
(b) 2 + 1
(c) 2 – 1
(d) None of these

Question. If ω =z /z-i/3 and |w|= 1, then z lies on
(a) a parabola
(b) a straight line
(c) a circle
(d) an ellipse 

Question. The imag i nary part of
( z – 1)(cos – i sin ) + ( z – 1)- ´ (cos + i sin ) a a 1 a a is zero, if
(a) |z – 1 | = 2
(b) arg (z – 1) = 2a
(c) arg (z – 1) = a
(d) |z | = 1

Question. If cos a + cos b + cos g = sin a + sin b + sin g = 0, then cos 3a + cos 3 b + cos 3 g is equal to
(a) 0
(b) cos (a + b + g)
(c) 3 cos (a + b + g)
(d) 3 sin(a + b + g)

Question. Let z1 and z2 be two roots of the equa tion z2 + az + b = 0, be ing com plex. Fur ther, as sume that the or i gin z1 and z2 form an equi lat eral tri an gle.
Then, 
(a) a² = b
(b) a² = 2b
(c) a² = 3b 
(d) a² = 4b 

Question. If A(z₁), B(z₂) and C(z₃) are the vertices of the DABC such that ( z₁ – z₂ )/( z₃ – z₂ ) = (1√2) – (i1√2) , then ΔABC is
(a) equilateral
(b) right angled
(c) isosceles
(d) obtuse angled

Question. If z₁ , z₂ , z₃ and are the vertices of an equilateral ΔABC such that |z₁ – i| |z₂ -i| |z₃ – i|, then
|z₁ + z₂ + z₃ | is equal to
(a) 3√3
(b) √3
(c) 3
(d) 1/3√3

Question. If z₁ = a + ib and z₂ = c+id 2  are com plex num bers such that |z₁| |z₂|= 1 and Re( z₁z₂ ) = 0 then the pair of com plex num bers ω1 = a + ic and ω2 = b + id satisfies
(a) |w₁| = 1
(b) |w₂ | = 1
(c) Re|w₁w₂ | = 0
(d) None of these   

Question. If |z₁| |z₂| = 1 and amp z₁ + amp  z₂ = 0, then
(a) z_1z2 = 1
(b) z₁ + z₂ = 0
(c) z₁ = z₂ 
(d) None of these  

Question. If |z₁| 1 = 15 and |z₂– 3 – 4i|= 5 then
(a) | z₁ – z₂ |min = 5
(b) | z₁ – z₂ |min = 10
(c) | z₁ – z₂ |max = 20
(d) | z₁ – z₂ |max = 25 

Question. Complex number z1 z̄2 is   
(a) purely real
(b) purely imaginary
(c) zero
(d) None of the above

Question. Complex number z1/z2 / is
(a) purely real
(b) purely imaginary
(c) zero
(d) None of these

Question. One of the possible argument of complex number i( z1 / z2 )
(a) π/2
(b) – π/2
(c) 0
(d) None of these

Question. If z is a complex number of unit modulus and argument θ, then arg (1+z/1+z) is equal to
(a) -q
(b) π/2 -θ
(c) q
(d) π – q

Question. If z ≠ 1 and z²/z-1 is real, then the point represented by the complex number z lies 
(a) either on the real axis or on a circle passing through the origin 
(b) on a circle with centre at the origin
(c) either on the real axis or on a circle not passing through the origin
(d) on the imaginary axis

Question. If w(≠ 1) is a cube root of unity and (1 )+ w 7 = A + Bw . 
Then, (A, B) is equal to
(a) (1, 1)
(b) (1, 0)
(c) (-1, 1)
(d) (0, 1)

Question. The equa tion zz̄ + (2 – 3 i) z + (2 + 3 i)z̄ + 4 = 0 rep re sents a cir cle of ra dius
(a) 2
(b) 3
(c) 4
(d) 6

Question. When z+i/z+2 is purely imag i nary, the lo cus de scribed by the point z in the ar gand di a gram is a
(a) circle of radius √5/2
(b) circle of radius 5/4
(c) straight line
(d) parabola

Question. The number of complex numbers z such that |z – 1|=|z + 1|=|z – i| is equal to 
(a) 0
(b) 1
(c) 2
(d) ∞

Question. If |z-4/z| =2 then the maximum value of| z| is equal to [AIEEE 2009]
(a) √3 + 1
(b) √5 + 1
(c) 2
(d) 2 +√2

Question. If |z + 4|£ 3, then the max i mum value of |z + 1| is
(a) 4
(b) 10
(c) 6
(d) 0

Question. If the cube roots of unity are 1 2 , wand w , then the roots of the equa tion (x – 1) + 8 = 0, 3 are 
(a) -1 1 + 2ω 1 + 2ω²
(b) -1 1 – 2ω – 2 , 1-2ω²
(c) -1, -1, -1
(d) -1 -1 + 2ω -1 – 2ω²

Question. If (1+i/1-i)^x = 1 then
(a) x = 4n, where n is any positive integer
(b) x = 2n, where n is any positive integer
(c) x = 4n + 1, where n is any positive integer
(d) x = 2n + 1, where n is any positive integer

Question. If ω is an imag i nary cube root of unity, then (1 + ω – ω2) 7 is equal to
(a) 128 ω
(b) -128 ω
(c) 128 ω²
(d) -128 ω²

Question. If z = r(cos θ + i sin θ), then the value of z/z̄ + z̄/z is
(a) cos 2θ
(b) 2 cos 2θ
(c) 2 cos θ
(d) 2 sin θ 

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. arg z̄ + arg z; z ≠ 0 is equal to :
(a) π/4
(b) π
(c) 0
(d) π/2 

Question. If z = x + iy, z^1/3 = a – ib and x/a – y/b = k(a² – b²), then value of k equals
(a) 2
(b) 4
(c) 6
(d) 1 

Question. If z = 3–i/2+i +3+i/2–i , then value of arg (zi) is
(a) 0
(b) π/6
(c) π/3
(d) π/2 

Question. If  (1–i /1+i)¹⁰⁰ = a+ib then
(a) a = 2, b = – 1
(b) a = 1, b = 0
(c) a = 0, b = 1
(d) a = – 1, b = 2   

Question. Simplify the complex numbers given in column-I and match with column-II. 

Codes:
     A B C
(a) 1 2 3
(b) 2 1 3
(c) 3 1 2
(d) 2 3 1 

Question. If a root of the equations x² + px + q = 0 and x² + αx + β = 0 is common, then its value will be (where p ≠ α and q ≠ β)

Question. If one root of the equation x² + px +12 = 0 is 4, while the equation x² + px + q = 0 has equal roots , then the value of ‘q’ is
(a) 4
(b) 12
(c) 3
(d) 49/4 

Question. The number of real roots of (x + 1/x)³ + (x + 1/x) = 0 is
(a) 0
(b) 2
(c) 4
(d) 6

Question. If 4x + i(3x – y) = 3 + i(–6), where x and y are real numbers, then the values of x and y are
(a) x= 3/5 and y= 33/4
(b) x= 3/4 and y= 22/3
(c) x= 3/4 and y= 33/4
(d) x= 3/4 and y= 33/5 

Question. If the roots of 4x² + 5k = (5k + 1)x differ by unity, then the negative value of k is
(a) –3
(b) –5
(c) – 1/5
(d) – 3/5 

Question. Value of (cosθ+ isinθ)⁴/(cosθ– isinθ)³is
(a) cos 5θ + i sin 5θ
(b) cos 7θ + i sin 7θ
(c) cos 4θ + i sin 4θ
(d) cosθ + i sin θ 

Question. If | z₂ – 1| = |z |² + 1, then z lies on
(a) imaginary axis
(b) real axis
(c) origin
(d) None of these 

Question. 1 + i² + i⁴ + i⁶ + … + i²ⁿ is
(a) positive
(b) negative
(c) 0
(d) cannot be determined 

Question. If z = 2 + i, then (z – 1) (z̄ – 5) + (z̄ – 1) (z – 5) is equal to
(a) 2
(b) 7
(c) –1
(d) –4 

Question. Sum of all real roots of the equation | x – 2 | ² + | x – 2 | – 2 = 0 is
(a) 2
(b) 4
(c) 5
(d) 6

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 = i⁹ + i1⁹, then z is equal to a + ai. The value of ‘a’ is
(a) 0
(b) 1
(c) 2
(d) 3 

Question. Roots of x2 + 2 = 0 are ± n i . The value of n is
(a) 1
(b) 2
(c) 3
(d) 4

Question. A number z = a + ib, where a and b are real numbers, is called
(a) complex number
(b) real number
(c) natural number
(d) integer 

Question. The modulus of √2i – √–2i is:
(a) 2
(b) √2
(c) 0
(d) 2√2 

Question. If z = 2 – 3i, then the value of z² – 4z + 13 is
(a) 1
(b) –1
(c) 0
(d) None of these 

Question. If a > 0, b > 0, c > 0, then both the roots of the equation ax² + bx + c = 0.
(a) Are real and negative
(b) Have negative real parts
(c) Are rational numbers
(d) None of these 

Question. The multiplicative inverse of 3 + 4i/4 – 5i is
(a) 8/25 – 31/25 i
(b) – 8/25 – 31/25 i
(c) – 8/25 + 31/25 i
(d) None of these 

ASSERTION – REASON TYPE QUESTIONS

(a) Assertion is correct, Reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, Reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, Reason is incorrect
(d) Assertion is incorrect, Reason is correct.

Question. Assertion : Let f(x) be a quadratic expression such that f(0) + f(1) = 0. If –2 is one of the root of f(x) = 0, then other root is 3/5.
Reason : If α and β are the zeroes of f(x) = ax² + bx + c, then sum of zeroes =– b/a , product of zeroes = c/a  

 Question. Assertion : Consider z₁ and z₂ are two complex numbers such that |z₁| = |z₂| + |z₁ – z₂|, then  Im (z₁/z₂) = 0.
Reason : arg(z) = 0 ⇒ z is purely real. 

Question. Assertion : If |z₁ + z₂|² = |z₁|² + |z₂|², then z₁/z₂ is purely imaginary.
Reason : If z is purely imaginary, then z + z̄ = 0.  

Question. Assertion : If P and Q are the points in the plane XOY representing the complex numbers z₁ and z₂ respectively, then distance |PQ| = |z₂ – z₁|.
Reason : Locus of the point P(z) satisfying |z – (2 + 3i)| = 4 is a straight line. 

Question. Assertion : The greatest integral value of λ for which (2λ – 1)x² – 4x + (2λ – 1) = 0 has real roots, is 2.
Reason : For real roots of ax² + bx + c = 0, D ≥ 0.  

Question. Assertion : The equation ix² – 3ix + 2i = 0 has non-real roots.
Reason : If a, b, c are real and b2 – 4ac ≥ 0, then the roots of the equation ax² + bx + c = 0 are real and if b² – 4ac < 0, then roots of ax² + bx + c = 0 are non-real. 

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