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NCERT Solutions for class 11 Maths | Chapter 5 - Complex Numbers and Quadratic Equations

Free download in PDF Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries./p>

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(1) If arg (z) < 0, then arg (-z) – arg (z) =
[A] π
[B] -π
[C] -π/2
[D] π/2
Answer: π
(2) The curve represented by Im(z²) = k, where k is a non-zero real number, is
[A] a pair of striaght line
[B] an ellipse
[C] a parabola
[D] a hyperbola
Answer: a hyperbola
(3) The value of i-999 is
[A] 1
[B] -1
[C] i
[D] -i
Answer: i
(4) The least value of n for which {(1 + i)/(1 – i)}n is real, is
[A] 1
[B] 2
[C] 3
[D] 4
Answer: 2
(5) The value of √(-16) is
[A] -4i
[B] 4i
[C] -2i
[D] 2i
Answer: 4i
(6) If ω is an imaginary cube root of unity, then (1 + ω – ω²)7 equals
[A] 128 ω
[B] -128 ω
[C] 128 ω²
[D] -128 ω²
Answer: -128 ω²
(7) Let z be a complex number such that |z| = 4 and arg(z) = 5π/6, then z =
[A] -2√3 + 2i
[B] 2√3 + 2i
[C] 2√3 – 2i
[D] -√3 + i
Answer: -2√3 + 2i
(8) The value of √(-25) + 3√(-4) + 2√(-9) is
[A] 13i
[B] -13i
[C] 17i
[D] -17i
Answer: 17i
(9) if z lies on |z| = 1, then 2/z lies on
[A] a circle
[B] an ellipse
[C] a straight line
[D] a parabola
Answer: a circle
(10) The value of √(-144) is
[A] 12i
[B] -12i
[C] ±12i
[D] None of these
Answer: 12i
(11) If {(1 + i)/(1 – i)}n = 1 then the least value of n is
[A] 1
[B] 2
[C] 3
[D] 4
Answer: 4
(12) (1 – w + w²)×(1 – w² + w4)×(1 – w4 + w8) × …………… to 2n factors is equal to
[A] 2n
[B] 22n
[C] 23n
[D] 24n
Answer: 22n
(13) The value of √(-144) is
[A] 12i
[B] -12i
[C] ±12i
[D] None of these
Answer: 12i
(14) The modulus of 5 + 4i is
[A] 41
[B] -41
[C] √41
[D] -√41
Answer: √41
(15) If the cube roots of unity are 1, ω, ω², then the roots of the equation (x – 1)³ + 8 = 0 are
[A] -1, -1 + 2ω, – 1 – 2ω²
[B] – 1, -1, – 1
[C] – 1, 1 – 2ω, 1 – 2ω²
[D] – 1, 1 + 2ω, 1 + 2ω²
Answer: – 1, 1 – 2ω, 1 – 2ω²
(16) The value of x and y if (3y – 2) + i(7 – 2x) = 0
[A] x = 7/2, y = 2/3
[B] x = 2/7, y = 2/3
[C] x = 7/2, y = 3/2
[D] x = 2/7, y = 3/2
Answer: x = 7/2, y = 2/3
(17) Find real θ such that (3 + 2i × sin θ)/(1 – 2i × sin θ) is imaginary
[A] θ = nπ ± π/2 where n is an integer
[B] θ = nπ ± π/3 where n is an integer
[C] θ = nπ ± π/4 where n is an integer
[D] None of these
Answer: θ = nπ ± π/3 where n is an integer
(18) if x + 1/x = 1 find the value of x2000 + 1/x2000 is
[A] 0
[B] 1
[C] -1
[D] None of these
Answer: -1
(19) Let z1 and z2 be two roots of the equation z² + az + b = 0, z being complex. Further assume that the origin, z1 and z1 form an equilateral triangle. Then
[A] a² = b
[B] a² = 2b
[C] a² = 3b
[D] a² = 3b
Answer: a² = 3b
(20) The complex numbers sin x + i cos 2x are conjugate to each other for
[A] x = nπ
[B] x = 0
[C] x = (n + 1/2) π
[D] no value of x
Answer: no value of x

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