Below you will find **MCQ Questions of Chapter 5 Complex Numbers and Quadratic Equations Class 11 Maths Free PDF Download** that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 11 MCQ Questions with answers will widen your skills and understand concepts in a better manner.

# MCQ Questions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations with answers

1. Let Z1 = 10+ 6i and Z2 = 4+6i . If Z be a complex number such that Then |Z - 7 -9i| =

(a) 3√2

(b) 4√2

(c) 2√2

(d) √2

► (a) 3√2

2. The number of the integer solutions of x2 + 9 < (x + 3)2 < 8x + 25 is

(a) 1

(b) 2

(c) 3

(d) None of these

► (d) None of these

3. If (a_{1} +ib_{1})(a_{2} +ib_{2}) ....(an + ibn) = A +iB, then is equal to

(a) 1

(b) (A^{2} + B^{2})

(c) (A + B)

(d) (1/A^{2} + 1/B^{2})

► (b) (A^{2} + B^{2})

4. The set of all solutions of the inequality (1/2)x^{2}-2x < 1/4 contains the set

(a) (–∞, 0)

(b) (–∞, 1)

(c) (1, ∞)

(d) (3, ∞)

► (d) (3, ∞)

5. The number of solutions of the equation is

(a) 2

(b) 3

(c) 4

(d) 1

► (c) 4

6. If two roots of the equation x^{3} – px^{2} + qx – r = 0 are equal in magnitude but opposite in sign, then

(a) pr = q

(b) qr = p

(c) pq = r

(d) None of these

► (c) pq = r

7. The equatiobn π^{x} = –2x^{2} + 6x – 9 has

(a) No solution

(b) One solution

(c) Two solutions

(d) Infinite solutions

► (a) No solution

8. Two real numbers a & b are such that a + b = 3 & |a - b| = 4, then a & b are the roots of the quadratic equation

(a) 4x^{2} – 12x – 7 = 0

(b) 4x^{2} – 12x + 7 = 0

(c) 4x^{2} – 12x + 25 = 0

(d) None of these

► (a) 4x^{2} – 12x – 7 = 0

9. The values of k, for which the equation x^{2} + 2(k – 1) x + k + 5 = 0 possess atleast one positive root, are

(a) [4, ∞)

(b) (∞, – 1] ∪ [4, ∞)

(c) [–1, 4]

(d) (–∞, – 1]

► (d) (–∞, – 1]

10. If α (≠ 1) is a fifth root of unity and b (≠ 1) is a fourth root of unity, then z = (1 + α) (1 + β) (1 + α^{2}) (1 + β^{2}) (1 + α^{3}) (1 + β^{3}) equals

(a) α

(b) β

(c) αβ

(d) 0

► (d) 0

11. The value of is

(a) 2i

(b) –2i

(c) 2

(d) 1

► (a) 2i

12. If | z - 3i| = 3, (where i = √-1) and arg z ∈ (0, π/2), then cot (arg (z)) -6/z is equal to

(a) 0

(b) –i

(c) i

(d) π

► (c) i

13. Let a, b and c are real numbers such that 4a + 2b + c = 0 and ab > 0. Then the equation ax^{2} + bx + c = 0 has

(a) Real roots

(b) Imaginary roots

(c) Exactly one root

(d) None of these

► (a) Real roots

14. If both the roots of the quadratic equation x2 – 2kx + k^{2} + k – 5 = 0 are less than 5, then k lies in the interval

(a) [4, 5]

(b) (– ∞, 4)

(c) (6, ∞)

(d) (5, 6]

► (b) (– ∞, 4)

15. For all complex numbers z_{1} ,z_{2} satisfying |z_{1}| = 12 and |z_{2} - 3 - 4i| = 5 , the minimum value of |z1 -z2| is

(a) 0

(b) 7

(c) 2

(d) 17

► (c) 2

16. Find the roots of the equation: x^{2}+ 6x + 5 = 0

(a) 5, -1

(b) -5, -1

(c) 5, 1

(d) -5, 1

► (b) -5, -1

17. The value of `a' for which one root of the quadratic equation (a2 – 5a + 3)x^{2} + (3a – 1)x + 2 = 0 is twice as large as the other, is

(a) 2/3

(b) - 2/3

(c) 1/3

(d) - 1/3

► (a) 2/3

18. If one root of the equation x^{2} + px + 12 = 0 is 4, while the equation x^{2} + px + q = 0 has equal roots then the value of `q' is

(a) 49/4

(b) 12

(c) 3

(d) 4

► (a) 49/4

19. Solve the quadratic equation x^{2} – ix + 6 = 0

(a) 1+2i, 1-2i

(b) -2, 3

(c) -2i, 3i

(d) 2, -3i

► (c) -2i, 3i

20. The least value of P for which the two curves arg z = π/6 and |z - 2 √3i| = P have a solution is ..

(a) √3

(b) 3

(c) 1/√3

(d) 1/3

► (b) 3

21. Solve the quadratic equation x2 +1 = 0

(a) 1 ± i

(b) ± i

(c) 1 ± i/2

(d) 1 ± √2i/2

► (b) ± i

22. If a, b ∈ R, a < 0 and the quadratic equation ax^{2 }– bx + 1 = 0 has imaginary roots then a + b + 1 is

(a) Positive

(b) Negative

(c) Zero

(d) Depends on the sign of b

► (a) Positive

Hope the given MCQ Questions will help you in cracking exams with good marks. These **Complex Numbers and Quadratic Equations MCQ Questions** will help you in practising more and more questions in less time.