NCERT MCQ CLASS-11 CHAPTER-5 | MATH NCERT MCQ | COMPLEX NUMBERS AND QUADRATIC EQUATION | EDUGROWN

In This Post we are  providing Chapter-5 Complex Numbers and Quadratic Equation NCERT MCQ for Class 11 Math  which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MCQ ON COMPLEX NUMBERS AND QUADRATIC EQUATION

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

Answer► (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

Answer► (d) None of these

3. If (a₁ +ib₁)(a₂ +ib₂) ….(an + ibn) = A +iB, then  is equal to

(a) 1

(b) (A² + B²)

(c) (A + B)

(d) (1/A² + 1/B²)

Answer► (b) (A² + B²)

4. The set of all solutions of the inequality (1/2)x²-2x < 1/4 contains the set

(a) (–∞, 0)

(b) (–∞, 1)

(c) (1, ∞)

(d) (3, ∞)

Answer► (d) (3, ∞)

5. The number of solutions of the equation  is

(a) 2

(b) 3

(c) 4

(d) 1

Answer► (c) 4

6. If two roots of the equation x³ – px² + 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

Answer► (c) pq = r

7. The equation π^x = –2x² + 6x – 9 has

(a) No solution

(b) One solution

(c) Two solutions

(d) Infinite solutions

Answer► (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) 4x² – 12x – 7 = 0

(b) 4x² – 12x + 7 = 0

(c) 4x² – 12x + 25 = 0 

(d) None of these

Answer► (a) 4x² – 12x – 7 = 0

9. The values of k, for which the equation x² + 2(k – 1) x + k + 5 = 0 possess at least one positive root, are

(a) [4, ∞) 

(b) (∞, – 1] ∪ [4, ∞)

(c) [–1, 4] 

(d) (–∞, – 1]

Answer► (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 + α²) (1 + β²) (1 + α³) (1 + β³) equals

(a) α

(b) β

(c) αβ

(d) 0

Answer► (d) 0

11. The value of   is

(a) 2i

(b) –2i

(c) 2

(d) 1

Answer► (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

Answer► (c) i

13. Let a, b and c are real numbers such that 4a + 2b + c = 0 and ab > 0. Then the equation ax² + bx + c = 0 has

(a) Real roots

(b) Imaginary roots 

(c) Exactly one root 

(d) None of these

Answer► (a) Real roots

14. If both the roots of the quadratic equation x2 – 2kx + k² + k – 5 = 0 are less than 5, then k lies in the interval

(a) [4, 5]

(b) (– ∞, 4)

(c) (6, ∞)

(d) (5, 6]

Answer► (b) (– ∞, 4)

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

(a) 0

(b) 7

(c) 2

(d) 17

Answer► (c) 2