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
(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 πx = –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
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