BITSAT Mathematics Complex Numbers and Quadratic Equations MCQs

Question: If α and β are roots of the equation  such that | α -β |= √10, then p belongs to the set :

• a) {2, – 5}
• b) {– 3, 2}
• c) {– 2, 5}
• d) {3, – 5}

Answer: {– 2, 5}

Question: If f(z) =  where z = 1 + 2i, then |f(z)| is equal to :

• a)

  

• b) | z |
• c) 2 | z |
• d) None of these

Answer: 

Question: If z1 = √3 + i √3 and z₂ = √3 + i , then the complex number

 lies in the :

• a) First quadrant
• b) Second quadrant
• c) Third quadrant
• d) Fourth quadrant

Answer: First quadrant

Question: If α, β are the roots of the equations x² – 2x– 1 = 0, then what is the value of α² β^–2+ α ^–2 β²

• a) –2
• b) 0
• c) 30
• d) 34

Answer: 34

Question: If a, b and c are real numbers then the roots of the equation (x – a) (x – b) + (x – b) (x – c)+ (x – c) (x – a) = 0 are always

• a) Real
• b) Imaginary
• c) Positive
• d) Negative

Answer: Real

Question: The root of the equation 2(1+ i)x ² - 4(2 - i)x - 5 - 3i = 0 which has greater modulus is

• a)

  

• b)

  

• c)

  

• d) None

Answer:

Question: If complex number z₁, z₂ and 0 are vertices of equilateral triangle, then   is equal to

• a) 0
• b) z₁ – z₂
• c) z₁ + z₂
• d) 1

Answer: 0

Question: Universal set

What is (A ∩ B)' equal to ?

• a) {1, 3}
• b) {1, 2, 3}
• c) {0, 1, 3}
• d) {0, 1, 2, 3}

Answer: {0, 1, 3}

Question: If z = x + iy, z^{1/ 3} = a – ib, then

 where k is equal to

• a) 1
• b) 2
• c) 3
• d) 4

Answer: 4

Question: 

when simplified has the value

• a) 0
• b) 2i
• c) – 2i
• d) 2

Answer: 0

Question: If the roots of x² + x + a = 0 exceed a then

• a) 2 < a < 3
• b) a > 3
• c) – 3 < a < 3
• d) a < – 2

Answer: a < – 2 

Question: If the real part of

 is 4, z ≠ 1, then the locus of the point representing z in the complex plane is

• a) A straight line parallel to x-axis
• b) A straight line equally inclined to axes
• c) A circle with radius 2
• d) a circle with radius
•  

Answer: a circle with radius 

Question: If α and β are the roots of x² – x + 1 = 0, then the equation whose roots are α¹⁰⁰ and β¹⁰⁰ are

• a) x² – x + 1 = 0
• b) x² + x – 1 = 0
• c) x² – x – 1 = 0
• d) x² + x + 1 = 0

Answer: x² + x + 1 = 0 

Question: The amplitude of sin 

• a) π/5
• b) 2π/5
• c) π/10
• d) π/15

Answer: π/10

Question: If x = ω – ω² –2, then the value of x⁴ + 3x³ + 2x²– 11x – 6 is

• a) 1
• b) -1
• c) 2
• d) None of these

Answer: 1

Question: If  then A² + B² equals to

• a) 1
• b) α²
• c) –1
• d) – α²

Answer: 1

Question: If the expression x² – 11x + a and x² – 14x + 2a must have a common factor and a ≠0, then, the common factor is

• a) (x – 3)
• b) (x – 6)
• c) (x – 8)
• d) None of these

Answer: (x – 8)

Question: If α, β are the roots of the equation ax² + bx + c = 0, then the roots of the equation ax² + bx (x + 1)+ c (x + 1)² = 0 are

• a) α – 1, β– 1
• b) α + 1, β + 1
• c)

  

• d)

  

Answer:

Question: If a > 0, aεR, z = a + 2i and z | z | – az + 1 = 0 then

• a) Z is always a positive real number
• b) Z is always a negative real number
• c) Z is purely imaginary number
• d) Such a complex z does not exist

Answer: Such a complex z does not exist

Question: The roots of the equation x² – 2 √2 x + 1 = 0 are

• a) Real and different
• b) Imaginary and different
• c) Real and equal
• d) Rational and different

Answer: Real and different

Question:  For the equation if the product of roots is zero, then the sum of roots is

• a) 0
• b)

  

• c)

  

• d)

  

Answer:

Question: If arg

= arg(z₂ ) , then

• a) z₂ = kz₁^–1 (k > 0)
• b) z₂ = kz₁(k > 0)
• c)

  

• d) None of these

Answer: z₂ = kz₁^–1 (k > 0)

Question: If

 and arg(z₁ z₂) = 0, then

• a) z₁ = z₂
• b) |z₂|² = z₁z₂
• c) z₁z₂ = 1
• d) None of these

Answer: |z₂|² = z₁z₂

Question: Let a, b, c € R and ax² + bx + c = 0 has two negative roots, then –

• a) a, b, c are of same sign
• b) a, –b, c are of same sign
• c) a, b, –c are of same sign
• d) a, – c are of same sign

Answer: a, b, c are of same sign

Question: If z then value of arg (zi) is

• a) 0
• b) 

  

• c)

  

• d)

  

Answer:

Question: Value of  is

• a) cos 5θ + i sin 5θ
• b) cos 7θ + i sin 7θ
• c) cos 4θ + i sin 4θ
• d) cosθ + i sinθ

Answer: cos 7θ + i sin 7θ

Question: If the roots of the equation x² + 2ax + b = 0 are real and differ by at most 2m, m ≠ 0 then b lies in the interval

• a) (a² -m² , a ² )
• b) [a² -m² , a² )
• c) (a ² , a² + m² )
• d) None of these

Answer: [a² -m² , a² )

Question: If the equation x² + 2 (k + 1) x + 9k – 5 = 0 has only negative roots, then –

• a) k≤0
• b) k≥0
• c) k≥6
• d) k≤6

Answer: k≥6

Question: The value of the expression x⁴ – 8x³ – 8x + 2 when x = 2 + √3 is –

• a) 0
• b) 1
• c) 2
• d) 3

Answer: 1

Question: If α,β are the roots of x² + px + q = 0, and w is an imaginary cube root of unity, then value of (wα +w²β) (w²α+ wβ) is

• a) p²
• b) 3q
• c) p² – 2q
• d) p² – 3q

Answer: p² – 3q