Class 11 Mathematics Complex Numbers and Quadratic Equation MCQs Set 02

Question: If |z + 1|= z + 2 (1 + i), then the value of z is
a) 1/2- 2i
b) 1/2+ 2i
c) 1/2- 3i
d) 1/3- 2i
Answer: a

Question: The value of x⁴+9x³+35x²-x+4 for
x = – 5 + 2√-4 is
a) 0
b) –160
c) 160
d) –164
Answer: b

Question: If the roots of the given equation

Answer: c

Question:

Answer: a

Question: Let z and ω be com plex num bers such that z + iw = 0 and arg ( zω) = p. Then, arg (z̄) is equal to
a) π /4
b) π /2
c) 3π /4
d) 5π /2
Answer: c

Question: If |z2 – | |z|2 + 1 = + 1 then z lies on
a) the real axis
b) the imaginary axis
c) a circle
d) an ellipse
Answer: b

Question: The real value of q for which the expression

Answer: b

Question: The solution set of the equation

Answer: d

Question: Let f (x)= x²+ax+b;a,b ∈R.If f (1)+f(2)+f (3)=0, then the roots of the equation f (x) = 0
a) are imaginary
b) are real and equal
c) are from the set {1, 2, 3}
d) real and distinct
Answer: d

Question: Given z=q+ir/1+P,, then p+iq/1+r=1+iz/1-iz, if
a) p²+ q²+ r²=1
b) p²+ q²+ r²=2
c) p²+ q²+ r²=1
d) None of the options
Answer: a

Question: If the roots of the equation ax²+bx+c=0 of the form

Answer: c

Question:The system y^(x2+7x+12)=1 andx+y=6,y>0 has
a) no solution
b) one solution
c) two solutions
d) more than 2 solutions
Answer: d

Question: The coefficient of x in the equation x²+px+q=0 was taken as 17 in place of 13 its roots were found to be – 2and -15. The roots of the original equation are
a) 3, 10,
b) – 3 -10 ,
c) – 5- 8 ,
d) None of the options
Answer: b

Question: The conjugate of

Answer: b

Question: If z-1/z+1is a purely imaginary number ( z≠ – 1), then the value of |z| is
a) –1
b) 1
c) 2
d) –2
Answer: b

Question: If the roots of (a²+b²)x²-2(bc+ad)x+c²+d²=0 are equal, then
a) a/b=c/d
b) a/c+b/d=0
c) a/d=b/c
d) a+ b= c +d
Answer: a

Question: If α,β,y are the roots of x³+2x²-3x-=0,then α^-2+β^-2+y^-2 is equal to
a) 12
b) 13
c) 14
d) 15
Answer: b

Question: The centre of the circle

Answer: a

Question: Re( z ) 2 = 1 is rep re sented by
a) the circle x² + y₂ = 1
b) the hyperbola x² – y² = 1
c) parabola or a circle
d) All of the options
Answer: b

Question: If sin and cos a a are the roots of the equation ax2+bx+c=0, then
a) a^2-b²+2ac=0
b) (a-c)²=b²+c²)
c) a²+b²-2ac=0
d) a²+b²+2ac=0
Answer: a

Question: The value of ( z + 3)( ¯z + 3) is equivalent to
a) | z + 3 |²
b) | z – 3 |
c) z² + 3
d) None of the options
Answer: a

Question: If one root of equation x²+ax+12=0 is 4 while the equation x²+ax+b=0 has equal roots, then the value of b is
a) 4/49
b) 49/4
c) 7/4
d) 4/7
Answer: b

Question:

Answer: b

Question: The val ues of ( ) / 16 1 4 are
a) ±2, ± 2 i
b) ±4 , ± 4 i
c) ±1, ± i
d) None of the options
Answer: a

Question: If(1+i/1-i)^x =1,then
a) x = 2n + 1
b) x = 4n
c) x = 2n
d) x = 4n + 1, where n ∈ N
Answer: b

Question: If z³ + z² – z + i = 0, then |z| is equal to
a) 1
b) i
c) -1
d) – i
Answer: a

Question: The centre of the circle zz̄ – (2 + 3i) z – (2 – 3i)z̄ + 9 = 0 is
a) (2, – 3)
b) (2, 3)
c) (-2, – 3)
d) (-2, 3)
Answer: a

Question: The value of 1 + i² + i⁴ + i⁶ +… + i²ⁿ is
a) positive
b) negative
c) zero
d) cannot be determined
Answer: d

Question: sin x+i cos 2x and cos x – i sin 2x are conjugate to each other for
a) x= nπ
b) x =(n+1/2) π/2
c) x = 0
d) No value of x
Answer: d

Question: The value of sum

a) i
b) i – 1
c) – i
d) 0

Answer: b

Question: If z₁ , z₂ , z₃ and z₄ are the af fixes of four points in the ar gand plane and z is the af fix of a point, such that |z – z₁|=|z – z₂|=|z – z₃|=|z – z₄|, then and are
a) concyclic
b) vertices of a parallelogram
c) vertices of a rhombus
d) in a straight line
Answer: a

Question: The area of the triangle whose Vertices are represented by the complex numbers

Answer: d

Question:

a) 0
b) 1/2
c) 1
d) 2
Answer: c

Question: If sin α sin β and cos α are in GP, then roots of x²+2x cot β+1=0 are always
a) real
b) real and negative
c) greater than one
d) non-real
Answer: a

Question: If P (x)= ax²+bx+c and Q(x) = – ax²+dx+c,where ac ≠0, then P(x) Q (x) = 0 has atleast
a) four real roots
b) two real roots
c) four imaginary roots
d) None of the options
Answer: b

Question:

Answer: d

Question: If the product of the roots of the equation (a+1)x²+(2a+3)x+(3a+4)=0 is 2,, then the sum of roots is
a) 1
b) -1
c) 2
d) -2
Answer: b

Question: When z+ i/z+2 is purely imaginary, the locus described by the point z in the argand diagram is a
a) circle of radius√5/2
b) circle of radius 5/4
c) straight line
d) parabola
Answer: a

Question: If z is a comp lex num ber, then ( z-1)( z) is equal to
a) 1
b) -1
c) 0
d) None of the options
Answer: a

Question: Com mon roots of the equa tions z₃+z₂ + 2z + 1 = 0 and z¹⁹⁸⁵ + z¹⁰⁰ = 0 are
a) ω, ω₂
b) ω, ω₃
c) ω₂ ω₃ ,
d) None of the options
Answer: b

Question: Let z1 and z2 be the non-real roots of the equa tion 3z²+ 3z+b=0. If the ori gin to gether with the points rep re sented by z₁ and z₂ form an equi lat eral tri an gle, then the value of b is
a) 1
b) 2
c) 3
d) None of the options
Answer: a

Question: Two students while solving a quadratic equation in x, one copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term coefficient of x2 correctly as -6 and 1 respectively the correct roots are
a) 3,- 2
b) – 3, 2
c) -6, 1
d) 6, -1
Answer: d

Question:

a) 2
b) 3
c) 4
d) 6

Answer: b

Question: The num ber of non-zero integral solutions of the equation |1 – i|x = 2x is
a) infinite
b) 1
c) 2
d) None of the options
Answer: b

Question:

Answer: d

Question: If(1+i)²/2-i=X+iY, then the value of x+y is equal to
a) 5/2
b) – 2/5
c) 2/5
d) – 5/2
Answer: c

Question: The equation of a circle whose radius and centre are r and z0 respectively, is

Answer: a

Question: If the com plex num bers z₁ z ₂ and and the origin from an equilateral triangle, then z₁² + z₂² is equal to
a) z₁z₂
b) z₁z₂
c) z₂z₁
d) |z₁|² = |z₂|²
Answer: a

Question: If the points z₁,z₂ and z₃ and are the verti ces of anequilateral triangle in the complex plane, then the value of

Answer: b

Question: In the argand plane the complex number z = 4 – 3 i is turned in the clockwise sense through 180° and stretched three times. The com plex num ber rep re sented by the new num ber is
a) 12 + 9i
b) 12 – 9i
c) -12 – 9i
d) -12 + 9i
Answer: d

Question: If the comp lex num bers iz, z and z + iz rep re sent the three ver ti ces of a tri an gle, then the area of the tri an gle is
a) 1/2|z|²
b) |z|²
c) 1/2|z – 1|
d) |z – 1|²
Answer: a