# MCQ Questions for Class 11 Complex Numbers and Quadratic Equations

Please refer to the MCQ Questions for Class 11 Complex Numbers and Quadratic Equationss Maths Chapter 5 with Answers. The following Complex Numbers and Quadratic Equations Class 11 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 11. Our experts have designed MCQ Questions for Class 11 Complex Numbers and Quadratic Equations with Answers for all chapters in your NCERT Class 11 Mathematics book. You can access all MCQs for Class 11 Mathematics

## Complex Numbers and Quadratic Equations Class 11 MCQ Questions with Answers

See below Complex Numbers and Quadratic Equations Class 11 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

Question. The least value of a such that the sum of the squares of the roots of the equation x2 – (a – 2) x – (a + 1) = 0 is
(a) a = – 1
(b) a = 1
(c) a = 0
(d) a = 2

B

Question: If z is a complex number, then the minimum value of
|z|+|z – 1| is
(a) 1
(b) 0
(c)1/2
(d) None of these

A

Question: If x2+ ax+1 is a factor of ax3+ bx + c,  then
(a) b+ a+ a2= 0, a=c
(b) b- a+ a2  = 0, a=c
(c) b+ a- a2 = 0, a=0
(d) None of these

B

Question:  If (x – 2) is a common factor of the expressions x2+ ax+ b  and x2+ cx+ d, 2 then b -d/c- a is equal to
(a) -2
(b) -1
(c) 1
(d) 2

D

Question:

B

Question: If roots of the equation (a-b)x2+(c-a)x+(b-c)=0
(a) AP
(b) HP
(c) GP
(d) None of these

A

Question: If a > 0, b>0, c>0 , then both the roots of the equation ax2+ bx+ c = 0
(a) are real and negative
(b) have negative real part
(c) are rational numbers
(d) None of these

B

Question:

D

Question: If roots of the equation ax2+bx+ c=0; (a,b,c ∈ N) are rational numbers, then which of the following cannot be true ?
(a) All a b c , and are even
(b) All a b, and c are odd
(c) b is even while a and c are odd
(d) None of the above

D

Question:

B

Question:

B

Question: Let α and α2 be the roots of x2+x+1=0, then the equation whose roots are α31 and α 62, is
(a) x2 -x+1=0
(b) x2+x-1=0
(c) x2+x+1=0
(d) x60 +x30+1=0

C

Question:

A

Question:

B

Question: If the equation 2x2+3x+5λ=0 and x2+2x+3λ = 0 have a common root, then λ is equal to
(a) 0
(b) -1
(c) 0, -1
(d) 2, -1

C

Question: If at least one root of the equation x3+ax2+bx+c=0 remains unchanged, when a b, and c are decreased by one, then which one of the following is always a root of the given equation ?
(a) 1
(b) -1
(c) ω, an imaginary cube root of unity
(d) i

C

Question: If at least one root of 2x2+3x+5=0 and ax2+bx+c=0,a,b,c∈ N  is common, then the maximum value of a+ b+ c  is
(a) 10
(b) 0
(c) does not exist
(d) None of these

C

Question: If each pair of the equation x2+ax+b=0,x2+bx+c=0and x2+cx+a=0  has a common root, then product of all common roots is
(a) √abc
(b) 2 √abc
(c) √ab +bc+ ca
(d) 2 √ab +bc+ ca

A

Question:

A

Question:

D

Question:

D

Question: For all x, x2+2ax+(10-3a)>0,then the interval in which a lies, is
(a) a <-5
(b) – 5< a<2
(c) a > 5
(d) 2<a<5

B

Question:

Question: If α and β (α<β )  are the roots of the equation x2+ bx+ c=0  where c b < < 0 , then

B

Question:

D

Question: The roots of a equation 2x2+x+1=0 are

A

Question:  If one root of the equation x2+(1-3i) x-2 (1+ i)=0 is -1+ i, then the other root is
(a) – 1 – i
(b) -1 – i
(c) i
(d) 2i

D

Question:  If the difference of the roots of the equation x2 -px+8=0 is 2, then the value of P is
(a) ±4
(b) ±6
(c) ±5
(d) None of these

B

Question:

A

Question:  If x2- 3x +2 be a factor of x4 -px2-q, then ( p,q ) equal to
(a) (3 , 4)
(b) (4 , 5)
(c) ( 4, 3)4 3
(d) (5 , 4)

D

Question:  If the sum of the squares of the roots of the equation x2-(a-2) x-(a+1)=0  is least, then the value of a is
(a) -1
(b) 1
(c) 2
(d) -2

B

Question:  If √3x2-7x-30+ √2x2-7x-5=x+5, then x is equal to
(a) 2
(b) 3
(c) 6
(d) 5

C

Question:  If x2+px+1 is a factor of the expression ax3+bx+c, then
(a) a2 +c2  = -ab
(b) a2– c2=-ab
(c) a2-c2=ab
(d) None of these

C

Question:

D

Question:  The number of real roots of the equation

D

Question:

B

Question: The number of real solutions of the equation |x2+4x+3|+2x+5=0 are
(a) 1
(b) 2
(c) 3
(d) 4

B

Question: How many roots of the equation x-2/x-1=1-2/x-1
(a) One
(b) Two
(c) Infinite
(d) None of these

D

Question: If 2+i √3 i is a root of the equation x2+px+q=0, where p and q are real, then (p ,q ) is equal to
(a) (-4,7)
(b) ( 4,- 7)
(c) (4,7)
(d) (-4,-7)

A

Question: The roots of the equation x4-8x2-9=0 2  are
(a) ± 1,± i
(b) ± 3, ± i
(c) ± 2 , ± i
(d) None of these

B

Question: Rational roots of the equation 2x4+x3-11x2+x+2=0 are
(a) 1/2 and 2
(b) 1/2,1/4,-2
(c) 1/2,2,3,4
(d) 1/2, 2, 3/4,-2

A

Question: The roots of the given equation

C

Question:

B

Question: tan α and tan β are the roots of the equation x2+ax+b=0, then the value of sin 2(α+β)+a sin((α+β) cos((α+β)+b cos2(α+β)is equal to
(a) ab
(b) b
(c) a/b
(d) a

B

Question: If 2 sin 2 π/8 is a root of the equation x2+ax+b=0, where a and b are rational numbers, then a- b – is equal to
(a) -5/2
(b) -3/2
(c) -1/2
(d) 1/2

A

Question: If |z + 4|≤ 3, then the great est and the least value of |z + 1| are
(a) 6, – 6
(b) 6, 0
(c) 7, 2
(d) 0, -1

B

Question:

(a) 7
(b) 10
(c) 12
(d) 14

B

Question:

(a) is less than 6
(b) is more than 3
(c) is less than 12
(d) lies between 6 and 12

C

Question: The maximum value of |z| where z sati fies the conditionz |z+2/z|=2, is
(a) √3 – 1
(b) √3 + 1
(c) √3
(d) √2 + √3

B

Question: Let z be a comp lex num ber sati sf y ing |z – 5 i|≤ 1 such that amp(z) is min i mum. Then, z is equal to
(a)2√6/5+24i/5
(b)24/5+2√6i
(c)2√6/5-24i/5
(d) None of these

A

Question:

(a) 1 – c cos θ
(b) 1 + 2c cos θ
(c) 1 + c cos θ
(d) 1 – 2c cos θ

C

Question:

D

Question: If (cosθ + i sin θ) (cos 2θ+ isin 2θ)….(cos nθ + isin nθ) = 1, then the value of θ is

C

Question. If a ¹ b but a2 = 5a – 3 and b2 = 5b – 3 then the equation having a/b and b/a as its roots is
(a) 3x2 – 19x + 3 = 0
(b) 3x2 + 19x – 3 = 0
(c) 3x2 – 19x – 3 = 0
(d) x2 – 5x + 3 = 0

A

Question. The quadratic equations x2 – 6x + a = 0 and x2 – cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is
(a) 1
(b) 4
(c) 3
(d) 2

D

Question. Let for a ≠ a1 ≠ 0,
f (x) = ax2 + bx + c, g(x) = a1x2 + b1 x + c1and p x = f x – g x .and p(x) = f (x)- g (x).
If p(x) = 0 only for x = -1 and p (– 2) = 2, then the value of p (2) is :
(a) 3
(b) 9
(c) 6
(d) 18

D

Question. If α,β are the roots of ax2 + bx + c = 0;  α+h, β+h are the roots of px2 + qx + r = 0; and D1, D2 the respective discriminants of these equations, then D1 : D2 is equal to :
(a) a2/b2
(b) b2/a2
(c) c2/r2
(d) none of these

A

Question. The number of real solutions of the equation (9/10) = – 3 + x – x2 is
(a) 0
(b) 1
(c) 2
(d) none of these

A

Question. If (x + 1) is a factor of x4 + (p – 3)x3 – (3p – 5) x2 + (2p – 10) x + 5, then the value of p is:
(a) 2
(b) 1
(c) 3
(d) 4

D

Question. If the root of the equation (x – c) (x – b) – k = 0 are c and d, then roots of the equation (x – a) (x–d) + k are:
(a) a and c
(b) b and c
(c) a and d
(d) a and b

C

Question. A quadratic equation with rational coefficient can have :
(a) both roots equal and irrational
(b) one root real and other imaginary
(c) both roots real and irrational
(d) none of these

B

Question. The solution of √3x2 – 2 = 2x -1 are :
(a) (2, 4)
(b) (1, 4)
(c) (3, 4)
(d) (1, 3)

D

Question. The equation whose roots are twice the roots of the equation, x2 – 3x + 3 = 0 is:
(a) 4x2 + 6x + 3 = 0
(b) 2x2 – 3x + 3 = 0
(c) x2 – 3x + 6 = 0
(d) x2 – 6x + 12 = 0

D

Question. If the roots of the equation,
(a2 + b2) t2 – 2(ac + bd) t + (c2 + d2) = 0 are equal then:
(a) ad + bc = 0
(b) a/b = c/d
(c) ab = dc
(d) ac = bc

B

Question. If the equations k (6x2 + 3) + rx + 2x2 – 1 = 0 and 6k (2x2 – 1) + px + 4x2 + 2 = 0 have both roots common, then the value of (2r – p) is :
(a) 0
(b) 1/2
(c) 1
(d) none of these

A

Question. If z = x + iy, z1/ 3 = a – ib, then x/a – y/b = k(a2-b2) where k is equal to
(a) 1
(b) 2
(c) 3
(d) 4

D

Question. The coefficients of x in the quadratic equation x2 + bx + c = 0 was taken as 17 in place of 13, its roots were found to be – 2 and – 15. The correct roots of the original equation are :
(a) – 10, – 3
(b) – 9, – 4
(c) – 8, – 5
(d) – 7, – 6

A

Question. If the quadratic x2 + ax + b + 1 = 0 has roots which are positive integers, then a2 + b2 can be equal to
(a) 19
(b) 33
(c) 50
(d) 59

C

Question. The roots of the equation 4x – 3 . 2x + 3 + 128 = 0 are
(a) 4 and 5
(b) 3 and 4
(c) 2 and 3
(d) 1 and 2

B

Question. If x2 + 3x – 2 = 8 / x2 +3x , then x ε
(a) {4, –2}
(b) {–4, 1}
(c) {1, –1, –4, –2}
(d) {2, –1}

C

Question. The root of the equation
2(1+ i)x2 – 4(2 – i)x – 5 – 3i = 0 which has greater modulus is
(a)  3- 5i/2
(b) 5 – 3i /2
(c) 3-i /2
(d) none

A

x2 + px + q = 0 and x 2 + rx + s = 0 are such that p, q, r , s are real and pr = 2(q + s). Then
(a) Both the equations always have real roots.
(b) At least one equation always has real roots.
(c) Both the equation always have non real roots.
(d) Atleast one equation always has real and equal roots.

B

Question. If c, d are the roots of (x – a)(x – b) = k then the roots of (x – c)(x – d) + k = 0 are
(a) a and b
(b) –a and –b
(c) ac and bd
(d) none

A

Question. For a complex number z, the minimum value of | z | + | z – 2 | is
(a) 1
(b) 2
(c) 3
(d) None

B

Question. Difference between the corresponding roots of x2+ax+b=0 and x2+bx+a = 0 is same and a ¹ b,then
(a) a + b + 4 = 0
(b) a + b – 4 = 0
(c) a – b – 4 = 0
(d) a – b + 4 = 0

A

Question. If a, b are the roots of ax2 + bx + c = 0, then ab2 + a2b + ab equals
(a)  c(a-b) /a2
(b) 0
(c) -bc/a2
(d) abc

A

Question. If the sum of the roots of the quadratic equation ax2 + bx + c = 0 is equal to the sum of the squares of their reciprocals, then , and ax2 + bx+ c =0 are in
(a) Arithmetic -Geometric Progression
(b) Arithmetic Progression
(c) Geometric Progression
(d) Harmonic Progression

D

Question. If the quadratic equation z2 + (a + ib) z + c + id = 0 where a, b, c, d are non-zero real number, has a real root then
(a) abd = b2c + d2
(b) abc = bc2 + d2
(c) abd = bc2 + ad2
(d) none of these.

A

Question. The value of a for which the sum of the squares of the roots of the equation
2x2 – 2(a – 2)x – (a +1) = 0 is least, is
(a) 1
(b) 3/2
(c) 2
(d) None

B

Question. If p and q are the roots of the equation x2 + px + q = 0, then
(a) p = 1, q = –2
(b) p = 0, q = 1
(c) p = –2, q = 0
(d) p = – 2, q = 1

A

Question. Number of real roots of the equation
sin x –e– sin x – 4 = 0 is
(a) 1
(b) 0
(c) 2
(d) None

1. Aakriti panthi says: