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

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 

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 

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 

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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 

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 

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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 

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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   

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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 

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   

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 

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   

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Question: 

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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 

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

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

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 

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 

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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) 

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 

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

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

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Question:  The number of real roots of the equation

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

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 

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) 

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   

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 

Question: The roots of the given equation

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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   

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 

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 

Question:

(a) 7
(b) 10
(c) 12
(d) 14 

Question:

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

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 

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 

Question:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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}

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

Question. Suppose the quadratic equations   
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.

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

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

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

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

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

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.

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

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

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