Worksheets Class 11 Mathematics Complex Numbers and Quadratic Equations

Students should refer to Worksheets Class 11 Mathematics Complex Numbers and Quadratic Equations Chapter 5 provided below with important questions and answers. These important questions with solutions for Chapter 5 Complex Numbers and Quadratic Equations have been prepared by expert teachers for Class 11 Mathematics based on the expected pattern of questions in the class 11 exams. We have provided Worksheets for Class 11 Mathematics for all chapters on our website. You should carefully learn all the important examinations questions provided below as they will help you to get better marks in your class tests and exams.

Complex Numbers and Quadratic Equations Worksheets Class 11 Mathematics

Question. Both the roots of given equation (x − a)(x − b) + (x − b)(x − c) + (x − c)(x − a) = 0 are always: 
a. Positive
b. Negative
c. Real
d. Imaginary

Question. The solution of the equation x+1/x = 2       
a. 2, –1
b. 0, –1, -1/5
c. -1 , 1/5
d. None of these

Question. For what values of k will the equation 2x − 2(1+ 3k)x + 7 (3 + 2k) = 0 have equal roots?     
a. 1, –10/9
b. 2, –10/9
c. 3, –10/9
d. 4, –10/9

Question. The value of ‘a’ for which one root of the quadratic equation (a² −5a + 3) x² + (3a −1)x + 2 = 0 is twice as large as the other is:   
a. 2/3
b. – 2/3
c. 1/3
d. – 1/3

Question. If the sum of the roots of the quadratic equation 0 ax² + bx + c = is equal to the sum of the squares of their reciprocals, then a / c,b / a, c / b are in:     
a. A.P.
b. G.P.
c. H.P.
d. None of these

Question. The value of x = √2+√2+√2+……..is:     
a. –1
b. 1
c. 2
d. 3

Question. If α and β are the roots of 6x² − 6x +1 = 0, then the value of

  a. 1/4(a+b+c+d)       
b. a/1 + b/2 + c/3 + d/4
c. a/2 – b/2 + c/3 – d/4
d. None of these

Question. If one root of a quadratic equation is 1/2+√5 ,then the equation is:     
a. x2 + 4x + 1 = 0
b. x2 + 4x − 1 = 0
c. x2 − 4x + 1 = 0
d. None of these

Question. If one root of 5x² +13x + k = 0 is reciprocal of the other, then k = ?       
a. 0
b. 5
c. 1/6
d. 6

Question. Ifα,β are roots of x² − 3x +1 = 0, then the equation whose roots are 1/α − 2 , 1/β − 2 is     
a. x2 + x −1 = 0
b. x2 + x +1 = 0
c. x2 − x −1 = 0
d. None of these

Question. If one of the roots of the equation x² + ax + b = 0 and x² + bx + a = 0 is coincident. Then the numerical value of (a + b) is:     
a. 0
b. – 1
c. 2
d. 5

Question. If x be real, then the minimum value of x² − 8x +17 is:     
a. 0– 1
b. 0
c. 1
d. 2

Question. The roots of the equation a(x² +1) − (a² +1)x = 0 are:   
a. a,1/a
b. a, 2a
c. a,1/2a
d. None of these

Question. The roots of the equation ix² − 4x − 4i = 0 are:     
a. – 2i
b. 2i
c. –2i, –2i
d. 2i, 2i

Question. The number of roots of the quadratic equation 2 8sec θ − 6secθ +1 = 0 is:     
a. Infinite
b. 1
c. 2
d. 0

Question. The number which exceeds its positive square root by 12 is:   
a. 9
b. 16
c. 25
d. None of these

Question. If x²/3 − 7x +10 = 0, then x = ?     
a. {125}
b. {8}
c. φ
d. {125, 8}

Question. If the sum of the roots of the equation λx² – 2x + 3λ = 0 be equal to their product, then λ = ?   
a. 4
b. −4
c. 6
d. None of these

Question. If the ratio of the roots of the equation ax² + bx + c = 0 be p : q , then:     
a. pqb² + ( p + q) ac = 0
b. pqb² − ( p + q) ac = 0
c. pqa² − ( p + q) bc = 0
d. None of these

Question. The number of real roots of the equation esin e^sinx − e^-sinx -4 = 0 are:     
a. 1
b. 2
c. Infinite
d. None

Question. If

 + 5 ,then x is equal to:     
a. 2
b. 3
c. 6
d. 5

Question. If α ,β are the roots of (x − a)(x − b) = c, c ≠ 0, then the roots of (x −α )(x −β ) + c = 0 shall be:     
a. a, c       
b. b,c
c. a,b
d. a + c,b + c

Question. If x₁ , x₂ , x₃ are distinct roots of the equation ax² + bx + c = 0 then:     
a. a = b = 0,c∈R
b. a = c = 0,b∈R
c. 2 b − 4ac ≥ 0
d. a = b = c = 0

Question. If 3 is a root of x² + kx – 24 = 0, it is also a root of :     
a. 2 x + 5x + k = 0
b. 2 x − 5x + k = 0
c. 2 x − kx + 6 = 0
d. 2 x + kx + 24 = 0

Question. The equation e^x − x −1 = 0 has:     
a. Only one real root x = 0
b. At least two real roots
c. Exactly two real roots
d. Infinitely many real roots

Question. A real root of the equation log4 {log2(√x+8 -√x )} = 0 is:     
a. 1
b. 2
c. 3
d. 4

Question. If the roots of the equations px² + 2qx + r = 0 and qx² – 2√prx+q = 0 be real, then:   
a. p = q
b. q² = pr
c. p² = qr
d. r² = pq

Question. Let α and β be the roots of the equation 2x + x +1 = 0 , the equation whose roots are α19, β7 is:   
a. 2x − x − 1 = 0
b. 2x − x +1 = 0
c. 2x + x −1 = 0
d. 2x + x + 1 = 0

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 parts
c. Are rational numbers
d. None of these

Question. If the difference between the corresponding roots of x²+ ax + b = 0 and x²+ bx + a = 0 is same and a ≠ b, then:     
a. a + b + 4 = 0
b. a + b − 4 = 0
c. a − b − 4 = 0
d. a − b + 4 = 0

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

Question. If α ,β are the roots of the equation ax2 + bx + c = 0 then the equation whose roots are α+1/β and β+1/α is:     
a. acx² + (a + c)bx + (a + c)² = 0
b. abx² + (a + c)bx + (a + c)² = 0
c. acx² + (a + b)cx + (a + c)² = 0
d. None of these

Question. If one root of the equation 2x + px + q = 0 is the square of the other, then:   
a. p3 + q2 − q(3p +1) = 0
b. p3 + q2 + q(1+ 3p) = 0
c. p3 + q2 + q(3p −1) = 0
d. p3 + q2 + q(1− 3p) = 0

Question. If α and β be the roots of the equation 2x² + 2(a+b)x + a²+b² = 0,then the equation whose roots are (α + β)² and (α −β)² is:     
a. x² – 2abx – (a²-b²)² = 0
b. x² – 4abx + (a²-b²)² = 0
c. x² – 4abx – (a²-b²)² = 0
d. None of these

Question. If α and β are the roots of the equation 2x² − 3x + 4 = 0 , then the equation whose roots are α² and β² is:     
a. 4x² + 7x +16 = 0
b. 4x² + 7x + 6 = 0
c. 4x² + 7x +1 = 0
d. 4x² − 7x +16 = 0

Question. If α ,β be the roots of the equation x² − 2x + 3= 0, then the equation whose roots are 1/α² and 1/β² is:     
a. x2 + 2x + 1 = 0
b. 9×2 + 2x + 1 = 0
c. 9×2 – 2x + 1 = 0
d. 9×2 + 2x −1= 0

Question. The solution set of the equation xlog(1-x)² = 9 is   
a. {– 2, 4}
b. {4}
c. {0, – 2, 4}
d. None of these

Question. If α ,β be the roots of x² − px + q = 0 and α ′,β ′ be the roots of x² − p’x + q’ = 0 then the value of  (α −α ‘)² + (β −α ′)² + (a −β ′)² + (β −β ′)² is:     
a. 2{p² − 2q + p′ − 2q′ − pp′}
b. 2{p² − 2q + p′ − 2q′ − qq′}
c. 2{p² − 2q − p′ − 2q′ − pp′}
d. 2{p² − 2q − p′ − 2q′ − qq′}

Question. If the roots of the equation x² – 5x + 16 = 0 are α, β and the roots of equation x² + px + q = 0 are α² +β² , αβ / 2 , then:       
a. p = 1, q = −56
b. p = −1, q = −56
c. p = 1, q = 56
d. p = −1, q = 56

Question. If the roots of the equation 1/x+p + 1/x+q = 1/r are equal in magnitude but opposite in sign, then the product of the roots will be:     
a. p²+q²/2
b. (p²+q²)/2
c. (p²-q²)/2
d. (p²-q²)/2

Question. If z = 1+i√3 /√3+i then (Z̅)100 lies in:       C
a. I quadrant
b. II quadrant
c. III quadrant
d. IV quadrant

Question. If Xr = cos (π/2r) + sin (π/2r) then x₁ . x₂ .x₃ …∞ is:       C
a. –3
b. –2
c. –1
d. 0

Question. Let z₁ and z₂ be two distinct complex number and let z = (1–t) z₁ = tz₂ for some real number t with 0 < t < 1. If arg (w) denotes the principle argument of a non-zero complex number w, then:       A,C,D
a. |z – z₁| + |z – z₂| = |z₁ – z₂|
b. arg (z–z₁) = arg (z –z₂)

d. arg (z–z₁) = arg (z₂ – z₁)

Question. If ω is the cube root of unity, then (3+5ω +3ω²)² + (3+5ω +3ω²)² ?     
a. 4
b. 0
c. – 4
d. 5

Question. If i = −1 ,then

is equal to:     
a. 1 − i√3
b. −1+i√3
c. i√3
d. − i√3

Question. If -1+√3 = reiθ then θ is equal to   
a.π/3
b. -π/3
c. 2π/3
d. -2π/3

Question. Let ω is an imaginary cube root of unity then the value of      
2(ω +1) (ω + 1) + 3(2ω +1) (2ω +1) + …..
2 +(n +1) (nω +1)(nω +1) is: 

Question. If 1/x + x = 2cosθ , then xⁿ + 1/xⁿ is equal to     
a. 2cos nθ
b. 2 sin nθ
c. cos nθ
d. sin nθ

Question. The roots of the equation x⁴ – 1 = 0, are:   
a. 1, 1, i, – i
b. 1, –1, i, – i
c. 1, –1, ω, ω²
d. None of these

Question. If (1+i√3 )⁹ , + i = a + ib then b is equal to:   
a. 1
b. 256
c. 0
d. 9³

Question. The common roots of the equations z³+(1+i)z² +(1+i) z +i = 0 (where i = √-1) and z¹⁹⁹³ + z¹⁹⁹⁴ + 1= 0 are:     
a. 1
b. ω
c. ω²
d. ω⁹⁸¹

Question. If x+1/x = √3, then x =?     
a. cos Π/3 + isin Π/3
b. cos Π/2 + isin Π/2
c. sin Π/6 + icos  Π/6
d. cos  Π/6 + isin Π/6

Question. If α is a complex constant such that 2 α z + z +α = 0 has a real root, then:     
a. α +α = 1
b. α +α = 0
c. α +α = −1
d. the absolute value of the real root is 1.

Question. i log (x-i/x+i) is equal to:   
a. Π+2 tan^-1x
b. Π–2 tan^-1x
c. –Π+2 tan^-1x
d. –Π–2 tan^-1x

Question. If eiθ = cosiθ +i sinθ  = + , then in %ABC value of e^iA .e^iB .e^iC is:       
a. – i
b. 1
c. –1
d. None of these

Read the following passage and answer the questions. Let S = S1∩S2 ∩S3 , where 1 S = {z∈C 😐 z |< 4}, 

Question. Area of S is equal to:     
a. 10π/3
b. 20π/3
c. 16π/3
d. 32π/3

Question. min |1 –3i –z | is equal to:     
a. 2–√3/2
b. 2+√3/2
c. 3–√3/2
d. 3+√3/2

Question. Match the statements/expression given is Column-I with the values given in Column-II:

a. A→ 2; B→ 4; C→ 2; D→ 3
b. A→ 3; B→ 1; C→ 5; D→ 4
c. A→ 4; B→ 3; C→ 5; D→1
d. A→ 1; B→ 2; C→ 3; D→ 4 

Question. Match the statements of Column I with these in Column II: [Note: Here z takes values in the complex plane and Im(z) and Re(z) denote respectively, the imaginary part and the real part of z] 

a. A→ 2; B→ 1; C→ 5; D→ 3
b. A→ 1; B→ 2; C→ 3,5; D→1
c. A→ 4; B→ 2; C→ 3; D→ 2
d. A→ 1; B→ 2; C→ 3; D→ 4

Question. Let  

a. A→ 2; B→ 1, C→ 2; D→ 1
b. A→ 1; B→ 2; C→ 3; D→ 4
c. A→ 4; B→ 2; C→ 3; D→ 2
d. A→ 1; B→ 2; C→ 4; D→ 3

Question. If z is any complex number satisfying | z − 3 − 2i |≤ 2, then the maximum value of |2z – 6 + 5i|is:     

Question. Let ω = e^iπ/3  and a,b,c,x, y, z be non – zero complex numbers such that 2 a+b+c = x,+bω +cω 2 = y,a +bω +cω = z. Then, the value of

Question. If | z₁ |= 2,| z₂ |= 3,| z₃ |= 4 and | 2z₁ + 3z₂ + 4z₃ |= 9, then absolute value 8z₂z₃ +27z₃z₁ + 64z₁z₂ must be equal to: