Complex Numbers & Quadratic Equations Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. If a, ß be the  roots of the equation , then the equation
whose roots are
 is
(a)
(b)
(c)
(d) None of these
2. If z
1
 =  and , then in which quadrant   lies?
(a) I
(b) II
(c) III
(d) IV
Page 2


PART-I (Single Correct MCQs)
1. If a, ß be the  roots of the equation , then the equation
whose roots are
 is
(a)
(b)
(c)
(d) None of these
2. If z
1
 =  and , then in which quadrant   lies?
(a) I
(b) II
(c) III
(d) IV
3. The root of the equation  which has
greater modulus is
(a)
(b)
(c)
(d) None of these
4. Value of   is
(a)
(b)
(c)
(d)
5. Let a > 0, b > 0 and c > 0. Then both the roots of the equation ax
2
 + bx
+ c = 0
(a) are real and negative
(b) have negative real parts
(c) are rational numbers
(d) None of these
6. Let z lies on the circle centred at the origin. If area of the triangle whose
vertices are z, ?z and z+?z, where ? is the cube root of unity is 
sq. unit. Then radius of the circle is :
(a) 1 unit
(b) 2 units
(c) 4 units
(d) None of these
7. The complex number z satisfying the equations
, is
Page 3


PART-I (Single Correct MCQs)
1. If a, ß be the  roots of the equation , then the equation
whose roots are
 is
(a)
(b)
(c)
(d) None of these
2. If z
1
 =  and , then in which quadrant   lies?
(a) I
(b) II
(c) III
(d) IV
3. The root of the equation  which has
greater modulus is
(a)
(b)
(c)
(d) None of these
4. Value of   is
(a)
(b)
(c)
(d)
5. Let a > 0, b > 0 and c > 0. Then both the roots of the equation ax
2
 + bx
+ c = 0
(a) are real and negative
(b) have negative real parts
(c) are rational numbers
(d) None of these
6. Let z lies on the circle centred at the origin. If area of the triangle whose
vertices are z, ?z and z+?z, where ? is the cube root of unity is 
sq. unit. Then radius of the circle is :
(a) 1 unit
(b) 2 units
(c) 4 units
(d) None of these
7. The complex number z satisfying the equations
, is
(a)
(b)
(c)
(d) 0
8. If  and a, b, c are complex numbers such that 
and , then the value of  is equal to
(a) –1
(b) 2i
(c) 0
(d) +1
9. If  = 14, then the value of x is
given by
(a) 2, 2 ± 
(b) 2 ± , 3
(c) 3 ± , 2
(d) None of these
10. is equal to
(a) 2
(b) zero
(c) – 1
(d) 1
11. is equal to :
(a)
Page 4


PART-I (Single Correct MCQs)
1. If a, ß be the  roots of the equation , then the equation
whose roots are
 is
(a)
(b)
(c)
(d) None of these
2. If z
1
 =  and , then in which quadrant   lies?
(a) I
(b) II
(c) III
(d) IV
3. The root of the equation  which has
greater modulus is
(a)
(b)
(c)
(d) None of these
4. Value of   is
(a)
(b)
(c)
(d)
5. Let a > 0, b > 0 and c > 0. Then both the roots of the equation ax
2
 + bx
+ c = 0
(a) are real and negative
(b) have negative real parts
(c) are rational numbers
(d) None of these
6. Let z lies on the circle centred at the origin. If area of the triangle whose
vertices are z, ?z and z+?z, where ? is the cube root of unity is 
sq. unit. Then radius of the circle is :
(a) 1 unit
(b) 2 units
(c) 4 units
(d) None of these
7. The complex number z satisfying the equations
, is
(a)
(b)
(c)
(d) 0
8. If  and a, b, c are complex numbers such that 
and , then the value of  is equal to
(a) –1
(b) 2i
(c) 0
(d) +1
9. If  = 14, then the value of x is
given by
(a) 2, 2 ± 
(b) 2 ± , 3
(c) 3 ± , 2
(d) None of these
10. is equal to
(a) 2
(b) zero
(c) – 1
(d) 1
11. is equal to :
(a)
(b)
(c)
(d)
12. If p, q, r are non-zero real numbers, the two equation, 
 and  have :
(a) no common root
(b) one common root if 
(c) two common roots if 3pq = 2ab
(d) two common roots if 3qb = 2 ap
13. The centre of a regular hexagon is at the point z = i. If one of its
vertices is at 2 + i, then the adjacent vertices of 2 + i are at the  points
(a) 1± 2i
(b)
(c)
(d)
14. If a, b, c are real numbers  If a, is a root of a
2
x
2
 + bx + c = 0, ß is
a root of a
2
x
2
 – bx – c = 0 and 0 < a < ß, then the equation a
2
x
2
 + 2bx +
2c = 0 has a ? root that always satisfies:
(a) ? = 
(b) ? = 
(c) ? = a
(d) a < ? < ß
15. If the roots of the equation (x – a) (x – b) + (x – b)(x – c) + (x – c) (x –
a) = 0 are equal, then a
2
 + b
2
 + c
2
 =
(a) a + b + c
(b) 2a + b + c
Page 5


PART-I (Single Correct MCQs)
1. If a, ß be the  roots of the equation , then the equation
whose roots are
 is
(a)
(b)
(c)
(d) None of these
2. If z
1
 =  and , then in which quadrant   lies?
(a) I
(b) II
(c) III
(d) IV
3. The root of the equation  which has
greater modulus is
(a)
(b)
(c)
(d) None of these
4. Value of   is
(a)
(b)
(c)
(d)
5. Let a > 0, b > 0 and c > 0. Then both the roots of the equation ax
2
 + bx
+ c = 0
(a) are real and negative
(b) have negative real parts
(c) are rational numbers
(d) None of these
6. Let z lies on the circle centred at the origin. If area of the triangle whose
vertices are z, ?z and z+?z, where ? is the cube root of unity is 
sq. unit. Then radius of the circle is :
(a) 1 unit
(b) 2 units
(c) 4 units
(d) None of these
7. The complex number z satisfying the equations
, is
(a)
(b)
(c)
(d) 0
8. If  and a, b, c are complex numbers such that 
and , then the value of  is equal to
(a) –1
(b) 2i
(c) 0
(d) +1
9. If  = 14, then the value of x is
given by
(a) 2, 2 ± 
(b) 2 ± , 3
(c) 3 ± , 2
(d) None of these
10. is equal to
(a) 2
(b) zero
(c) – 1
(d) 1
11. is equal to :
(a)
(b)
(c)
(d)
12. If p, q, r are non-zero real numbers, the two equation, 
 and  have :
(a) no common root
(b) one common root if 
(c) two common roots if 3pq = 2ab
(d) two common roots if 3qb = 2 ap
13. The centre of a regular hexagon is at the point z = i. If one of its
vertices is at 2 + i, then the adjacent vertices of 2 + i are at the  points
(a) 1± 2i
(b)
(c)
(d)
14. If a, b, c are real numbers  If a, is a root of a
2
x
2
 + bx + c = 0, ß is
a root of a
2
x
2
 – bx – c = 0 and 0 < a < ß, then the equation a
2
x
2
 + 2bx +
2c = 0 has a ? root that always satisfies:
(a) ? = 
(b) ? = 
(c) ? = a
(d) a < ? < ß
15. If the roots of the equation (x – a) (x – b) + (x – b)(x – c) + (x – c) (x –
a) = 0 are equal, then a
2
 + b
2
 + c
2
 =
(a) a + b + c
(b) 2a + b + c
(c) 3abc
(d) ab + bc + ca
16. If , then the simplified form of  is
(a) b + ai
(b) a + bi
(c) (1 + b)
2
 + a
2
(d) ai
17. If  is a non-real cube root of unity, then
 is equal to
(a) – 2
(b) 2
(c)
(d) 0
18. If a, ß are the roots of the equation  ax
2
 + bx + c = 0 such that ß < a < 0,
then the quadratic equation whose roots are |a|, |ß|, is given by
(a) |a| x
2
 + |b| x + |c| = 0
(b) ax
2
 – |b| x + c = 0
(c) |a| x
2
 – |b| x + |c| = 0
(d) a|x|
2
 + b|x| + |c| = 0
19. If z = 2 + i, then  is equal to
(a) 2
(b) 7
(c) –1
(d) –4
20. If a, ß are the roots of the equation 2x
2
 + 6x + b = 0, (b < 0) then 
is less than :
(a) 1
(b) –1
(c) 2
(d) – 2