JEE-ADVANCED SERIES Mathematics
Complex Numbers And Quadratic Equations
21 previous year questions.
Volume: 21 Ques
Yield: High
High-Yield Trend
1
2014 1
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2009 2
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2000 1
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1992 1
1980 Chapter Questions 21 MCQs
01
PYQ 1980
medium
mathematics ID: jee-adva
Both the roots of the equation are always
1
positive
2
negative
3
real
4
None of these
02
PYQ 1992
medium
mathematics ID: jee-adva
Let be the roots of the equation, .Then the roots of the equation are
1
a, c
2
b, c
3
a, b
4
a + c, b + c
03
PYQ 1997
medium
mathematics ID: jee-adva
The equation has
1
no solution
2
one solution
3
two solutions
4
more than two solutions
04
PYQ 1998
medium
mathematics ID: jee-adva
If is an imaginary cube root of unity, then (1 + - is equal to
1
128
2
-128
3
128
4
-128
05
PYQ 1998
medium
mathematics ID: jee-adva
The value of is
1
-1
2
0
3
-i
4
i
06
PYQ 1999
medium
mathematics ID: jee-adva
If then is equal to
1
1-i
2
-1 + i
3
i
4
-i
07
PYQ 2000
medium
mathematics ID: jee-adva
If and are the roots of the equation where ,the
1
0
2
3
4
08
PYQ 2000
medium
mathematics ID: jee-adva
For the equation if one of the root is square of the other, then p is equal to
1
44564
2
1
3
3
4
44595
09
PYQ 2001
easy
mathematics ID: jee-adva
The complex numbers and satisfying are the vertices of a triangle which is
1
of area zero
2
right angled isosceles
3
equilateral
4
obtuse angled isosceles
10
PYQ 2001
medium
mathematics ID: jee-adva
Let and be nth roots of unity which subtend a right angled at the origin, then n must be of the form (where, k is an integer)
1
4k+1
2
4k+2
3
4k+3
4
4k
11
PYQ 2004
medium
mathematics ID: jee-adva
If one root is square of the other root of the equation then the relation between p and q is
1
2
3
4
12
PYQ 2004
medium
mathematics ID: jee-adva
If be a cube root of unity and then the least positive value of n is
1
2
2
3
3
5
4
6
13
PYQ 2005
medium
mathematics ID: jee-adva
The shaded region, where is represented by
1
| z + 1| >2,| arg (z + 1) |
2
| z + 1| < 2,| arg (z + 1) |
3
| z + 1| >2,| arg (z + 1) |>
4
| z - 1| < 2,| arg (z + 1) |>
14
PYQ 2005
medium
mathematics ID: jee-adva
The minimum value of , where and are all not equal integers and is a cube root of unity, is
1
2
3
1
4
0
15
PYQ 2006
medium
mathematics ID: jee-adva
If a, b,c are the sides of a triangle ABC such that has real roots, then
1
$\lambda
2
3
4
16
PYQ 2007
medium
mathematics ID: jee-adva
Let , be the roots of the equation and be the roots of the equation Then, the value of r is
1
2
3
4
17
PYQ 2007
medium
mathematics ID: jee-adva
A man walks a distance of 3 units from the origin towards the North-East (N 45 E) direction. From there, he walks a distance of 4 units towards the North-West (N 45 W) direction to reach a point P. Then, the position of P in the Arg and plane is
1
2
3
4
18
PYQ 2009
medium
mathematics ID: jee-adva
Let . Then, the value of at is
1
2
3
4
19
PYQ 2011
medium
mathematics ID: jee-adva
A value of for which the equations have one root in common is
1
2
3
4
20
PYQ 2013
easy
mathematics ID: jee-adva
Let and Further and $H_2=\bigg[ z\in C: Re \,z
1
2
3
4
21
PYQ 2014
medium
mathematics ID: jee-adva
In the quadratic equation with real coefficients has purely imaginary roots. Then, the equation has
1
only purely imaginary roots
2
all real roots
3
two real and two purely imaginary roots
4
neither real nor purely imaginary roots