GUIDED REVISION
ENTHUSIAST & LEADER
COURSE
Target : JEE(Main + Advanced) - 2019
REVISION ASSINGMENT # 04
TIME : 60 MIN.
(COMPLEX NUMBER)
MATHEMATICS
M.M. : 71
SECTION–I(i)
Straight Objective Type (3 Marks each, –1 for wrong answer)
1.
2.
Let z1 & z2 be non zero complex numbers satisfying the equation, z12 2 z1z2 + 2 z22 = 0. The geometrical
nature of the triangle whose vertices are the origin and the points representing z1 & z2 is :
(A) an isosceles right angled triangle
(B) a right angled triangle which is not isosceles
(C) an equilateral triangle
(D) an isosceles triangle which is not right angled.
Number of ordered pairs(s) (a, b) of real numbers such that (a + ib)2008 = a – ib holds good, is
(A) 2008
3.
(B) 2009
(C) 2010
If w = + i where 0 and z 1, satisfies the condition that
(D) 1
w wz
is purely real, then the set of values
1 z
of z is
(A) {z : | z | = 1}
4.
(C) {z : z 1}
(D) {z : | z | = 1, z 1}
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 Argand plane is
(A) 3ei 4 + 4i
5.
(B) {z : z = z )
(B) (3 4i )ei 4
(C) ( 4 3i )ei 4
(D) (3 4i )ei 4
A particle starts from a point z0 = 1 + i, where i 1 . It moves horizontally away from origin by 2 units and
then vertically away from origin by 3 units to reach a point z1. From z1 particle moves 5 units in the
direction of 2iˆ ˆj and then it moves through an angle of cosec1 2 in anticlockwise direction of a circle with
centre at origin to reach a point z2. The arg z2 is given by
(A) sec–12
(B) cot–10
3 1
1
(C) sin
2 2
1 1
(D) cos
2
SECTION–I(ii)
Linked Comprehension Type (One or more than one correct) (3 Marks each, –1 for wrong answer)
Paragraph for question nos. 6 to 8
Let A, B, C be three sets of complex numbers as defined below.
z 1
1
A = {z : | z +1 | 2 + Re(z)}, B = {z : | z –1 | 1} and C = z :
z 1
6.
The number of point(s) having integral coordinates in the region A B C is
(A) 4
MATHEMATICS /RA # 04
(B) 5
(C) 6
(D) 10
E-1/2
GUIDED REVISION
ENTHUSIAST & LEADER
COURSE
Target : JEE(Main + Advanced) - 2019
7.
The area of region bounded by A B C is
(A) 2 3
8.
(B) 3
(C) 4 3
(D) 2
The real part of the complex number in the region A B C and having maximum amplitude is
(A) –1
(B)
REVISION ASSINGMENT # 04
SECTION-I
E-2/2
Q.
A.
1
A
2
C
3
2
(C)
3
D
1
2
(D) – 2
(COMPLEX NUMBER)
4
D
5
B
6
B
7
A
8
B
MATHEMATICS
MATHEMATICS /RA # 04
0
