1
JEE Advanced 2013 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
Let $$S = {S_1} \cap {S_2} \cap {S_3}$$, where $${S_1} = \left\{ {z \in C:\left| z \right| < 4} \right\},{S_2} = \left\{ {z \in C:{\mathop{\rm Im}\nolimits} \left[ {{{z - 1 + \sqrt 3 i} \over {1 - \sqrt 3 i}}} \right] > 0} \right\}$$ and $${S_3} = \left\{ {z \in C:{\mathop{\rm Re}\nolimits} z > 0} \right\}\,$$.

Area of S =

A
$${{10\pi } \over 3}$$
B
$${{20\pi } \over 3}$$
C
$${{16\pi } \over 3}$$
D
$${{32\pi } \over 3}$$
2
JEE Advanced 2013 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
Let $$S = {S_1} \cap {S_2} \cap {S_3}$$, where $${S_1} = \left\{ {z \in C:\left| z \right| < 4} \right\},{S_2} = \left\{ {z \in C:{\mathop{\rm Im}\nolimits} \left[ {{{z - 1 + \sqrt 3 i} \over {1 - \sqrt 3 i}}} \right] > 0} \right\}$$ and $${S_3} = \left\{ {z \in C:{\mathop{\rm Re}\nolimits} z > 0} \right\}\,$$.

$$\,\mathop {\min }\limits_{z \in S} \left| {1 - 3i - z} \right| = $$

A
$${{2 - \sqrt 3 } \over 2}$$
B
$${{2 + \sqrt 3 } \over 2}$$
C
$${{3 - \sqrt 3 } \over 2}$$
D
$${{3 + \sqrt 3 } \over 2}$$
3
JEE Advanced 2013 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
Let complex numbers $$\alpha \,and\,{1 \over {\overline \alpha }}\,$$ lie on circles $${\left( {x - {x_0}} \right)^2} + \,\,{\left( {y - {y_0}} \right)^2} = {r^2}$$ and $$\,{\left( {x - {x_0}} \right)^2} + \,\,{\left( {y - {y_0}} \right)^2} = 4{r^2}$$ respextively. If $${z_0} = {x_0} + i{y_0}$$ satisfies the equation $$2{\left| {{z_0}} \right|^2}\, = {r^2} + 2,\,then\,\left| a \right| = $$
A
$${1 \over {\sqrt 2 }}$$
B
$${1 \over 2}\,$$
C
$${1 \over {\sqrt 7 }}$$
D
$${1 \over 3}$$
4
IIT-JEE 2012 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
Let z be a complex number such that the imaginary part of z is non-zero and $$a\, = \,{z^2} + \,z\, + 1$$ is real. Then a cannot take the value
A
- 1
B
$${1 \over 3}$$
C
$${1 \over 2}$$
D
$${3 \over 4}$$
JEE Advanced Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12