1
IIT-JEE 2008 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Let A, B, C be three sets of complex numbers as defined below :
$$A = \left\{ {z:\,{\mathop{\rm Im}\nolimits} \,\,z\,\, \ge \,1} \right\}$$
$$B = \left\{ {z:\,\,\left| {z - 2 - i} \right| = 3} \right\}$$
$$C = \left\{ {z:\,{\mathop{\rm Re}\nolimits} (1 - i)z) = \sqrt 2 \,} \right\}$$
$$A = \left\{ {z:\,{\mathop{\rm Im}\nolimits} \,\,z\,\, \ge \,1} \right\}$$
$$B = \left\{ {z:\,\,\left| {z - 2 - i} \right| = 3} \right\}$$
$$C = \left\{ {z:\,{\mathop{\rm Re}\nolimits} (1 - i)z) = \sqrt 2 \,} \right\}$$
Let z be any point in $$A \cap B \cap C$$
Then, $${\left| {z + 1 - i} \right|^2} + {\left| {z - 5 - i} \right|^2}$$ lies between :
2
IIT-JEE 2008 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Let A, B, C be three sets of complex numbers as defined below
$$A = \left\{ {z:\,{\mathop{\rm Im}\nolimits} \,\,z\,\, \ge \,1} \right\}$$
$$B = \left\{ {z:\,\,\left| {z - 2 - i} \right| = 3} \right\}$$
$$C = \left\{ {z:\,{\mathop{\rm Re}\nolimits} (1 - i)z) = \sqrt 2 \,} \right\}$$
$$A = \left\{ {z:\,{\mathop{\rm Im}\nolimits} \,\,z\,\, \ge \,1} \right\}$$
$$B = \left\{ {z:\,\,\left| {z - 2 - i} \right| = 3} \right\}$$
$$C = \left\{ {z:\,{\mathop{\rm Re}\nolimits} (1 - i)z) = \sqrt 2 \,} \right\}$$
Let z be any point $$A \cap B \cap C$$ and let w be any point satisfying $$\left| {w - 2 - i} \right| < 3\,$$. Then, $$\left| z \right| - \left| w \right| + 3$$ lies between :
3
IIT-JEE 2007 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
If $$|z|=1$$ and $$z \neq \pm 1$$, then all the values of $$\frac{z}{1-z^{2}}$$ lie on
4
IIT-JEE 2007 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
A man walks a distance of 3 units from the origin towards the north-east (N 45$$^\circ$$E) direction. From there, he walks a distance of 4 units towards the north-west (N 45$$^\circ$$W) direction to reach a point P. Then the position of P in the Argand plane is
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