Sign In

JEE Advance - Mathematics (2008 - Paper 1 Offline - No. 1)

Let A, B, C be three sets of complex numbers as defined below :

$$A = \left\{ {z:\,{\mathop{\rm Im}\nolimits} \,\,z\,\, \ge \,1} \right\}$$

$$B = \left\{ {z:\,\,\left| {z - 2 - i} \right| = 3} \right\}$$

$$C = \left\{ {z:\,{\mathop{\rm Re}\nolimits} (1 - i)z) = \sqrt 2 \,} \right\}$$
Let A, B, C be three sets of complex numbers as defined below :

$$A = \left\{ {z:\,{\mathop{\rm Im}\nolimits} \,\,z\,\, \ge \,1} \right\}$$

$$B = \left\{ {z:\,\,\left| {z - 2 - i} \right| = 3} \right\}$$

$$C = \left\{ {z:\,{\mathop{\rm Re}\nolimits} (1 - i)z) = \sqrt 2 \,} \right\}$$
Let A, B, C be three sets of complex numbers as defined below :

$$A = \left\{ {z:\,{\mathop{\rm Im}\nolimits} \,\,z\,\, \ge \,1} \right\}$$

$$B = \left\{ {z:\,\,\left| {z - 2 - i} \right| = 3} \right\}$$

$$C = \left\{ {z:\,{\mathop{\rm Re}\nolimits} (1 - i)z) = \sqrt 2 \,} \right\}$$

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 :

25 and 29
30 and 34
35 and 39
40 and 44

Explanation

$$|z + 1 - i{|^2} + |z - 5 - i{|^2}$$

The points ($$-1,1$$) and (5, 1) are the extremities of the diameter of the given circle of radius 3

Hence, PA$$^2$$ + PB$$^2$$ = AB$$^2$$ = 36

Comments (0)

Advertisement