IIT-JEE 2008 Paper 1 Offline | JEE Advanced Year Wise Previous Years Questions

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

-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 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 :

- 6 and 3

- 3 and 6

- 6 and 6

- 3 and 9

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

-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 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

IIT-JEE 2008 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

A straight line through the vertex p of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then :

$${1 \over {PS}} + {1 \over {ST}} < {2 \over {\sqrt {QS \times SR} }}$$

$${1 \over {PS}} + {1 \over {ST}} > {2 \over {\sqrt {QS \times SR} }}$$

$${1 \over {PS}} + {1 \over {ST}} < {4 \over {QR}}$$

$${1 \over {PS}} + {1 \over {ST}} > {4 \over {QR}}$$

IIT-JEE 2008 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Let $${S_n} = \sum\limits_{k = 1}^n {{n \over {{n^2} + kn + {k^2}}}} $$ and $${T_n} = \sum\limits_{k = 0}^{n - 1} {{n \over {{n^2} + kn + {k^2}}}} $$ for $$n$$ $$=1, 2, 3, ............$$ Then,

$${S_n} < {\pi \over {3\sqrt 3 }}$$

$${S_n} > {\pi \over {3\sqrt 3 }}$$

$${T_n} < {\pi \over {3\sqrt 3 }}$$

$${T_n} > {\pi \over {3\sqrt 3 }}$$

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