1
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.

The probability that $$X\ge3$$ equals :

A
$${{125} \over {216}}$$
B
$${{25} \over {36}}$$
C
$${{5} \over {36}}$$
D
$${{25} \over {216}}$$
2
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1

If $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c $$ and $$\overrightarrow d $$ are unit vectors such that $$(\overrightarrow a \times \overrightarrow b )\,.\,(\overrightarrow c \times \overrightarrow d ) = 1$$ and $$\overrightarrow a \,.\,\overrightarrow c = {1 \over 2}$$, then

A
$$\overrightarrow a \,,\,\overrightarrow b ,\overrightarrow c $$ are non-coplanar
B
$$\overrightarrow b \,,\,\overrightarrow c ,\overrightarrow d $$ are non-coplanar
C
$$\overrightarrow b \,,\overrightarrow d $$ are non-parallel
D
$$\overrightarrow a ,\overrightarrow d $$ parallel and $$\overrightarrow b ,\overrightarrow c $$ are parallel
3
IIT-JEE 2009 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
Let $$P(3,2,6)$$ be a point in space and $$Q$$ be a point on the line $$$\widehat r = \left( {\widehat i - \widehat j + 2\widehat k} \right) + \mu \left( { - 3\widehat i + \widehat j + 5\widehat k} \right)$$$

Then the value of $$\mu $$ for which the vector $${\overrightarrow {PQ} }$$ is parallel to the plane $$x - 4y + 3z = 1$$ is :

A
$${1 \over 4}$$
B
$$-{1 \over 4}$$
C
$${1 \over 8}$$
D
$$-{1 \over 8}$$
4
IIT-JEE 2009 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

Let $$L = \mathop {\lim }\limits_{x \to 0} {{a - \sqrt {{a^2} - {x^2}} - {{{x^2}} \over 4}} \over {{x^4}}},a > 0$$. If L is finite, then

A
$$a = 2$$
B
$$a = 1$$
C
$$L = {1 \over {64}}$$
D
$$L = {1 \over {32}}$$
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