1
IIT-JEE 2012 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A ship is fitted with three engines $${E_1},{E_2}$$ and $${E_3}$$. The engines function independently of each other with respective probabilities $${1 \over 2},{1 \over 4}$$ and $${1 \over 4}$$. For the ship to be operational at least two of its engines must function. Let $$X$$ denote the event that the ship is operational and Let $${X_1},{X_2}$$ and $${X_3}$$ denote respectively the events that the engines $${E_1},{E_2}$$ and $${E_3}$$ are functioning. Which of the following is (are) true?
A
$$P\left[ {X_1^c|X} \right] = {3 \over {16}}$$
B
$$P$$ [exactly two engines of the ship are functioning $$\left. {|X} \right] = {7 \over 8}$$
C
$$P\left[ {X|{X_2}} \right] = {5 \over {16}}$$
D
$$P\left[ {X|{X_1}} \right] = {7 \over {16}}$$
2
IIT-JEE 2012 Paper 1 Offline
+4
-1
The point $$P$$ is the intersection of the straight line joining the points $$Q(2, 3, 5)$$ and $$R(1, -1, 4)$$ with the plane $$5x-4y-z=1.$$ If $$S$$ is the foot of the perpendicular drawn from the point $$T(2, 1, 4)$$ to $$QR,$$ then the length of the line segment $$PS$$ is
A
$${{1 \over {\sqrt 2 }}}$$
B
$${\sqrt 2 }$$
C
$$2$$
D
$${2\sqrt 2 }$$
3
IIT-JEE 2012 Paper 1 Offline
Numerical
+4
-0
If $$\overrightarrow a ,\overrightarrow b$$ and $$\overrightarrow c$$ are unit vectors satisfying
$${\left| {\overrightarrow a - \overrightarrow b } \right|^2} + {\left| {\overrightarrow b - \overrightarrow c } \right|^2} + {\left| {\overrightarrow c - \overrightarrow a } \right|^2} = 9,$$ then $$\left| {2\overrightarrow a + 5\overrightarrow b + 5\overrightarrow c } \right|$$ is
4
IIT-JEE 2012 Paper 1 Offline
+3
-1

If $$\mathop {\lim }\limits_{x \to \infty } \left( {{{{x^2} + x + 1} \over {x + 1}} - ax - b} \right) = 4$$, then

A
a = 1, b = 4
B
a = 1, b = $$-$$4
C
a = 2, b = $$-$$3
D
a = 2, b = 3
EXAM MAP
Medical
NEET