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
MCQ (Single Correct Answer)
+4
-1
The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is
A
75
B
150
C
210
D
243
3
IIT-JEE 2012 Paper 1 Offline
MCQ (Single Correct Answer)
+4
-1
The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x - 5y = 20 to the circle $${x^2}\, + \,{y^2} = 9$$ is
A
$$20\,({x^2}\, + \,{y^2}) - \,\,36x\,\, + \,\,45y = 0$$
B
$$20\,({x^2}\, + \,{y^2}) + \,\,36x\,\, - \,\,45y = 0$$
C
$$36\,({x^2}\, + \,{y^2}) - \,\,20x\,\, + \,\,45y = 0$$
D
$$36\,({x^2}\, + \,{y^2}) + \,\,20x\,\, - \,\,45y = 0$$
4
IIT-JEE 2012 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-0.75
The ellipse $${E_1}:{{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ is inscribed in a rectangle $$R$$ whose sides are parallel to the coordinate axes. Another ellipse $${E_2}$$ passing through the point $$(0, 4)$$ circumscribes the rectangle $$R$$. The eccentricity of the ellipse $${E_2}$$ is
A
$${{\sqrt 2 } \over 2}$$
B
$${{\sqrt 3 } \over 2}$$
C
$${{1 \over 2}}$$
D
$${{3 \over 4}}$$
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