1
IIT-JEE 2012 Paper 2 Offline
+4
-1
Four fair dice $${D_1,}$$ $${D_2,}$$ $${D_3}$$ and $${D_4}$$ ; each having six faces numbered $$1, 2, 3, 4, 5$$ and $$6$$ are rolled simultaneously. The probability that $${D_4}$$ shows a number appearing on one of $${D_1},$$ $${D_2}$$ and $${D_3}$$ is
A
$${{91} \over {216}}$$
B
$${{108} \over {216}}$$
C
$${{125} \over {216}}$$
D
$${{127} \over {216}}$$
2
IIT-JEE 2012 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$X$$ and $$Y$$ be two events such that $$P\left( {X|Y} \right) = {1 \over 2},$$ $$P\left( {Y|X} \right) = {1 \over 3}$$ and $$P\left( {X \cap Y} \right) = {1 \over 6}.$$ Which of the following is (are) correct ?
A
$$P\left( {X \cup Y} \right) = {2 \over 3}$$
B
$$X$$ and $$Y$$ are independent
C
$$X$$ and $$Y$$ are not independent
D
$$P\left( {{X^c} \cap Y} \right) = {1 \over 3}$$
3
IIT-JEE 2012 Paper 2 Offline
+4
-1
The equation of a plane passing through the line of intersection of the planes $$x+2y+3z=2$$ and $$x-y+z=3$$ and at a distance $${2 \over {\sqrt 3 }}$$ from the point $$(3, 1, -1)$$ is
A
$$5x-11y+z=17$$
B
$$\sqrt 2 x + y = 3\sqrt 2 - 1$$
C
$$x + y + z = \sqrt 3$$
D
$$x - \sqrt 2 y = 1 - \sqrt 2$$
4
IIT-JEE 2012 Paper 2 Offline
+4
-1
If $$\overrightarrow a$$ and $$\overrightarrow b$$ are vectors such that $$\left| {\overrightarrow a + \overrightarrow b } \right| = \sqrt {29}$$ and $$\,\overrightarrow a \times \left( {2\widehat i + 3\widehat j + 4\widehat k} \right) = \left( {2\widehat i + 3\widehat j + 4\widehat k} \right) \times \widehat b,$$ then a possible value of $$\left( {\overrightarrow a + \overrightarrow b } \right).\left( { - 7\widehat i + 2\widehat j + 3\widehat k} \right)$$ is
A
$$0$$
B
$$3$$
C
$$4$$
D
$$8$$
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