1
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is :
A
$${2 \over 9}$$
B
$${1 \over 9}$$
C
$${8 \over 9}$$
D
$${7 \over 9}$$
2
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
Let $$A$$ and $$B$$ two events such that $$P\left( {\overline {A \cup B} } \right) = {1 \over 6},$$ $$P\left( {A \cap B} \right) = {1 \over 4}$$ and $$P\left( {\overline A } \right) = {1 \over 4},$$ where $${\overline A }$$ stands for complement of event $$A$$. Then events $$A$$ and $$B$$ are :
A
equally likely and mutually exclusive
B
equally likely but not independent
C
independent but not equally likely
D
mutually exclusive and independent
3
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
If the angel $$\theta $$ between the line $${{x + 1} \over 1} = {{y - 1} \over 2} = {{z - 2} \over 2}$$ and

the plane $$2x - y + \sqrt \lambda \,\,z + 4 = 0$$ is such that $$\sin \,\,\theta = {1 \over 3}$$ then value of $$\lambda $$ is :
A
$${5 \over 3}$$
B
$${-3 \over 5}$$
C
$${3 \over 4}$$
D
$${-4 \over 3}$$
4
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
If $$C$$ is the mid point of $$AB$$ and $$P$$ is any point outside $$AB,$$ then :
A
$$\overrightarrow {PA} + \overrightarrow {PB} = 2\overrightarrow {PC} $$
B
$$\overrightarrow {PA} + \overrightarrow {PB} = \overrightarrow {PC} $$
C
$$\overrightarrow {PA} + \overrightarrow {PB} = 2\overrightarrow {PC} = \overrightarrow 0 $$
D
$$\overrightarrow {PA} + \overrightarrow {PB} = \overrightarrow {PC} = \overrightarrow 0 $$
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