1
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
The solution of the differential equation

$${{dy} \over {dx}} = {{x + y} \over x}$$ satisfying the condition $$y(1)=1$$ is :
A
$$y = \ln x + x$$
B
$$y = x\ln x + {x^2}$$
C
$$y = x{e^{\left( {x - 1} \right)}}\,$$
D
$$y = x\,\ln x + x$$
2
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
It is given that the events $$A$$ and $$B$$ are such that
$$P\left( A \right) = {1 \over 4},P\left( {A|B} \right) = {1 \over 2}$$ and $$P\left( {B|A} \right) = {2 \over 3}.$$ Then $$P(B)$$ is :
A
$${1 \over 6}$$
B
$${1 \over 3}$$
C
$${2 \over 3}$$
D
$${1 \over 2}$$
3
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
A die is thrown. Let $$A$$ be the event that the number obtained is greater than $$3.$$ Let $$B$$ be the event that the number obtained is less than $$5.$$ Then $$P\left( {A \cup B} \right)$$ is :
A
$${3 \over 5}$$
B
$$0$$
C
$$1$$
D
$${2 \over 5}$$
4
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The vector $$\overrightarrow a = \alpha \widehat i + 2\widehat j + \beta \widehat k$$ lies in the plane of the vectors
$$\overrightarrow b = \widehat i + \widehat j$$ and $$\overrightarrow c = \widehat j + \widehat k$$ and bisects the angle between $$\overrightarrow b $$ and $$\overrightarrow c $$.Then which one of the following gives possible values of $$\alpha $$ and $$\beta $$ ?
A
$$\alpha = 2,\,\,\beta = 2$$
B
$$\alpha = 1,\,\,\beta = 2$$
C
$$\alpha = 2,\,\,\beta = 1$$
D
$$\alpha = 1,\,\,\beta = 1$$
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