1
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
$${2 \over 5}$$
2
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
$$\alpha = 1,\,\,\beta = 1$$
3
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
The non-zero vectors are $${\overrightarrow a ,\overrightarrow b }$$ and $${\overrightarrow c }$$ are related by $${\overrightarrow a = 8\overrightarrow b }$$ and $${\overrightarrow c = - 7\overrightarrow b \,\,.}$$ Then the angle between $${\overrightarrow a }$$ and $${\overrightarrow c }$$ is :
A
$$0$$
B
$${\pi \over 4}$$
C
$${\pi \over 2}$$
D
$$\pi $$
4
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
The line passing through the points $$(5,1,a)$$ and $$(3, b, 1)$$ crosses the $$yz$$-plane at the point $$\left( {0,{{17} \over 2}, - {{ - 13} \over 2}} \right)$$ . Then
A
$$a=2,$$ $$b=8$$
B
$$a=4,$$ $$b=6$$
C
$$a=6,$$ $$b=4$$
D
$$a=8,$$ $$b=2$$
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