1
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
If $$C$$ and $$D$$ are two events such that $$C \subset D$$ and $$P\left( D \right) \ne 0,$$ then the correct statement among the following is :
A
$$P\left( {{C \over D}} \right)$$$$ \ge P\left( C \right)$$
B
$$P\left( {{C \over D}} \right)$$$$ < P\left( C \right)$$
C
$$P\left( {{C \over D}} \right)$$$$ = {{P\left( D \right)} \over {P\left( C \right)}}$$
D
$$P\left( {{C \over D}} \right)$$$$ = P\left( C \right)$$
2
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
The vectors $$\overrightarrow a $$ and $$\overrightarrow b $$ are not perpendicular and $$\overrightarrow c $$ and $$\overrightarrow d $$ are two vectors satisfying $$\overrightarrow b \times \overrightarrow c = \overrightarrow b \times \overrightarrow d $$ and $$\overrightarrow a .\overrightarrow d = 0\,\,.$$ Then the vector $$\overrightarrow d $$ is equal to :
A
$$\overrightarrow c + \left( {{{\overrightarrow a .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow b $$
B
$$\overrightarrow b + \left( {{{\overrightarrow b .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow c $$
C
$$\overrightarrow c - \left( {{{\overrightarrow a .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow b $$
D
$$\overrightarrow b - \left( {{{\overrightarrow b .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow c $$
3
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
If the angle between the line $$x = {{y - 1} \over 2} = {{z - 3} \over \lambda }$$ and the plane

$$x+2y+3z=4$$ is $${\cos ^{ - 1}}\left( {\sqrt {{5 \over {14}}} } \right),$$ then $$\lambda $$ equals :
A
$${3 \over 2}$$
B
$${2 \over 5}$$
C
$${5 \over 3}$$
D
$${2 \over 3}$$
4
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Statement - 1 : The point $$A(1,0,7)$$ is the mirror image of the point

$$B(1,6,3)$$ in the line : $${x \over 1} = {{y - 1} \over 2} = {{z - 2} \over 3}$$

Statement - 2 : The line $${x \over 1} = {{y - 1} \over 2} = {{z - 2} \over 3}$$ bisects the line

segment joining $$A(1,0,7)$$ and $$B(1, 6, 3)$$
A
Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1.
B
Statement -1 is true, Statement - 2 is false.
C
Statement - 1 is false , Statement -2 is true.
D
Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for Statement -1.
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