1
AIEEE 2011
+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
$${2 \over 3}$$
2
AIEEE 2011
+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.
3
AIEEE 2010
+4
-1
Out of Syllabus
Statement-1 : The point $$A(3, 1, 6)$$ is the mirror image of the point $$B(1, 3, 4)$$ in the plane $$x-y+z=5.$$

Statement-2 : The plane $$x-y+z=5$$ bisects the line segment joining $$A(3, 1, 6)$$ and $$B(1, 3, 4).$$
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.
4
AIEEE 2010
+4
-1
A line $$AB$$ in three-dimensional space makes angles $${45^ \circ }$$ and $${120^ \circ }$$ with the positive $$x$$-axis and the positive $$y$$-axis respectively. If $$AB$$ makes an acute angle $$\theta$$ with the positive $$z$$-axis, then $$\theta$$ equals :
A
$${45^ \circ }$$
B
$${60^ \circ }$$
C
$${75^ \circ }$$
D
$${30^ \circ }$$
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