1
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The distance between the line

$$\overrightarrow r = 2\widehat i - 2\widehat j + 3\widehat k + \lambda \left( {i - j + 4k} \right),$$ and the plane

$$\overrightarrow r .\left( {\widehat i + 5\widehat j + \widehat k} \right) = 5$$ is
A
$${{10} \over 9}$$
B
$${{10} \over {3\sqrt 3 }}$$
C
$${{3} \over 10}$$
D
$${{10} \over 3}$$
2
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
The angle between the lines $$2x=3y=-z$$ and $$6x=-y=-4z$$ is :
A
$${0^ \circ }$$
B
$${90^ \circ }$$
C
$${45^ \circ }$$
D
$${30^ \circ }$$
3
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The plane $$x+2y-z=4$$ cuts the sphere $${x^2} + {y^2} + {z^2} - x + z - 2 = 0$$ in a circle of radius
A
$$3$$
B
$$1$$
C
$$2$$
D
$${\sqrt 2 }$$
4
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
A line makes the same angle $$\theta $$, with each of the $$x$$ and $$z$$ axis.

If the angle $$\beta \,$$, which it makes with y-axis, is such that $$\,{\sin ^2}\beta = 3{\sin ^2}\theta ,$$ then $${\cos ^2}\theta $$ equals :
A
$${2 \over 5}$$
B
$${1 \over 5}$$
C
$${3 \over 5}$$
D
$${2 \over 3}$$
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