1
AIEEE 2005
+4
-1
Out of Syllabus
If the plane $$2ax-3ay+4az+6=0$$ passes through the midpoint of the line joining the centres of the spheres

$${x^2} + {y^2} + {z^2} + 6x - 8y - 2z = 13$$ and

$${x^2} + {y^2} + {z^2} - 10x + 4y - 2z = 8$$ then a equals :
A
$$-1$$
B
$$1$$
C
$$-2$$
D
$$2$$
2
AIEEE 2005
+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
$${\sqrt 2 }$$
3
AIEEE 2004
+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
$${2 \over 3}$$
4
AIEEE 2004
+4
-1
Out of Syllabus
Distance between two parallel planes

$$\,2x + y + 2z = 8$$ and $$4x + 2y + 4z + 5 = 0$$ is :
A
$${9 \over 2}$$
B
$${5 \over 2}$$
C
$${7 \over 2}$$
D
$${3 \over 2}$$
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