1
AIEEE 2004
+4
-1
Out of Syllabus
The intersection of the spheres
$${x^2} + {y^2} + {z^2} + 7x - 2y - z = 13$$ and
$${x^2} + {y^2} + {z^2} - 3x + 3y + 4z = 8$$
is the same as the intersection of one of the sphere and the plane
A
$$2x-y-z=1$$
B
$$x-2y-z=1$$
C
$$x-y-2z=1$$
D
$$x-y-z=1$$
2
AIEEE 2004
+4
-1
A line with direction cosines proportional to $$2,1,2$$ meets each of the lines $$x=y+a=z$$ and $$x+a=2y=2z$$ . The co-ordinates of each of the points of intersection are given by :
A
$$\left( {2a,3a,3a} \right),\left( {2a,a,a} \right)$$
B
$$\left( {3a,2a,3a} \right),\left( {a,a,a} \right)$$
C
$$\left( {3a,2a,3a} \right),\left( {a,a,2a} \right)$$
D
$$\left( {3a,3a,3a} \right),\left( {a,a,a} \right)$$
3
AIEEE 2004
+4
-1
If the straight lines
$$x=1+s,y=-3$$$$- \lambda s,$$ $$z = 1 + \lambda s$$ and $$x = {t \over 2},y = 1 + t,z = 2 - t,$$ with parameters $$s$$ and $$t$$ respectively, are co-planar, then $$\lambda$$ equals :
A
$$0$$
B
$$-1$$
C
$$- {1 \over 2}$$
D
$$-2$$
4
AIEEE 2003
+4
-1
Out of Syllabus
The shortest distance from the plane $$12x+4y+3z=327$$ to the sphere

$${x^2} + {y^2} + {z^2} + 4x - 2y - 6z = 155$$ is
A
$$39$$
B
$$26$$
C
$$11{4 \over {13}}$$
D
$$13$$
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