1
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
The two lines $$x=ay+b,z=cy+d$$ and $$x = a'y + b',z = c'y + d'$$ will be perpendicular, if and only if :
A
$$aa' + cc' + 1 = 0$$
B
$$aa' + bb'cc' + 1 = 0$$
C
$$aa' + bb'cc' = 0$$
D
$$\left( {a + a'} \right)\left( {b + b'} \right) + \left( {c + c'} \right) = 0$$
2
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
The lines $${{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}$$ and $${{x - 1} \over k} = {{y - 4} \over 2} = {{z - 5} \over 1}$$ are coplanar if :
A
$$k=3$$ or $$-2$$
B
$$k=0$$ or $$-1$$
C
$$k=1$$ or $$-1$$
D
$$k=0$$ or $$-3$$
3
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The radius of the circle in which the sphere

$${x^2} + {y^2} + {z^2} + 2x - 2y - 4z - 19 = 0$$ is cut by the plane

$$x+2y+2z+7=0$$ is
A
$$4$$
B
$$1$$
C
$$2$$
D
$$3$$
4
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Two systems of rectangular axes have the same origin. If a plane cuts then at distances $$a,b,c$$ and $$a', b', c'$$ from the origin then
A
$${1 \over {{a^2}}} + {1 \over {{b^2}}} + {1 \over {{c^2}}} - {1 \over {a{'^2}}} - {1 \over {b{'^2}}} - {1 \over {c{'^2}}} = 0$$
B
$$\,{1 \over {{a^2}}} + {1 \over {{b^2}}} + {1 \over {{c^2}}} + {1 \over {a{'^2}}} + {1 \over {b{'^2}}} + {1 \over {c{'^2}}} = 0$$
C
$${1 \over {{a^2}}} + {1 \over {{b^2}}} - {1 \over {{c^2}}} + {1 \over {a{'^2}}} - {1 \over {b{'^2}}} - {1 \over {c{'^2}}} = 0$$
D
$${1 \over {{a^2}}} - {1 \over {{b^2}}} - {1 \over {{c^2}}} + {1 \over {a{'^2}}} - {1 \over {b{'^2}}} - {1 \over {c{'^2}}} = 0$$
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