1
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
The values of a, for which the points $$A, B, C$$ with position vectors $$2\widehat i - \widehat j + \widehat k,\,\,\widehat i - 3\widehat j - 5\widehat k$$ and $$a\widehat i - 3\widehat j + \widehat k$$ respectively are the vertices of a right angled triangle with $$C = {\pi \over 2}$$ are :
A
$$2$$ and $$1$$
B
$$-2$$ and $$-1$$
C
$$-2$$ and $$1$$
D
$$2$$ and $$-1$$
2
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
The two lines $$x=ay+b, z=cy+d;$$ and $$x=a'y+b' ,$$ $$z=c'y+d'$$ are perpendicular to each other if :
A
$$aa'+cc'=-1$$
B
$$aa'+cc'=1$$
C
$${a \over {a'}} + {c \over {c'}} = - 1$$
D
$${a \over {a'}} + {c \over {c'}} = 1$$
3
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
If $$0 < x < \pi $$ and $$\cos x + \sin x = {1 \over 2},$$ then $$\tan x$$ is :
A
$${{\left( {1 - \sqrt 7 } \right)} \over 4}$$
B
$${{\left( {4 - \sqrt 7 } \right)} \over 3}$$
C
$$ - {{\left( {4 + \sqrt 7 } \right)} \over 3}$$
D
$${{\left( {1 + \sqrt 7 } \right)} \over 4}$$
4
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
If $${z^2} + z + 1 = 0$$, where z is complex number, then value of $${\left( {z + {1 \over z}} \right)^2} + {\left( {{z^2} + {1 \over {{z^2}}}} \right)^2} + {\left( {{z^3} + {1 \over {{z^3}}}} \right)^2} + .......... + {\left( {{z^6} + {1 \over {{z^6}}}} \right)^2}$$ is :
A
18
B
54
C
6
D
12
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