1
AIEEE 2002
+4
-1
A triangle with vertices $$\left( {4,0} \right),\left( { - 1, - 1} \right),\left( {3,5} \right)$$ is
A
isosceles and right angled
B
isosceles but not right angled
C
right angled but not isosceles
D
neither right angled nor isosceles
2
AIEEE 2002
+4
-1
Locus of mid point of the portion between the axes of

$$x$$ $$cos$$ $$\alpha + y\,\sin \alpha = p$$ where $$p$$ is constant is
A
$${x^2} + {y^2} = {4 \over {{p^2}}}$$
B
$${x^2} + {y^2} = 4{p^2}$$
C
$${1 \over {{x^2}}} + {1 \over {{y^2}}} = {2 \over {{p^2}}}$$
D
$${1 \over {{x^2}}} + {1 \over {{y^2}}} = {4 \over {{p^2}}}$$
3
AIEEE 2002
+4
-1
The pair of lines represented by $$3a{x^2} + 5xy + \left( {{a^2} - 2} \right){y^2} = 0$$\$

are perpendicular to each other for
A
two values of $$a$$
B
$$\forall \,a$$
C
for one value of $$a$$
D
for no values of $$a$$
4
AIEEE 2002
+4
-1
If the pair of lines

$$a{x^2} + 2hxy + b{y^2} + 2gx + 2fy + c = 0$$

intersect on the $$y$$-axis then
A
$$2fgh = b{g^2} + c{h^2}$$
B
$$b{g^2} \ne c{h^2}$$
C
$$abc = 2fgh$$
D
none of these
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