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1

### IIT-JEE 2002

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 values of $$a$$
D
for no values of $$a$$
2

### IIT-JEE 2002

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
3

### IIT-JEE 2002

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
$${1 \over {{x^2}}} + {1 \over {{y^2}}} = {4 \over {{p^2}}}$$
4

### IIT-JEE 2002

A triangle with vertices $$(4, 0), (-1, -1), (3, 5)$$is
A
isosceles and right angled
B
isosceles but not right angled
C
right angled but not isosceles
D
neither right angled nor isosceles

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