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1

IIT-JEE 1990

MCQ (Single Correct Answer)
Line $$L$$ has intercepts $$a$$ and $$b$$ on the coordinate axes. When the axes are rotated through a given angle, keeping the origin fixed, the same line $$L$$ has intercepts $$p$$ and $$q$$, then
A
$${a^2} + {b^2} = {p^2} + {q^2}$$
B
$${1 \over {{a^2}}} + {1 \over {{b^2}}} = {1 \over {{p^2}}} + {1 \over {{q^2}}}$$
C
$${a^2} + {p^2} = {b^2} + {q^2}$$
D
$${1 \over {{a^2}}} + {1 \over {{p^2}}} = {1 \over {{b^2}}} + {1 \over {{q^2}}}$$
2

IIT-JEE 1988

MCQ (Single Correct Answer)
If $$P=(1, 0),$$ $$Q=(-1, 0)$$ and $$R=(2, 0)$$ are three given points, then locus of the point $$S$$ satisfying the relation $$S{Q^2} + S{R^2} = 2S{P^2},$$ is
A
a straight line parallel to x-axis
B
a circle passing through the origin
C
a circle with the centre at the origin
D
a straight line parallel to y-axis.
3

IIT-JEE 1986

MCQ (Single Correct Answer)
A vector $$\overline a $$ has components $$2p$$ and $$1$$ with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to the new system, $$\overline a $$ has components $$p + 1$$ and $$1$$, then
A
$$p = 0$$
B
$$p = 1$$ or $$p = - {1 \over 3}$$
C
$$\,p = - 1$$ or $$p = {1 \over 3}$$
D
$$p = 1$$ or $$p = -1$$
4

IIT-JEE 1986

MCQ (Single Correct Answer)
The points $$\left( {0,{8 \over 3}} \right),\,\,\left( {1,\,3} \right)$$ and $$\left( {82,\,30} \right)$$ are vertices of
A
an obtuse angled triangle
B
an acute angled triangle
C
a right angled triangle
D
none of these

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