1

IIT-JEE 1986

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 $$p = -1$$
2

IIT-JEE 1986

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
3

IIT-JEE 1983

The straight lines $$x + y = 0,\,3x + y - 4 = 0,\,x + 3y - 4 = 0$$ form a triangle which is
A
isosceles
B
equilateral
C
right angled
D
none of these
4

IIT-JEE 1980

The point $$\,\left( {4,\,1} \right)$$ undergoes the following three transformations successively.
Reflection about the line $$y=x$$.
Translation through a distance 2 units along the positive direction of x-axis.
Rotation through an angle $$p/4$$ about the origin in the counter clockwise direction.
Then the final position of the point is given by the coordinates.
A
$$\left( {{1 \over {\sqrt 2 }},{7 \over {\sqrt 2 }}} \right)$$
B
$$\left( { - \sqrt 2 ,\,7\sqrt 2 } \right)$$
C
$$\left( { - {1 \over {\sqrt 2 }},{7 \over {\sqrt 2 }}} \right)$$
D
$$\left( { \sqrt 2 ,\,7\sqrt 2 } \right)$$

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