1
IIT-JEE 1986
MCQ (Single Correct Answer)
+2
-0.5
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
MCQ (More than One Correct Answer)
+2
-0.5
Let $${z_1}$$ and $${z_2}$$ be complex numbers such that $${z_1}$$ $$ \ne $$ $${z_2}$$ and $$\left| {{z_1}} \right| =\,\left| {{z_2}} \right|$$. If $${z_1}$$ has positive real and $${z_2}$$ has negative imaginary part, then $${{{z_1}\, + \,{z_2}} \over {{z_1}\, - \,{z_2}}}$$ may be
A
zero
B
real and positive
C
real and negative
D
purely imaginary
3
IIT-JEE 1986
Fill in the Blanks
+2
-0
The equation of the line passing through the points of intersection of the circles $$3{x^2} + 3{y^2} - 2x + 12y - 9 = 0$$ and $${x^2} + {y^2} - 6x + 2y - 15 = 0$$ is..............................
4
IIT-JEE 1986
Subjective
+5
-0
Lines 5x + 12y - 10 = 0 and 5x - 12y - 40 = 0 touch a circle $$C_1$$ of diameter 6. If the centre of $$C_1$$ lies in the first quadrant, find the equation of the circle $$C_2$$ which is concentric with $$C_1$$ and cuts intercepts of length 8 on these lines.
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