1
IIT-JEE 1988
Subjective
+3
-0
Let $$OA$$ $$CB$$ be a parallelogram with $$O$$ at the origin and $$OC$$ a diagonal. Let $$D$$ be the midpoint of $$OA.$$ Using vector methods prove that $$BD$$ and $$CO$$ intersect in the same ratio. Determine this ratio.
2
IIT-JEE 1988
Subjective
+5
-0
Evaluate $$\int\limits_0^1 {\log \left[ {\sqrt {1 - x} + \sqrt {1 + x} } \right]dx} $$
3
IIT-JEE 1988
MCQ (Single Correct Answer)
+2
-0.5
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.
4
IIT-JEE 1988
Fill in the Blanks
+2
-0
For any two complex numbers $${z_1},{z_2}$$ and any real number a and b.

$$\,{\left| {a{z_1} - b{z_2}} \right|^2} + {\left| {b{z_1} + a{z_2}} \right|^2} = .........$$

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