1
IIT-JEE 1994
MCQ (Single Correct Answer)
+1
-0.25
Which one of the following curves cut the parabola $${y^2} = 4ax$$ at right angles?
A
$${x^2} + {y^2} = {a^2}$$
B
$$y = {e^{ - x/2a}}$$
C
$$y = ax$$
D
$${x^2} = 4ay$$
2
IIT-JEE 1994
Subjective
+5
-0
The curve $$y = a{x^3} + b{x^2} + cx + 5$$, touches the $$x$$-axis at $$P(-2, 0)$$ and cuts the $$y$$ axis at a point $$Q$$, where its gradient is $$3$$. Find $$a, b, c$$.
3
IIT-JEE 1994
Subjective
+5
-0
The circle $${x^2} + {y^2} = 1$$ cuts the $$x$$-axis at $$P$$ and $$Q$$. Another circle with centre at $$Q$$ and variable radius intersects the first circle at $$R$$ above the $$x$$-axis and the line segment $$PQ$$ at $$S$$. Find the maximum area of the triangle $$QSR$$.
4
IIT-JEE 1994
Subjective
+5
-0
Find the indefinite integral $$\,\int {\cos 2\theta {\mkern 1mu} ln\left( {{{\cos \theta + \sin \theta } \over {\cos \theta - \sin \theta }}} \right)} {\mkern 1mu} d\theta $$
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