1
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 $$QSR$$.
2
IIT-JEE 1993
Subjective
+5
-0
Let $$f\left( x \right) = \left\{ {\matrix{
{ - {x^3} + {{\left( {{b^3} - {b^2} + b - 1} \right)} \over {\left( {{b^2} + 3b + 2} \right)}},} & {0 \le x < 1} \cr
{2x - 3} & {1 \le x \le 3} \cr
} } \right.$$
Find all possible real values of $$b$$ such that $$f(x)$$ has the smallest value at $$x=1$$.
3
IIT-JEE 1993
Subjective
+3
-0
Find the equation of the normal to the curve
$$y = {\left( {1 + x} \right)^y} + {\sin ^{ - 1}}\left( {{{\sin }^2}x} \right)$$ at $$x=0$$
$$y = {\left( {1 + x} \right)^y} + {\sin ^{ - 1}}\left( {{{\sin }^2}x} \right)$$ at $$x=0$$
4
IIT-JEE 1992
Subjective
+2
-0
In this questions there are entries in columns $$I$$ and $$II$$. Each entry in column $$I$$ is related to exactly one entry in column $$II$$. Write the correct letter from column $$II$$ against the entry number in column $$I$$ in your answer book.
Let the functions defined in column $$I$$ have domain $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$
$$\,\,\,\,$$Column $$I$$
(A) $$x + \sin x$$
(B) $$\sec x$$
$$\,\,\,\,$$Column $$II$$
(p) increasing
(q) decreasing
(r) neither increasing nor decreasing
Questions Asked from Application of Derivatives (Subjective)
Number in Brackets after Paper Indicates No. of Questions
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