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1

IIT-JEE 1994

Fill in the Blanks
Let $$P$$ be a variable point on the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ with foci $${F_1}$$ and $${F_2}$$. If $$A$$ is the area of the triangle $$P{F_1}{F_2}$$ then the maximum value of $$A$$ is ..........

Answer

$$abc$$
2

IIT-JEE 1994

Fill in the Blanks
Let $$C$$ be the curve $${y^3} - 3xy + 2 = 0$$. If $$H$$ is the set of points on the curve $$C$$ where the tangent is horizontal and $$V$$ is the set of the point on the curve $$C$$ where the tangent is vertical then $$H=$$.............. and $$V=$$ .................

Answer

$$H = \phi $$
$$V = \left\{ {\left( {1,1} \right)} \right\}$$
3

IIT-JEE 1987

Fill in the Blanks
The set of all $$x$$ for which $$in\left( {1 + x} \right) \le x$$ is equal to ..........

Answer

$$x \ge 0$$
4

IIT-JEE 1983

Fill in the Blanks
The function $$y = 2{x^2} - In\,\left| x \right|$$ is monotonically increasing for values of $$x\left( {x \ne 0} \right)$$ satisfying the inequalities ......... and monotonically decreasing for values of $$x$$ satisfying the inequalities ............

Answer

$$x \in \left( { - {1 \over 2},{\mkern 1mu} 0} \right) \cup \left( {{1 \over 2},{\mkern 1mu} \alpha } \right);{\mkern 1mu} {\mkern 1mu} \left( { - \alpha ,{\mkern 1mu} - {1 \over 2}} \right) \cup \left( {0,{\mkern 1mu} {1 \over 2}} \right)$$

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