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1

### IIT-JEE 1990

Subjective
A point $$P$$ is given on the circumference of a circle of radius $$r$$. Chord $$QR$$ is parallel to the tangent at $$P$$. Determine the maximum possible area of the triangle $$PQR$$.

$${{3\sqrt 3 } \over 4}\,\,{r^2}$$
2

### IIT-JEE 1990

Subjective
Show that $$2\sin x + \tan x \ge 3x$$ where $$0 \le x < {\pi \over 2}$$.

Solve it.
3

Subjective
Find all maxima and minima of the function $$y = x{\left( {x - 1} \right)^2},0 \le x \le 2$$$Also determine the area bounded by the curve $$y = x{\left( {x - 1} \right)^2}$$, the $$y$$-axis and the line $$y-2$$. ## Answer $${{10 \over 3}}$$ sq. units 4 ### IIT-JEE 1988 Subjective Investigate for maxima and minimum the function $$f\left( x \right) = \int\limits_1^x {\left[ {2\left( {t - 1} \right){{\left( {t - 2} \right)}^3} + 3{{\left( {t - 1} \right)}^2}{{\left( {t - 2} \right)}^2}} \right]} dt$$$

min at $$x = {7 \over 5}$$
max at $$x = 1$$.

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