1
IIT-JEE 1991
Subjective
+4
-0
In a triangle of base a the ratio of the other two sides is $$r\left( { < 1} \right)$$. Show that the altitude of the triangle is less than of equal to $${{ar} \over {1 - {r^2}}}$$
2
IIT-JEE 1991
Subjective
+4
-0
The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Determine the sides of the triangle.
3
IIT-JEE 1991
Subjective
+4
-0
A window of perimeter $$P$$ (including the base of the arch) is in the form of a rectangle surmounded by a semi circle. The semi-circular portion is fitted with coloured glass while the rectangular part is fitted with clear glass transmits three times as such light per square meter as the coloured glass does.

What is the ratio for the sides of the rectangle so that the window transmits the maximum light ?

4
IIT-JEE 1991
Subjective
+4
-0
Sketch the curves and identify the region bounded by
$$x = {1 \over 2},x = 2,y = \ln \,x$$ and $$y = {2^x}.$$ Find the area of this region.
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