1

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 ?

2

IIT-JEE 1990

Subjective

+4

-0

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

3

IIT-JEE 1990

Subjective

+4

-0

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 $$PQR$$.

4

IIT-JEE 1989

Subjective

+5

-0

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 $$y-2$$.

Also determine the area bounded by the curve $$y = x{\left( {x - 1} \right)^2}$$,

the $$y$$-axis and the line $$y-2$$.

Questions Asked from Application of Derivatives (Subjective)

Number in Brackets after Paper Indicates No. of Questions

IIT-JEE 2006 (1)
IIT-JEE 2005 (2)
IIT-JEE 2004 (2)
IIT-JEE 2003 (4)
IIT-JEE 2001 (1)
IIT-JEE 2000 (1)
IIT-JEE 1998 (2)
IIT-JEE 1997 (1)
IIT-JEE 1996 (3)
IIT-JEE 1995 (1)
IIT-JEE 1994 (2)
IIT-JEE 1993 (2)
IIT-JEE 1992 (3)
IIT-JEE 1991 (1)
IIT-JEE 1990 (2)
IIT-JEE 1989 (1)
IIT-JEE 1988 (1)
IIT-JEE 1987 (1)
IIT-JEE 1985 (2)
IIT-JEE 1983 (2)
IIT-JEE 1982 (2)
IIT-JEE 1981 (3)
IIT-JEE 1979 (1)

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