1
IIT-JEE 1989
Subjective
+4
-0
If $$f$$ and $$g$$ are continuous function on $$\left[ {0,a} \right]$$ satisfying
$$f\left( x \right) = f\left( {a - x} \right)$$ and $$g\left( x \right) + g\left( {a - x} \right) = 2,$$
then show that $$\int\limits_0^a {f\left( x \right)g\left( x \right)dx = \int\limits_0^a {f\left( x \right)dx} } $$
2
IIT-JEE 1988
Subjective
+5
-0
Find the area of the region bounded by the curve $$C:y=$$
$$\tan x,$$ tangent drawn to $$C$$ at $$x = {\pi \over 4}$$ and the $$x$$-axis.
3
IIT-JEE 1988
Subjective
+5
-0
Evaluate $$\int\limits_0^1 {\log \left[ {\sqrt {1 - x} + \sqrt {1 + x} } \right]dx} $$
4
IIT-JEE 1987
Subjective
+6
-0
Find the area bounded by the curves, $${x^2} + {y^2} = 25,\,4y = \left| {4 - {x^2}} \right|$$ and $$x=0$$ above the $$x$$-axis.
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