1
AIEEE 2007
+4
-1
The area enclosed between the curves $${y^2} = x$$ and $$y = \left| x \right|$$ is :
A
$$1/6$$
B
$$1/3$$
C
$$2/3$$
D
$$1$$
2
AIEEE 2005
+4
-1
The area enclosed between the curve $$y = {\log _e}\left( {x + e} \right)$$ and the coordinate axes is :
A
$$1$$
B
$$2$$
C
$$3$$
D
$$4$$
3
AIEEE 2005
+4
-1
The parabolas $${y^2} = 4x$$ and $${x^2} = 4y$$ divide the square region bounded by the lines $$x=4,$$ $$y=4$$ and the coordinate axes. If $${S_1},{S_2},{S_3}$$ are respectively the areas of these parts numbered from top to bottom ; then $${S_1},{S_2},{S_3}$$ is :
A
$$1:2:1$$
B
$$1:2:3$$
C
$$2:1:2$$
D
$$1:1:1$$
4
AIEEE 2005
+4
-1
Let $$f(x)$$ be a non - negative continuous function such that the area bounded by the curve $$y=f(x),$$ $$x$$-axis and the ordinates $$x = {\pi \over 4}$$ and $$x = \beta > {\pi \over 4}$$ is $$\left( {\beta \sin \beta + {\pi \over 4}\cos \beta + \sqrt 2 \beta } \right).$$ Then $$f\left( {{\pi \over 2}} \right)$$ is
A
$$\left( {{\pi \over 4} + \sqrt 2 - 1} \right)$$
B
$$\left( {{\pi \over 4} - \sqrt 2 + 1} \right)$$
C
$$\left( {1 - {\pi \over 4} - \sqrt 2 } \right)$$
D
$$\left( {1 - {\pi \over 4} + \sqrt 2 } \right)$$
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