1
AIEEE 2008
+4
-1
The area of the plane region bounded by the curves $$x + 2{y^2} = 0$$ and $$\,x + 3{y^2} = 1$$ is equal to
A
$${5 \over 3}$$
B
$${1 \over 3}$$
C
$${2 \over 3}$$
D
$${4 \over 3}$$
2
AIEEE 2007
+4
-1
Let $$F\left( x \right) = f\left( x \right) + f\left( {{1 \over x}} \right),$$ where $$f\left( x \right) = \int\limits_l^x {{{\log t} \over {1 + t}}dt,}$$ Then $$F(e)$$ equals
A
$$1$$
B
$$2$$
C
$$1/2$$
D
$$0$$
3
AIEEE 2007
+4
-1
The solution for $$x$$ of the equation $$\int\limits_{\sqrt 2 }^x {{{dt} \over {t\sqrt {{t^2} - 1} }} = {\pi \over 2}}$$ is
A
$${{\sqrt 3 } \over 2}$$
B
$$2\sqrt 2$$
C
$$2$$
D
None
4
AIEEE 2007
+4
-1
Let $$I = \int\limits_0^1 {{{\sin x} \over {\sqrt x }}dx}$$ and $$J = \int\limits_0^1 {{{\cos x} \over {\sqrt x }}dx} .$$ Then which one of the following is true?
A
$$1 > {2 \over 3}$$ and $$J > 2$$
B
$$1 < {2 \over 3}$$ and $$J < 2$$
C
$$1 < {2 \over 3}$$ and $$J > 2$$
D
$$1 > {2 \over 3}$$ and $$J < 2$$
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