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1
AIEEE 2009
MCQ (Single Correct Answer)
+4
-1
The area of the region bounded by the parabola $${\left( {y - 2} \right)^2} = x - 1,$$ the tangent of the parabola at the point $$(2, 3)$$ and the $$x$$-axis is :
A
$$6$$
B
$$9$$
C
$$12$$
D
$$3$$
2
AIEEE 2009
MCQ (Single Correct Answer)
+4
-1
$$\int\limits_0^\pi {\left[ {\cot x} \right]dx,} $$ where $$\left[ . \right]$$ denotes the greatest integer function, is equal to:
A
$$1$$
B
$$-1$$
C
$$ - {\pi \over 2}$$
D
$$ {\pi \over 2}$$
3
AIEEE 2008
MCQ (Single Correct Answer)
+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
$${4 \over 3}$$
4
AIEEE 2007
MCQ (Single Correct Answer)
+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
$$0$$
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