1
AIEEE 2010
+4
-1
Let $$p(x)$$ be a function defined on $$R$$ such that $$p'(x)=p'(1-x),$$ for all $$x \in \left[ {0,1} \right],p\left( 0 \right) = 1$$ and $$p(1)=41.$$ Then $$\int\limits_0^1 {p\left( x \right)dx}$$ equals
A
$$21$$
B
$$41$$
C
$$42$$
D
$$\sqrt {41}$$
2
AIEEE 2010
+4
-1
The area bounded by the curves $$y = \cos x$$ and $$y = \sin x$$ between the ordinates $$x=0$$ and $$x = {{3\pi } \over 2}$$ is
A
$$4\sqrt 2 + 2$$
B
$$4\sqrt 2 - 1$$
C
$$4\sqrt 2 + 1$$
D
$$4\sqrt 2 - 2$$
3
AIEEE 2009
+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
$$3$$
4
AIEEE 2009
+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
$${\pi \over 2}$$
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