1
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
If $$\int\limits_0^\pi {xf\left( {\sin x} \right)dx = A\int\limits_0^{\pi /2} {f\left( {\sin x} \right)dx,} } $$ then $$A$$ is
A
$$2\pi $$
B
$$\pi $$
C
$${\pi \over 4}$$
D
$$0$$
2
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
If $$f\left( x \right) = {{{e^x}} \over {1 + {e^x}}},{I_1} = \int\limits_{f\left( { - a} \right)}^{f\left( a \right)} {xg\left\{ {x\left( {1 - x} \right)} \right\}dx} $$
and $${I_2} = \int\limits_{f\left( { - a} \right)}^{f\left( a \right)} {g\left\{ {x\left( {1 - x} \right)} \right\}dx} ,$$ then the value of $${{{I_2}} \over {{I_1}}}$$ is
A
$$1$$
B
$$-3$$
C
$$-1$$
D
$$2$$
3
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
The area of the region bounded by the curves
$$y = \left| {x - 2} \right|,x = 1,x = 3$$ and the $$x$$-axis is :
A
$$4$$
B
$$2$$
C
$$3$$
D
$$1$$
4
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The differential equation for the family of circle $${x^2} + {y^2} - 2ay = 0,$$ where a is an arbitrary constant is :
A
$$\left( {{x^2} + {y^2}} \right)y' = 2xy$$
B
$$2\left( {{x^2} + {y^2}} \right)y' = xy$$
C
$$\left( {{x^2} - {y^2}} \right)y' =2 xy$$
D
$$2\left( {{x^2} - {y^2}} \right)y' = xy$$
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