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 2003
MCQ (Single Correct Answer)
+4
-1
The value of the integral $$I = \int\limits_0^1 {x{{\left( {1 - x} \right)}^n}dx} $$ is
A
$${1 \over {n + 1}} + {1 \over {n + 2}}$$
B
$${1 \over {n + 1}}$$
C
$${1 \over {n + 2}}$$
D
$${1 \over {n + 1}} - {1 \over {n + 2}}$$
4
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
$$\mathop {\lim }\limits_{n \to \infty } {{1 + {2^4} + {3^4} + .... + {n^4}} \over {{n^5}}}$$ - $$\mathop {\lim }\limits_{n \to \infty } {{1 + {2^3} + {3^3} + .... + {n^3}} \over {{n^5}}}$$
A
$${1 \over 5}$$
B
$${1 \over 30}$$
C
zero
D
$${1 \over 4}$$
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