1
AIEEE 2006
MCQ (Single Correct Answer)
+4
-1
$$\int\limits_0^\pi {xf\left( {\sin x} \right)dx} $$ is equal to
A
$$\pi \int\limits_0^\pi {f\left( {\cos x} \right)dx} $$
B
$$\,\pi \int\limits_0^\pi {f\left( {sinx} \right)dx} $$
C
$${\pi \over 2}\int\limits_0^{\pi /2} {f\left( {sinx} \right)dx} $$
D
$$\pi \int\limits_0^{\pi /2} {f\left( {\cos x} \right)dx} $$
2
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
Let $$f:R \to R$$ be a differentiable function having $$f\left( 2 \right) = 6$$,
$$f'\left( 2 \right) = \left( {{1 \over {48}}} \right)$$. Then $$\mathop {\lim }\limits_{x \to 2} \int\limits_6^{f\left( x \right)} {{{4{t^3}} \over {x - 2}}dt} $$ equals :
A
$$24$$
B
$$36$$
C
$$12$$
D
$$18$$
3
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
$$\mathop {\lim }\limits_{n \to \infty } \left[ {{1 \over {{n^2}}}{{\sec }^2}{1 \over {{n^2}}} + {2 \over {{n^2}}}{{\sec }^2}{4 \over {{n^2}}}.... + {1 \over n}{{\sec }^2}1} \right]$$
equals
A
$${1 \over 2}\sec 1$$
B
$${1 \over 2}$$cosec 1
C
tan 1
D
$${1 \over 2}$$tan 1
4
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
If $${I_1} = \int\limits_0^1 {{2^{{x^2}}}dx,{I_2} = \int\limits_0^1 {{2^{{x^3}}}dx,\,{I_3} = \int\limits_1^2 {{2^{{x^2}}}dx} } } $$ and $${I_4} = \int\limits_1^2 {{2^{{x^3}}}dx} $$ then
A
$${I_2} > {I_1}$$
B
$${I_1} > {I_2}$$
C
$${I_3} = {I_4}$$
D
$${I_3} > {I_4}$$
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