1
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
$${I_3} > {I_4}$$
2
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
The value of $$\int\limits_{ - \pi }^\pi {{{{{\cos }^2}} \over {1 + {a^x}}}dx,\,\,a > 0,} $$ is
A
$$a\,\pi $$
B
$${\pi \over 2}$$
C
$${\pi \over a}$$
D
$${2\pi }$$
3
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
The value of integral, $$\int\limits_3^6 {{{\sqrt x } \over {\sqrt {9 - x} + \sqrt x }}} dx $$ is
A
$${1 \over 2}$$
B
$${3 \over 2}$$
C
$$2$$
D
$$1$$
4
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
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