1
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Change Language
$${I_n} = \int\limits_0^{\pi /4} {{{\tan }^n}x\,dx} $$ then $$\,\mathop {\lim }\limits_{n \to \infty } \,n\left[ {{I_n} + {I_{n + 2}}} \right]$$ equals
A
$${1 \over 2}$$
B
$$1$$
C
$$\infty $$
D
zero
2
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\int\limits_0^{10\pi } {\left| {\sin x} \right|dx} $$ is
A
$$20$$
B
$$8$$
C
$$10$$
D
$$18$$
3
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\int\limits_0^2 {\left[ {{x^2}} \right]dx} $$ is
A
$$2 - \sqrt 2 $$
B
$$2 + \sqrt 2 $$
C
$$\,\sqrt 2 - 1$$
D
$$ - \sqrt 2 - \sqrt 3 + 5$$
4
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\int_{ - \pi }^\pi {{{2x\left( {1 + \sin x} \right)} \over {1 + {{\cos }^2}x}}} dx$$ is
A
$${{{\pi ^2}} \over 4}$$
B
$${{\pi ^2}}$$
C
zero
D
$${\pi \over 2}$$
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