1
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
If $$f\left( y \right) = {e^y},$$ $$g\left( y \right) = y;y > 0$$ and

$$F\left( t \right) = \int\limits_0^t {f\left( {t - y} \right)g\left( y \right)dy,} $$ then :
A
$$F\left( t \right) = t{e^{ - t}}$$
B
$$F\left( t \right) = 1t - t{e^{ - 1}}\left( {1 + t} \right)$$
C
$$F\left( t \right) = {e^t} - \left( {1 + t} \right)$$
D
$$F\left( t \right) = t{e^t}$$.
2
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
$$\mathop {\lim }\limits_{n \to \infty } {{{1^p} + {2^p} + {3^p} + ..... + {n^p}} \over {{n^{p + 1}}}}$$ is
A
$${1 \over {p + 1}}$$
B
$${1 \over {1 - p}}$$
C
$${1 \over p} - {1 \over {p - 1}}$$
D
$${1 \over {p + 2}}$$
3
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
4
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
$$18$$
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