1
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
$${1 \over {n + 1}} - {1 \over {n + 2}}$$
2
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
$$\mathop {\lim }\limits_{n \to \infty } {{1 + {2^4} + {3^4} + .... + {n^4}} \over {{n^5}}}$$ - $$\mathop {\lim }\limits_{n \to \infty } {{1 + {2^3} + {3^3} + .... + {n^3}} \over {{n^5}}}$$
A
$${1 \over 5}$$
B
$${1 \over 30}$$
C
zero
D
$${1 \over 4}$$
3
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
The value of $$\mathop {\lim }\limits_{x \to 0} {{\int\limits_0^{{x^2}} {{{\sec }^2}tdt} } \over xsinx}$$ is
A
0
B
3
C
2
D
1
4
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
$$F\left( t \right) = t{e^t}$$.
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