1
AIEEE 2003
+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
+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
+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 2002
+4
-1
$${I_n} = \int\limits_0^{\pi /4} {{{\tan }^n}x\,dx}$$ 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
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