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1
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
Let $$f(x) = {{1 - \tan x} \over {4x - \pi }}$$, $$x \ne {\pi \over 4}$$, $$x \in \left[ {0,{\pi \over 2}} \right]$$.

If $$f(x)$$ is continuous in $$\left[ {0,{\pi \over 2}} \right]$$, then $$f\left( {{\pi \over 4}} \right)$$ is
A
$$-1$$
B
$${1 \over 2}$$
C
$$-{1 \over 2}$$
D
$$1$$
2
AIEEE 2004
MCQ (Single Correct Answer)
+4
-1
If $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} + {b \over {{x^2}}}} \right)^{2x}} = {e^2}$$, then the value of $$a$$ and $$b$$, are
A
$$a$$ = 1 and $$b$$ = 2
B
$$a$$ = 1 and $$b$$ $$ \in R$$
C
$$a$$ $$ \in R$$ and $$b$$ = 2
D
$$a$$ $$ \in R$$ and $$b$$ $$ \in R$$
3
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
$$\mathop {\lim }\limits_{n \to \infty } {{1 + {2^4} + {3^4} + .... + {n^4}} \over {{n^5}}}$$ - $$\mathop {\lim }\limits_{n \to \infty } {{1 + {2^3} + {3^3} + .... + {n^3}} \over {{n^5}}}$$
A
$${1 \over 5}$$
B
$${1 \over 30}$$
C
zero
D
$${1 \over 4}$$
4
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
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