1
AIEEE 2004
+4
-1
If $$x = {e^{y + {e^y} + {e^{y + .....\infty }}}}$$ , $$x > 0,$$ then $${{{dy} \over {dx}}}$$ is
A
$${{1 + x} \over x}$$
B
$${1 \over x}$$
C
$${{1 - x} \over x}$$
D
$${x \over {1 + x}}$$
2
AIEEE 2003
+4
-1
If $$f\left( x \right) = {x^n},$$ then the value of

$$f\left( 1 \right) - {{f'\left( 1 \right)} \over {1!}} + {{f''\left( 1 \right)} \over {2!}} - {{f'''\left( 1 \right)} \over {3!}} + ..........{{{{\left( { - 1} \right)}^n}{f^n}\left( 1 \right)} \over {n!}}$$ is

A
$$1$$
B
$${{2^n}}$$
C
$${{2^n} - 1}$$
D
$$0$$
3
AIEEE 2003
+4
-1
Let $$f\left( x \right)$$ be a polynomial function of second degree. If $$f\left( 1 \right) = f\left( { - 1} \right)$$ and $$a,b,c$$ are in $$A.P,$$ then $$f'\left( a \right),f'\left( b \right),f'\left( c \right)$$ are in
A
Arithmetic -Geometric Progression
B
$$A.P$$
C
$$G.P$$
D
$$H.P$$
4
AIEEE 2002
+4
-1
If $$y = {\left( {x + \sqrt {1 + {x^2}} } \right)^n},$$ then $$\left( {1 + {x^2}} \right){{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}}$$ is
A
$${n^2}y$$
B
$$-{n^2}y$$
C
$$-y$$
D
$$2{x^2}y$$
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