1
AIEEE 2003
+4
-1
The function $$f\left( x \right)$$ $$= \log \left( {x + \sqrt {{x^2} + 1} } \right)$$, is
A
neither an even nor an odd function
B
an even function
C
an odd function
D
a periodic function
2
AIEEE 2003
+4
-1
A function $$f$$ from the set of natural numbers to integers defined by $$f\left( n \right) = \left\{ {\matrix{ {{{n - 1} \over 2},\,when\,n\,is\,odd} \cr { - {n \over 2},\,when\,n\,is\,even} \cr } } \right.$$\$ is
A
neither one -one nor onto
B
one-one but not onto
C
onto but not one-one
D
one-one and onto both
3
AIEEE 2003
+4
-1
If $$f:R \to R$$ satisfies $$f$$(x + y) = $$f$$(x) + $$f$$(y), for all x, y $$\in$$ R and $$f$$(1) = 7, then $$\sum\limits_{r = 1}^n {f\left( r \right)}$$ is
A
$${{7n\left( {n + 1} \right)} \over 2}$$
B
$${{7n} \over 2}$$
C
$${{7\left( {n + 1} \right)} \over 2}$$
D
$$7n + \left( {n + 1} \right)$$
4
AIEEE 2003
+4
-1
Domain of definition of the function f(x) = $${3 \over {4 - {x^2}}}$$ + $${\log _{10}}\left( {{x^3} - x} \right)$$, is
A
(-1, 0)$$\cup$$(1, 2)$$\cup$$(2, $$\infty$$)
B
(1, 2)
C
(-1, 0) $$\cup$$ (1, 2)
D
(1, 2)$$\cup$$(2, $$\infty$$)
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