1
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
Let f : R $$\to$$ R be defined by f(x) = $${x \over {1 + {x^2}}},x \in R$$.   Then the range of f is :
A
$$\left[ { - {1 \over 2},{1 \over 2}} \right]$$
B
$$R - \left[ { - {1 \over 2},{1 \over 2}} \right]$$
C
($$-$$ 1, 1) $$-$$ {0}
D
R $$-$$ [$$-$$1, 1]
2
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
Let fk(x) = $${1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)$$ for k = 1, 2, 3, ... Then for all x $$\in$$ R, the value of f4(x) $$-$$ f6(x) is equal to
A
$${1 \over 4}$$
B
$${5 \over {12}}$$
C
$${{ - 1} \over {12}}$$
D
$${1 \over {12}}$$
3
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
Let N be the set of natural numbers and two functions f and g be defined as f, g : N $$\to$$ N such that

f(n) = $$\left\{ {\matrix{ {{{n + 1} \over 2};} & {if\,\,n\,\,is\,\,odd} \cr {{n \over 2};} & {if\,\,n\,\,is\,\,even} \cr } \,\,} \right.$$;

and g(n) = n $$-$$($$-$$ 1)n.

Then fog is -
A
neither one-one nor onto
B
onto but not one-one
C
both one-one and onto
D
one-one but not onto
4
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
Let A = {x $$\in$$ R : x is not a positive integer}.

Define a function $$f$$ : A $$\to$$  R   as  $$f(x)$$ = $${{2x} \over {x - 1}}$$,

then $$f$$ is :
A
not injective
B
neither injective nor surjective
C
surjective but not injective
D
injective but not surjective
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