1
JEE Main 2019 (Online) 8th April Morning Slot
+4
-1
If $$f(x) = {\log _e}\left( {{{1 - x} \over {1 + x}}} \right)$$, $$\left| x \right| < 1$$ then $$f\left( {{{2x} \over {1 + {x^2}}}} \right)$$ is equal to
A
2f(x2)
B
2f(x)
C
(f(x))2
D
-2f(x)
2
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
The number of functions f from {1, 2, 3, ...., 20} onto {1, 2, 3, ...., 20} such that f(k) is a multiple of 3, whenever k is a multiple of 4, is :
A
65 $$\times$$ (15)!
B
56 $$\times$$ 15
C
(15)! $$\times$$ 6!
D
5! $$\times$$ 6!
3
JEE Main 2019 (Online) 11th January Evening Slot
+4
-1
Let a function f : (0, $$\infty$$) $$\to$$ (0, $$\infty$$) be defined by f(x) = $$\left| {1 - {1 \over x}} \right|$$. Then f is :
A
not injective but it is surjective
B
neiter injective nor surjective
C
injective only
D
both injective as well as surjective
4
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]
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