1
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
Let ƒ : (1, 3) $$\to$$ R be a function defined by
$$f(x) = {{x\left[ x \right]} \over {1 + {x^2}}}$$ , where [x] denotes the greatest integer $$\le$$ x. Then the range of ƒ is
A
$$\left( {{2 \over 5},{1 \over 2}} \right) \cup \left( {{3 \over 4},{4 \over 5}} \right]$$
B
$$\left( {{3 \over 5},{4 \over 5}} \right)$$
C
$$\left( {{2 \over 5},{4 \over 5}} \right]$$
D
$$\left( {{2 \over 5},{3 \over 5}} \right] \cup \left( {{3 \over 4},{4 \over 5}} \right)$$
2
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
The inverse function of

f(x) = $${{{8^{2x}} - {8^{ - 2x}}} \over {{8^{2x}} + {8^{ - 2x}}}}$$, x $$\in$$ (-1, 1), is :
A
$${1 \over 4}{\log _e}\left( {{{1 - x} \over {1 + x}}} \right)$$
B
$${1 \over 4}\left( {{{\log }_8}e} \right){\log _e}\left( {{{1 - x} \over {1 + x}}} \right)$$
C
$${1 \over 4}\left( {{{\log }_8}e} \right){\log _e}\left( {{{1 + x} \over {1 - x}}} \right)$$
D
$${1 \over 4}{\log _e}\left( {{{1 + x} \over {1 - x}}} \right)$$
3
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
If g(x) = x2 + x - 1 and
(goƒ) (x) = 4x2 - 10x + 5, then ƒ$$\left( {{5 \over 4}} \right)$$ is equal to:
A
$${1 \over 2}$$
B
$${3 \over 2}$$
C
-$${1 \over 2}$$
D
-$${3 \over 2}$$
4
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
For x $$\in$$ (0, 3/2), let f(x) = $$\sqrt x$$ , g(x) = tan x and h(x) = $${{1 - {x^2}} \over {1 + {x^2}}}$$. If $$\phi$$ (x) = ((hof)og)(x), then $$\phi \left( {{\pi \over 3}} \right)$$ is equal to :
A
$$\tan {{7\pi } \over {12}}$$
B
$$\tan {{11\pi } \over {12}}$$
C
$$\tan {\pi \over {12}}$$
D
$$\tan {{5\pi } \over {12}}$$
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