JEE Main 2020 (Online) 8th January Evening Slot | Functions Question 117 | Mathematics

JEE Main 2020 (Online) 8th January Evening Slot

MCQ (Single Correct Answer)

-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

$$\left( {{2 \over 5},{1 \over 2}} \right) \cup \left( {{3 \over 4},{4 \over 5}} \right]$$

$$\left( {{3 \over 5},{4 \over 5}} \right)$$

$$\left( {{2 \over 5},{4 \over 5}} \right]$$

$$\left( {{2 \over 5},{3 \over 5}} \right] \cup \left( {{3 \over 4},{4 \over 5}} \right)$$

JEE Main 2020 (Online) 8th January Morning Slot

MCQ (Single Correct Answer)

-1

The inverse function of

f(x) = $${{{8^{2x}} - {8^{ - 2x}}} \over {{8^{2x}} + {8^{ - 2x}}}}$$, x $$ \in $$ (-1, 1), is :

$${1 \over 4}{\log _e}\left( {{{1 - x} \over {1 + x}}} \right)$$

$${1 \over 4}\left( {{{\log }_8}e} \right){\log _e}\left( {{{1 - x} \over {1 + x}}} \right)$$

$${1 \over 4}\left( {{{\log }_8}e} \right){\log _e}\left( {{{1 + x} \over {1 - x}}} \right)$$

$${1 \over 4}{\log _e}\left( {{{1 + x} \over {1 - x}}} \right)$$

JEE Main 2020 (Online) 8th January Morning Slot

MCQ (Single Correct Answer)

-1

Let ƒ(x) = xcos^–1(–sin|x|), $$x \in \left[ { - {\pi \over 2},{\pi \over 2}} \right]$$, then which of the following is true?

ƒ' is decreasing in $$\left( { - {\pi \over 2},0} \right)$$ and increasing in $$\left( {0,{\pi \over 2}} \right)$$

ƒ '(0) = $${ - {\pi \over 2}}$$

ƒ is not differentiable at x = 0

ƒ' is increasing in $$\left( { - {\pi \over 2},0} \right)$$ and decreasing in $$\left( {0,{\pi \over 2}} \right)$$

JEE Main 2020 (Online) 7th January Morning Slot

MCQ (Single Correct Answer)

-1

If g(x) = x² + x - 1 and
(goƒ) (x) = 4x² - 10x + 5, then ƒ$$\left( {{5 \over 4}} \right)$$ is equal to:

$${1 \over 2}$$

$${3 \over 2}$$

-$${1 \over 2}$$

-$${3 \over 2}$$

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