JEE Main 2021 (Online) 18th March Morning Shift | Functions Question 83 | Mathematics

JEE Main 2021 (Online) 18th March Morning Shift

MCQ (Single Correct Answer)

-1

The real valued function
$$f(x) = {{\cos e{c^{ - 1}}x} \over {\sqrt {x - [x]} }}$$, where [x] denotes the greatest integer less than or equal to x, is defined for all x belonging to :

all real except integers

all non-integers except the interval [ $$-$$1, 1 ]

all integers except 0, $$-$$1, 1

all real except the interval [ $$-$$1, 1 ]

JEE Main 2021 (Online) 18th March Morning Shift

MCQ (Single Correct Answer)

-1

If the functions are defined as $$f(x) = \sqrt x $$ and $$g(x) = \sqrt {1 - x} $$, then what is the common domain of the following functions :

f + g, f $$-$$ g, f/g, g/f, g $$-$$ f where $$(f \pm g)(x) = f(x) \pm g(x),(f/g)x = {{f(x)} \over {g(x)}}$$

$$0 \le x \le 1$$

$$0 \le x < 1$$

$$0 < x < 1$$

$$0 < x \le 1$$

JEE Main 2021 (Online) 17th March Evening Shift

MCQ (Single Correct Answer)

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Consider the function f : R $$ \to $$ R defined by

$$f(x) = \left\{ \matrix{ \left( {2 - \sin \left( {{1 \over x}} \right)} \right)|x|,x \ne 0 \hfill \cr 0,\,\,x = 0 \hfill \cr} \right.$$. Then f is :

not monotonic on ($$-$$$$\infty $$, 0) and (0, $$\infty $$)

monotonic on (0, $$\infty $$) only

monotonic on ($$-$$$$\infty $$, 0) only

monotonic on ($$-$$$$\infty $$, 0) $$\cup$$ (0, $$\infty $$)

JEE Main 2021 (Online) 17th March Morning Shift

MCQ (Single Correct Answer)

-1

The inverse of $$y = {5^{\log x}}$$ is :

$$x = {5^{\log y}}$$

$$x = {y^{{1 \over {\log 5}}}}$$

$$x = {5^{{1 \over {\log y}}}}$$

$$x = {y^{\log 5}}$$