1
JEE Main 2021 (Online) 18th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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 :
A
all real except integers
B
all non-integers except the interval [ $$-$$1, 1 ]
C
all integers except 0, $$-$$1, 1
D
all real except the interval [ $$-$$1, 1 ]
2
JEE Main 2021 (Online) 18th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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 $$(f \pm g)(x) = f(x) \pm g(x),(f/g)x = {{f(x)} \over {g(x)}}$$
A
$$0 \le x \le 1$$
B
$$0 \le x < 1$$
C
$$0 < x < 1$$
D
$$0 < x \le 1$$
3
JEE Main 2021 (Online) 17th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The inverse of $$y = {5^{\log x}}$$ is :
A
$$x = {5^{\log y}}$$
B
$$x = {y^{{1 \over {\log 5}}}}$$
C
$$x = {5^{{1 \over {\log y}}}}$$
D
$$x = {y^{\log 5}}$$
4
JEE Main 2021 (Online) 16th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The range of a$$\in$$R for which the

function f(x) = (4a $$-$$ 3)(x + loge 5) + 2(a $$-$$ 7) cot$$\left( {{x \over 2}} \right)$$ sin2$$\left( {{x \over 2}} \right)$$, x $$\ne$$ 2n$$\pi$$, n$$\in$$N has critical points, is :
A
[1, $$\infty $$)
B
($$-$$3, 1)
C
$$\left[ { - {4 \over 3},2} \right]$$
D
($$-$$$$\infty $$, $$-$$1]
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