1
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
Let [ x ] denote the greatest integer $$\le$$ x, where x $$\in$$ R. If the domain of the real valued function $$f(x) = \sqrt {{{\left| {[x]} \right| - 2} \over {\left| {[x]} \right| - 3}}}$$ is ($$-$$ $$\infty$$, a) $$]\cup$$ [b, c) $$\cup$$ [4, $$\infty$$), a < b < c, then the value of a + b + c is :
A
8
B
1
C
$$-$$2
D
$$-$$3
2
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Let f : R $$-$$ {3} $$\to$$ R $$-$$ {1} be defined by f(x) = $${{x - 2} \over {x - 3}}$$.

Let g : R $$\to$$ R be given as g(x) = 2x $$-$$ 3. Then, the sum of all the values of x for which f$$-$$1(x) + g$$-$$1(x) = $${{13} \over 2}$$ is equal to :
A
3
B
5
C
2
D
7
3
JEE Main 2021 (Online) 18th March Morning Shift
+4
-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 :
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 ]
4
JEE Main 2021 (Online) 18th March Morning Shift
+4
-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 $$(f \pm g)(x) = f(x) \pm g(x),(f/g)x = {{f(x)} \over {g(x)}}$$
A
$$0 \le x \le 1$$
B
$$0 \le x < 1$$
C
$$0 < x < 1$$
D
$$0 < x \le 1$$
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