1
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
$$0 < x \le 1$$
2
JEE Main 2021 (Online) 17th March Morning Shift
+4
-1
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
$$x = {y^{\log 5}}$$
3
JEE Main 2021 (Online) 16th March Morning Shift
+4
-1
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]
4
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
Let $$A = \{ 1,2,3,....,10\}$$ and $$f:A \to A$$ be defined as

$$f(k) = \left\{ {\matrix{ {k + 1} & {if\,k\,is\,odd} \cr k & {if\,k\,is\,even} \cr } } \right.$$

Then the number of possible functions $$g:A \to A$$ such that $$gof = f$$ is :
A
55
B
105
C
5!
D
10C5
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