1
JEE Main 2023 (Online) 25th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f:(0,1)\to\mathbb{R}$$ be a function defined $$f(x) = {1 \over {1 - {e^{ - x}}}}$$, and $$g(x) = \left( {f( - x) - f(x)} \right)$$. Consider two statements

(I) g is an increasing function in (0, 1)

(II) g is one-one in (0, 1)

Then,

A
Both (I) and (II) are true
B
Neither (I) nor (II) is true
C
Only (II) is true
D
Only (I) is true
2
JEE Main 2023 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f(x)$$ be a function such that $$f(x+y)=f(x).f(y)$$ for all $$x,y\in \mathbb{N}$$. If $$f(1)=3$$ and $$\sum\limits_{k = 1}^n {f(k) = 3279} $$, then the value of n is

A
9
B
7
C
6
D
8
3
JEE Main 2023 (Online) 24th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$f(x) = {{{2^{2x}}} \over {{2^{2x}} + 2}},x \in \mathbb{R}$$, then $$f\left( {{1 \over {2023}}} \right) + f\left( {{2 \over {2023}}} \right)\, + \,...\, + \,f\left( {{{2022} \over {2023}}} \right)$$ is equal to

A
2011
B
2010
C
1010
D
1011
4
JEE Main 2022 (Online) 29th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The domain of the function $$f(x)=\sin ^{-1}\left(\frac{x^{2}-3 x+2}{x^{2}+2 x+7}\right)$$ is:

A
$$[1, \infty)$$
B
$$[-1,2]$$
C
$$[-1, \infty)$$
D
$$(-\infty, 2]$$
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