1
JEE Main 2023 (Online) 29th January Morning Shift
+4
-1

The domain of $$f(x) = {{{{\log }_{(x + 1)}}(x - 2)} \over {{e^{2{{\log }_e}x}} - (2x + 3)}},x \in \mathbb{R}$$ is

A
$$( - 1,\infty ) - \{ 3\}$$
B
$$\mathbb{R} - \{ - 1,3)$$
C
$$(2,\infty ) - \{ 3\}$$
D
$$\mathbb{R} - \{ 3\}$$
2
JEE Main 2023 (Online) 29th January Morning Shift
+4
-1

Let $$f:R \to R$$ be a function such that $$f(x) = {{{x^2} + 2x + 1} \over {{x^2} + 1}}$$. Then

A
$$f(x)$$ is many-one in $$( - \infty , - 1)$$
B
$$f(x)$$ is one-one in $$( - \infty ,\infty )$$
C
$$f(x)$$ is one-one in $$[1,\infty )$$ but not in $$( - \infty ,\infty )$$
D
$$f(x)$$ is many-one in $$(1,\infty )$$
3
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1

The number of functions

$$f:\{ 1,2,3,4\} \to \{ a \in Z|a| \le 8\}$$

satisfying $$f(n) + {1 \over n}f(n + 1) = 1,\forall n \in \{ 1,2,3\}$$ is

A
2
B
3
C
1
D
4
4
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1

Let $$f:\mathbb{R}\to\mathbb{R}$$ be a function defined by $$f(x) = {\log _{\sqrt m }}\{ \sqrt 2 (\sin x - \cos x) + m - 2\}$$, for some $$m$$, such that the range of $$f$$ is [0, 2]. Then the value of $$m$$ is _________

A
4
B
3
C
5
D
2
EXAM MAP
Medical
NEET