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

Consider a function $$f:\mathbb{N}\to\mathbb{R}$$, satisfying $$f(1)+2f(2)+3f(3)+....+xf(x)=x(x+1)f(x);x\ge2$$ with $$f(1)=1$$. Then $$\frac{1}{f(2022)}+\frac{1}{f(2028)}$$ is equal to

A
8000
B
8400
C
8100
D
8200
2
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
$$\mathbb{R} - \{ 3\}$$
3
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 $$(1,\infty )$$
4
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
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