1
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
2
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
3
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1 Let $$f(x) = 2{x^n} + \lambda ,\lambda \in R,n \in N$$, and $$f(4) = 133,f(5) = 255$$. Then the sum of all the positive integer divisors of $$(f(3) - f(2))$$ is

A
60
B
58
C
61
D
59
4
JEE Main 2023 (Online) 25th January Morning Shift
+4
-1 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
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