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) 24th January Evening Shift
+4
-1

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
EXAM MAP
Medical
NEET