sets, Relation and Function-NEET/JEE/MTH mock test-1

The number of elements in the set $\left\{n \in \mathbb{N}: 10 \leq n \leq 100\right.$ and $3^n-3$ is a multiple of 7$\}$ is

Let $f: R \rightarrow R $be a function defined by $f(x) = (2 (1- \frac{x^{25}}{2}) (2+ x^25)^\frac{1}{50}$ . If the function $f(x) =f (f (f(x))) + f(f(x))$, the greatest integer less than or equal to g(1)is JEE MAIN 2022 (25 June — 1)