The function $f(x) = \tan x - x$ is:

In which interval is the function $f(x) = \frac{x}{\ln x}$ increasing?

If $f(x) = x^5 - 20x^3 + 240x$,then $f(x)$ satisfies which of the following?

If $f(x) = \frac{\lambda \sin x + 6 \cos x}{2 \sin x + 3 \cos x}$ is a strictly increasing function,then .......

Assertion $(A)$: The function $f(x) = x - \log \left(\frac{1+x}{x}\right), x > 0$ has no maximum. Reason $(R)$: If a function $f(x)$ is strictly increasing in an interval $(a, b)$,then at any point in $(a, b)$,$f^{\prime}(x) \neq 0$. The correct option among the following is

If the tangent drawn to the curve $y=x^3-ax^2+x+1$ at each point $x \in R$ is inclined at an acute angle with the positive direction of the $X$-axis,then the set of all possible values of '$a$' is