If $f(x)=x^2+ax+b$ has a minima at $x=3$ whose value is $5$,then the values of $a$ and $b$ are respectively.

If two sides of a triangle are given,then the area of the triangle will be maximum if the angle between the given sides is

Let $f :[2,4] \rightarrow R$ be a differentiable function such that $(x \ln x) f'(x) + (\ln x + 1) f(x) \geq 1$ for all $x \in [2,4]$,with $f(2) = \frac{1}{2}$ and $f(4) = \frac{1}{4}$. Consider the following two statements:
$(A): f(x) \leq 1$ for all $x \in [2,4]$
$(B): f(x) \geq \frac{1}{8}$ for all $x \in [2,4]$
Then,

Let $f(x) = x^2 + \frac{1}{x^2}$ and $g(x) = x - \frac{1}{x}$,$x \in R - \{-1, 1, 0\}$. If $h(x) = \frac{f(x)}{g(x)}$,then the local minimum value of $h(x)$ is:

If $a_n$ is the greatest term in the sequence $a_n = \frac{n^3}{n^4+147}$,$n = 1, 2, 3, \ldots$,then $n$ is equal to $..........$.

$x^x$ has a stationary point at