If $x+\log _{15}\left(5+3^x\right)=x \log _{15} 5+\log _{15} 24, \quad$ then $x=$ _________

If $\mathrm{f}(x)$ is continuous at point $x=0$ where $$ f(x)=\left\{\begin{array}{cc} \frac{3 \sin x+5 \tan x}{\mathrm{a}^x-1} & , x<0 \\ \frac{2}{\log 2} & , x=0 \\ \frac{8 x+2 x \cos x}{\mathrm{~b}^x-1} & , x>0 \end{array}\right. $$ then the values of a and b , respectively, are __________

The smallest angle of the triangle whose sides are $6+\sqrt{12}, \sqrt{48}, \sqrt{24}$ is

Consider the three statements

$\mathrm{p}: \forall \mathrm{n} \in \mathbb{N}, 10 \mathrm{n}-3$ is a prime number, when n is not divisible by 3.

$\mathrm{q}: \frac{2}{\sqrt{3}}, \frac{-2}{\sqrt{3}}, \frac{-1}{\sqrt{3}}$ are the direction cosines of a directed line.

$\mathrm{r}: \sin x$ is an increasing function in the interval $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$.

Then which of the following statement pattern has truth value true?