$$ \lim\limits_{x \rightarrow 5} \frac{\sqrt{2-2 \cos \left(x^2-12 x+35\right)}}{(x-5)}=\ldots \ldots $$

If ${ }^n \mathrm{C}_0+\frac{1}{2}{ }^n \mathrm{C}_1+\frac{1}{3}{ }^n \mathrm{C}_2$$$+\ldots \frac{1}{n}^n C_{n-1}+\frac{1}{n+1}{ }^n C_n=\frac{1023}{10} \,\,\, then \,\,\,\,\mathrm{n}=$$

A pair of fair dice is thrown 4 times. If getting the same number on both dice is considered as a success, then the probability of two successes are