If $[t]$ represents the greatest integer $\leq t$, then the value of $\lim\limits_{x \rightarrow 3} \frac{11-[2-x]}{[x+10]}$ is

If the real valued function

$$ f(x)=\left\{\begin{array}{ccc} \frac{\cos 3 x-\cos x}{x \sin x}, & \text { if } & x<0 \\ p, & \text { if } & x=0 \\ \frac{\log (1+q \sin x)}{x}, & \text { if } & x>0 \end{array}\right. $$

is continuous at $x=0$, then $p+q=$

If $\{x\}=x-[x]$, where $[x]$ is the greatest integer $\leq x$ and $\mathop {\lim }\limits_{x \to {0^ - }} \frac{\cos ^{-1}\left(1-\{x\}^2\right) \sin ^{-1}(1-\{x\})}{\{x\}-\{x\}^4}=\theta$, then $\tan \theta$

For $a \neq 0$ and $b \neq 0$, if the real valued function $f(x)=\frac{\sqrt[5]{a(625+x)}-5}{\sqrt[4]{625+b x}-5}$ is continuous at $x=0$, then $f(0)=$