If the following system has non - trivial solution $$$px+qy+rz=0$$$ $$$qx+ry+pz=0$$$ $$$rx+py+qz=0$$$

Then which one of the following Options is TRUE?

Suppose $$𝑈$$ is the power set of the set $$S = \left\{ {1,2,3,4,5,6,} \right\}$$. For any $$T \in U,$$ let $$\left| T \right|$$ denote the number of elements in $$𝑇$$ and $$T'$$ denote the complement of $$𝑇.$$ For any $$T,R \in U,$$ let $$T\backslash R$$ be the set of all elements in $$𝑇$$ which are not in $$𝑅.$$ Which one of the following is true?

The number of $$4$$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $${1, 2, 3}$$ is____________.

Consider the following policies for preventing deadlock in a system with mutually exclusive resources.

$$\,\,\,\,\,\,\,{\rm I}.$$ $$\,\,\,\,\,\,$$ Processes should acquire all their resources at the beginning of execution. If
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ any resource is not available, all resources acquired so far are released
$$\,\,\,\,\,{\rm II}.$$ $$\,\,\,\,\,\,$$ The resources are numbered uniquely, and processes are allowed to request
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ for resources only in increasing resource numbers
$$\,\,\,{\rm III}.$$ $$\,\,\,\,\,\,$$ The resources are numbered uniquely, and processes are allowed to request
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ for resources only in decreasing resource numbers
$$\,\,\,{\rm IV}.$$ $$\,\,\,\,\,\,$$ The resources are numbered uniquely. A process is allowed to request only
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ for a resource with resource number larger than its currently held resources

Which of the above policies can be used for preventing deadlock?