Let $$R$$ be a relation on the set of ordered pairs of positive integers such that $$\left( {\left( {p,q} \right),\left( {r,s} \right)} \right) \in R$$ if and only if $$p - s = q - r.$$ Which one of the following is true about $$R$$?

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?

If for non-zero $$x,$$ $$af\left( x \right) + bf\left( {{1 \over x}} \right) = {1 \over x} - 25$$
where $$a \ne b$$ then $$\int\limits_1^2 {f\left( x \right)dx} \,$$ is

A function $$f(x)$$ is linear and has a value of $$29$$ at $$x=-2$$ and $$39$$ at $$x=3.$$ Find its value at $$x=5.$$