Match gases under specified conditions listed in Column I with their properties/laws in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 $$\times$$ 4 matrix given in the ORS.

Let $$\alpha,\beta$$ be the roots of the equation $$x^2-px+r=0$$ and $$\frac{\alpha}{2},2\beta$$ be the roots of the equation $$x^2-qx+r=0$$. Then the value of r is

Let $$f(x)$$ be differentiable on the interval (0, $$\infty$$) such that $$f(1)=1$$, and $$\mathop {\lim }\limits_{t \to x} {{{t^2}f(x) - {x^2}f(t)} \over {t - x}} = 1$$ for each $$x > 0$$. Then $$f(x)$$ is

One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is