For better survival of the human population,which of the following steps is most important?

If $x^2+y^2=t+\frac{1}{t}$ and $x^4+y^4=t^2+\frac{1}{t^2}$, then $x^3 y \frac{d y}{d x}$ is equal to

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod perpendicular to its length. The acceleration of the centre of mass of the rod is:

$A$ gas mixture consists of $2$ moles of $O_2$ and $4$ moles of $Ar$ at temperature $T$. Neglecting all vibrational modes,the total internal energy of the system is: (in $RT$)

The solution of $\frac{dy}{dx} = \frac{x \log x^2 + x}{\sin y + y \cos y}$ is

The half-life period of a first-order chemical reaction is $6.93 \ min$. The time required for $99\%$ completion of the reaction is ........ minutes. $(\log 2 = 0.301)$