If $^nP_4 = 30 \times ^nC_5$,then $n = \dots$

Two bodies have their moments of inertia $I$ and $2I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal,their angular momenta will be in the ratio

$\int \frac{dx}{\sqrt{x}(x+9)}$ is equal to

Taxon is a

Match the thermodynamic processes taking place in a system with the correct conditions. In the table: $\Delta Q$ is the heat supplied,$\Delta W$ is the work done and $\Delta U$ is change in internal energy of the system.

Process	Condition
$(I)$ Adiabatic	$(A)$ $\Delta W = 0$
$(II)$ Isothermal	$(B)$ $\Delta Q = 0$
$(III)$ Isochoric	$(C)$ $\Delta U \neq 0, \Delta W \neq 0, \Delta Q \neq 0$
$(IV)$ Isobaric	$(D)$ $\Delta U = 0$

$y + x^2 = \frac{dy}{dx}$ has the solution