The work function of a substance is $4.0 \, eV$. The longest wavelength of light that can cause photoelectron emission from this substance is approximately ............ $nm$.

The solution of $\frac{dy}{dx} + y = e^x$ is

Given that $a, b \in \{0, 1, 2, \ldots, 9\}$ with $a+b \neq 0$ and that $\left(a+\frac{b}{10}\right)^x = \left(\frac{a}{10}+\frac{b}{100}\right)^y = 1000$. Then,$\frac{1}{x}-\frac{1}{y}$ is equal to

Which characteristic of living organisms ensures that the population size of each species remains limited?

$A$ spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ (where $\rho_2 < \rho_1$). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$,i.e.,$F_{\text{viscous}} = -kv^2$ (where $k > 0$). Then the terminal speed of the ball is:

$\sqrt{2+\sqrt{5}-\sqrt{6-3 \sqrt{5}+\sqrt{14-6 \sqrt{5}}}}$ is equal to