In $\triangle ABC$,with usual notation,observe the two statements given below:
$(I)$ $r r_1 r_2 r_3 = \Delta^2$
$(II)$ $r_1 r_2 + r_2 r_3 + r_3 r_1 = s^2$
Which of the following is correct?

When a big drop of water is formed from $n$ small drops of water,the energy loss is $3E$,where $E$ is the energy of the bigger drop. If $R$ is the radius of the bigger drop and $r$ is the radius of the smaller drop,then the number of smaller drops $(n)$ is:

If the system of equations $x + 2y - 3z = 1$,$(k + 3)z = 3$,and $(2k + 1)x + z = 0$ is inconsistent,then the value of $k$ is:

$y=A e^x+B e^{2 x}+C e^{3 x}$ satisfies the differential equation

Which one of the following conditions is incorrect for a well-behaved wave function $(\psi)$?

The acceleration due to gravity on the moon is $\left(\frac{1}{6}\right)$ times the acceleration due to gravity on the earth. If the ratio of the density of the earth $\rho_{e}$ to the density of the moon $\rho_{m}$ is $\frac{5}{3}$,then the radius of the moon $R_{m}$ in terms of the radius of the earth $R_{e}$ is: