Which of the following quantities does not depend upon the orbital radius of the satellite?

The integrating factor of the differential equation $(x \log x) \frac{dy}{dx} + y = 2 \log x$ is

If $u=\log \left(x^3+y^3+z^3-3 x y z\right)$, then $(x+y+z)(u_x+u_y+u_z)$ is equal to

The equivalent resistance between $A$ and $B$ is

$A$ parallel plate capacitor of capacity $100 \mu F$ is charged by a battery of $50 \text{ V}$. The battery remains connected,and if the plates of the capacitor are separated so that the distance between them becomes double the original distance,the additional energy supplied by the battery to the capacitor in joules is:

In $\triangle ABC$,if $\frac{1}{b+c} + \frac{1}{c+a} = \frac{3}{a+b+c}$,then $C$ is equal to (in $^{\circ}$)