The equation $\frac{dV}{dt} = At - BV$ describes the rate of change of velocity of a body falling from rest in a resisting medium. The dimensions of $A$ and $B$ are

$A$ physical quantity $x$ depends on quantities $y$ and $z$ as follows: $x = Ay + B \tan(Cz)$,where $A, B,$ and $C$ are constants. Which of the following do not have the same dimensions?

Obtain the relation between the units of some physical quantity in two different systems of units. Obtain the relation between the $MKS$ and $CGS$ unit of work.

$A$ physical quantity obtained from the ratio of the coefficient of thermal conductivity to the universal gravitational constant has a dimensional formula $[M^{2a} L^{4b} T^{2c} K^d]$. Then the value of $\frac{a+b}{c+b}-d$ is

Assume that the drag force on a football depends only on the density of the air,the velocity of the ball,and the cross-sectional area of the ball. Balls of different sizes but the same density are dropped in an air column. The terminal velocity reached by balls of masses $250 \,g$ and $125 \,g$ are in the ratio:

If the velocity of light $(c)$,gravitational constant $(G)$,and Planck's constant $(h)$ are chosen as fundamental units,then the dimensions of mass in this new system are: