The force $F$ is given in terms of time $t$ and displacement $x$ by the equation $F = A \cos(Bx) + C \sin(Dt)$. The dimensional formula of $\frac{AD}{B}$ is -

The potential energy of a particle varies with distance $x$ from a fixed origin as $U = \frac{A\sqrt{x}}{x^2 + B}$,where $A$ and $B$ are dimensional constants. Find the dimensional formula for $A/B$.

If velocity $(V)$,force $(F)$ and time $(T)$ are chosen as fundamental quantities,then the dimensions of energy are:

If $C$ is the velocity of light,$h$ is Planck's constant,and $G$ is the gravitational constant,and these are taken as fundamental quantities,then the dimensional formula of mass is:

The foundations of dimensional analysis were laid down by

$A$ quantity $z$, to be estimated, has a dependency on the variables $a, b$ and $c$ as $z = a b^2 c^{-2}$. The percentage errors in the measurement of $a, b$ and $c$ are $2.1 \%$, $1.3 \%$ and $2.2 \%$, respectively. The percentage error in the measurement of $z$ would then be: (in $\%$)