A hypothetical equation is given as $\rho = a \sqrt{P} + bT^2$, where $\rho$ is density, $P$ is pressure, and $T$ is temperature. The dimensions of $\frac{a}{b}$ are:

The time taken by an electron to go from ground state to excited state is one shake (one shake = ${10^{ - 8}}$ s) this time in nanosecond will be

Universal time is based on

If the equation $P = \frac{F}{A}$ is dimensionally homogeneous, where $P$ is pressure, $F$ is force, and $A$ is area, what are the dimensions of pressure?

Precision in measurement depends on

Light year is a unit of

A weber is equivalent to

The time period ($T$) of a simple pendulum depends on its length ($l$) and acceleration due to gravity ($g$). Which of the following is dimensionally consistent with the principle of homogeneity?

Oersted is a unit of

One femtometre is equivalent to

Which of the following equations is dimensionally inconsistent?