Units and Measu...

Dimension of electrical resistance is : 

The velocity $$v$$ of a particle at time$$ t$$ is given by $$\displaystyle v = at + \frac {b} {t + c} $$ where $$a, b$$ and $$c$$ are constants. The dimensions of $$a, b$$ and $$c$$ are respectively :

Which of the following does not have the dimensions of force ?

Two quantities $$A$$ and $$B$$ are related by $$\dfrac{A}{B} = m$$, where $$m$$ is linear density and $$A$$ is force. The dimensions of $$B$$ will be same as that of 

A unitless quantity ?

If the unit of length is doubled the numerical value of Area will become ________ times its original value.

External and internal diameters of a hollow cylinder are measured to be $$(4.23 \pm 0.01)$$ cm and $$(3.89 \pm 0.01)$$ cm. The thickness of the wall of the cylinder is

The pair of quantities that do not have the same dimensions is 

Statement -1: Kinetic energy can be divided by volume 
and
Statement -2: Dimensions of kinetic energy and volumeare different 

In the relation $$\displaystyle P = \frac {\alpha} {\beta} e^{-\dfrac {\alpha Z} {k \theta}} $$, $$P$$ is pressure, $$Z$$ is distance, $$k$$ is Boltzmann constant and $$ \theta $$ is the temperature. The dimensional formula of $$ \beta $$ will be :