If $y$ represents pressure and $x$ represents velocity gradient,then the dimensions of $\frac{d^2 y}{d x^2}$ 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:

$A$ book with many printing errors contains four different formulas for the displacement $y$ of a particle undergoing a certain periodic motion:
$(a) \; y = a \sin \left(\frac{2 \pi t}{T}\right)$
$(b) \; y = a \sin v t$
$(c) \; y = \left(\frac{a}{T}\right) \sin \frac{t}{a}$
$(d) \; y = (a \sqrt{2}) \left(\sin \frac{2 \pi t}{T} + \cos \frac{2 \pi t}{T}\right)$
($a =$ maximum displacement of the particle,$v =$ speed of the particle,$T =$ time-period of motion). Rule out the wrong formulas on dimensional grounds.

Which one of the following combinations of constants has the dimensions of time? $[G=$ gravitational constant,$h=$ Planck's constant,$c=$ velocity of light$]$

From the following,the quantity (constructed from the basic constants of nature) that has the dimensions of length,as well as the correct order of magnitude for a typical atomic size,is:

Which of the following relations cannot be deduced using dimensional analysis? [the symbols have their usual meanings]