Units and Measu...

In the equation $${ S }_{ nth }=u+\dfrac { a }{ 2 } \left( 2n-1 \right) $$, the letters have their usual meanings. The dimensional formula of $$S_{nth}$$ is

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 same dimensions ?

Dimensions of rate of change of flux are equivalent to those of 

The dimension of the ratio of magnetic flux and the resistance is equal to that of:

If pressure is (P), velocity (V), and time (T) are taken as the fundamental quantities, then the dimensional formula of force is

In a system of units if force (F), acceleration (A) and time, (T) are taken as fundamental units then the dimensional formula of energy is -

The dimensions of the ratio of angular momentum to linear momentum:

The term $$(1/2)pv^{ 2 }$$ occurs in Bernoulli's  equation , with $$\beta $$ being the density of fluid and V its speed . The dimensions of this term are 

Two resistance are measured in ohm and is given as:-
$${ R }_{ 1 }=3\Omega \neq 1%$$
$${ R }_{ 2 }=6\Omega \neq 2%$$
When they are connectrd in parallel, the percentage error in equivalent resistance is

If the radius of the earth were to shrink by 1% its mass remaining the same, the acceleration due to gravity on the earth's surface would