Consider the equation `[|x-1|-|x+2|=p`.Let `rho` be the value of `rho` for which the equationOne solution. Also `rho_2`, is the value of `rho` for which the equation has infinite solution.Let a be the sum of all the integral values of `rho` for which this equation has solution `rho` , is equal to

The sum of all positive integral values of a , where a in[1,500] for which the equation [x]^(3)+x-a=0 has a solution is:

rho is such a relation on the set real numbers RR where x rho y if and xy gt 0 . Then which of the following is / are true ?

Consider the following equation of Bernoulli's theorem. P + (1)/(2) rho v^(2) + rhogh = K (constant) The dimensions of K/P are same as that of which of the following

Write the limitations of dimensions and obtain the values of a,b and c in the equation TpropP^(a)rho^(b)E^(c) where, T is time, P is pressure E is energy and rho is density.

An ideal gas equation can be written as P = rho R T/ M_0 where rho and M are resp.

An ideal gas equation can be written as P = rho R T/ M_0 where rho and M are resp.

A thin uniform circular tube is kept in a vertical plane. Equal volume of two immiscible liquids whose densites are rho_(1) and rho_(2) fill half of the tube as shown. In equilibrium the radius passing through the interface makes an angle of 30^(@) with vertical. The ratio of densities (rho_(1)//rho_(2)) is equal to

A thin uniform circular tube is kept in a vertical plane. Equal volume of two immiscible liquids whose densites are rho_(1) and rho_(2) fill half of the tube as shown. In equilibrium the radius passing through the interface makes an angle of 30^(@) with vertical. The ratio of densities (rho_(1)//rho_(2)) is equal to

The densities at points A and B are rho_(0) and (3 rho_(0))/(2) . Find the value of x on P-axis.

Three liquids of densities rho_1rho_2and rho_3 (with rho_1>rho_2>rho_3) , having the same value of surface tension T, rise to the same height in three identical capillaries.The angles of contact theta_1 theta_2 and theta_3 obey