The equation of the hyperbola which passes through the point $(2,3)$ and has the asymptotes $4x+3y-7=0$ and $x-2y-1=0$ is

If the pair of lines $ax^2 + 2(a + b)xy + by^2 = 0$ represent the diameters of a circle and divide the circle into four sectors such that the area of one sector is three times the area of the other,then:

On heating a mixture of $SO_2Cl_2$ and $CO$,two equilibria are simultaneously established:
$SO_2Cl_{2(g)} \rightleftharpoons SO_{2(g)} + Cl_{2(g)}$
$CO_{(g)} + Cl_{2(g)} \rightleftharpoons COCl_{2(g)}$
On adding more $SO_2$ at equilibrium,what will happen?

One mole of an ideal monoatomic gas $(\gamma = 5/3)$ is mixed with one mole of a diatomic gas $(\gamma = 7/5)$. What is the $\gamma$ for the mixture? Here,$\gamma$ denotes the ratio of specific heat at constant pressure to that at constant volume.

From a disc of radius $R$ and mass $M$,a circular hole of diameter $R$,whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis,passing through the centre?

$A$ closed hollow insulated cylinder is filled with gas at $0^oC$ and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to $100^oC$. If the piston moves $5\,cm$,the length of the hollow cylinder is ..... $cm$.