If the angles of dip at two places are $30^o$ and $45^o$ respectively,then the ratio of horizontal components of earth's magnetic field at the two places will be

If $R = \{ (x, y) | x, y \in Z, x^2 + y^2 \le 4 \}$ is a relation in $Z$,then the domain of $R$ is

Two spheres each of mass $M$ and radius $\frac{R}{2}$ are connected at their centres with a massless rod of length $2R$. What will be the moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod?

If the pair of lines given by $(x^2+y^2) \cos^2 \theta = (x \cos \theta + y \sin \theta)^2$ are perpendicular to each other,then $\theta$ is equal to

An ideal gas undergoes a quasi-static, reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $P$ and volume $V$ is given by $PV^n = \text{constant}$, then $n$ is given by (Here $C_P$ and $C_V$ are molar specific heat at constant pressure and constant volume, respectively).

The radius of the circle $r = 12 \cos \theta + 5 \sin \theta$ is