$A$ gramophone record is revolving with an angular velocity $\omega$. $A$ coin is placed at a distance $R$ from the centre of the record. The static coefficient of friction is $\mu$. The coin will revolve with the record if

$A$ block of mass $m$ lying on a rough horizontal plane is acted upon by a horizontal force $P$ and another force $Q$ inclined at an angle $\theta$ to the vertical. The minimum value of the coefficient of friction between the block and the surface for which the block will remain in equilibrium is:

The image of the point $(3, 8)$ in the line $x + 3y = 7$ is

$A$ meter bridge is set up as shown to determine end corrections at $A$ and $B$. When a resistance of $15 \ \Omega$ is used in the left gap and $20 \ \Omega$ in the right gap,the null point is obtained at a distance of $42 \ cm$ from $A$. When these resistances are interchanged,the null point is obtained at a distance of $57 \ cm$ from $A$. The values of the end corrections are:

Which relation is incorrect?

If $\theta = \frac{\pi}{6}$,then the $10^{th}$ term of the series $1 + (\cos \theta + i \sin \theta) + (\cos \theta + i \sin \theta)^2 + (\cos \theta + i \sin \theta)^3 + \dots$ is equal to: