$A$ centigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers $140^{\circ}F$. What is the fall in temperature as registered by the Centigrade thermometer in $^{\circ}C$?

Find the value of $V_{AB}$ in the given circuit.

An ideal gas is taken around the cycle $ABCA$ as shown in the $P-V$ diagram. The work done during the cycle is

$\int \frac{dx}{1-\cos x-\sin x}$ is equal to

$A$ regular polygon of $n$ sides has $170$ diagonals,then $n$ is equal to

$A$ deflection magnetometer is adjusted and a magnet of magnetic moment $M$ is placed on it in the usual manner and the observed deflection is $\theta$. The period of oscillation of the needle before settling of the deflection is $T$. When the magnet is removed,the period of oscillation of the needle is $T_0$ before settling to $0^{\circ}-0^{\circ}$. If the earth's horizontal magnetic field is $B_H$,the relation between $T$ and $T_0$ is