$A$ 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 $^{\circ}C$?

Consider two statements $S_1$ and $S_2$.
$S_1$: If $f(x)$ is a differentiable function with $f'(x) = 0$ in $(a, b)$ and $f(x)$ is increasing in $(a, b)$,then $\frac{f(x)}{f'(x)}$ is also increasing in $(a, b)$.
$S_2$: Both $\sin x$ and $\tan x$ are increasing functions in $(0, \frac{\pi}{2})$.
Which of the following is true?

The change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $d$ below the surface of the earth. When both $d$ and $h$ are much smaller than the radius of the earth,then which one of the following is correct?

$A$ spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ $(\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$,i.e.,$F_{viscous} = -kv^2$ $(k > 0)$. The terminal speed of the ball is

$A$ wheel of mass $10 \ kg$ has a moment of inertia of $160 \ kg \cdot m^2$ about its own axis. The radius of gyration will be ....... $m$.

The electric field component of an electromagnetic wave in vacuum is given as $\vec E = 3\cos(1.8y + 5.4 \times 10^8 t)\hat i$. Its direction of propagation and wavelength are: