Total internal reflection of light is possible when light enters from

$A$ parallel plate capacitor of area $A$,plate separation $d$ and capacitance $C$ is filled with three different dielectric materials having dielectric constants $K_1, K_2$ and $K_3$ as shown in the figure. If a single dielectric material is to be used to have the same capacitance $C$ in this capacitor,then its dielectric constant $K$ is given by: ($A =$ Area of plates)

$A$ sound source is moving towards a stationary observer with $1/10$ of the speed of sound. The ratio of apparent to real frequency is

If $u=\sin ^{-1}\left(\frac{x^2+y^2}{x+y}\right)$ then $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is equal to:

If $|a| < 1$ and $b = \sum_{k=1}^{\infty} \frac{a^k}{k}$,then $a$ is equal to

If $p \rightarrow (\sim p \vee \sim q)$ is false,then the truth values of $p$ and $q$ are respectively: