$A$ black body has a maximum wavelength ${\lambda _m}$ at a temperature of $2000 \; K$. Its corresponding wavelength at a temperature of $3000 \; K$ will be:

Two point charges $+8q$ and $-2q$ are located at $x = 0$ and $x = L$ respectively. The location of a point on the $x$-axis at which the net electric field due to these two point charges is zero is

The ratio of angular speeds of the minute hand and the hour hand of a watch is:

At a certain temperature,$\operatorname{rod} A$ and $\operatorname{rod} B$ of different materials have lengths $L_A$ and $L_B$ respectively. Their coefficients of linear expansion are $\alpha_A$ and $\alpha_B$ respectively. It is observed that the difference between their lengths remains constant at all temperatures. The ratio $L_{A}: L_{B}$ is given by

The compound,found in nature in gas phase but ionic in solid state is

The vector diagram of current and voltage for a circuit is as shown. The components of the circuit will be