When the temperature of a black body increases,it is observed that the wavelength corresponding to maximum energy changes from $0.26 \mu m$ to $0.13 \mu m$. The ratio of the emissive powers of the body at the respective temperatures is

An alternating voltage $E = 200 \sqrt{2} \sin(100 t)$ is connected to a $1 \mu F$ capacitor through an $AC$ ammeter. The reading of the ammeter shall be: (in $text{ mA}$)

$A$ particle of mass $m$ moves with a velocity $v$ along the line $PC$ (as shown in the figure). The angular momentum of the particle about point $O$ is:

$\tanh ^{-1}\left(\frac{1}{2}\right)+\operatorname{coth}^{-1}(2)$ is equal to

Name the gas that can readily decolourise acidified $KMnO_4$ solution.

$A$ water barrel having water up to a depth $d$ is placed on a table of height $h$. $A$ small hole is made on the wall of the barrel at its bottom. If the stream of water coming out of the hole falls on the ground at a horizontal distance $R$ from the barrel,then the value of $d$ is