The Davisson-Germer experiment that first demonstrated the wave nature of matter used electrons accelerated to $54 \ V$. Determine the wavelength of the electrons in the Davisson-Germer experiment in $\mathring{A}$.

For a first order reaction at $27^{\circ} C$,the ratio of time required for $75 \%$ completion to $25 \%$ completion of reaction is

$A$ block of mass $1\, kg$ lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is $0.6$. If the acceleration of the truck is $5\, m\, s^{-2}$,the frictional force acting on the block is ........ $N$.

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

$A$ coil of $50$ turns and $4$ cm radius carries $2$ $A$ current. The magnetic field at its centre is ...... mT.

The foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{b^2} = 1$ and the hyperbola $\frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25}$ coincide. Then the value of $b^2$ is -