The half-life of radioactive Radon is $3.8 \ days$. The time at the end of which $1/20^{th}$ of the Radon sample will remain undecayed is ............ $days$ (Given $\log_{10}e = 0.4343$)

If $y=\frac{\log _e x}{x}$ and $z=\log _e x$,then $\frac{d^2 y}{d z^2}+\frac{d y}{d z}$ is equal to

The number of geometrical isomers for octahedral $[Co(NH_3)_2Cl_4]^-$,square planar $[AuCl_2Br_2]^-$ and $[Pt(en)Cl_2]$ are

$A$ parallel plate capacitor with air between the plates has a capacitance of $9 \, pF$. The separation between its plates is $d$. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1 = 3$ and thickness $d/3$,while the other one has dielectric constant $K_2 = 6$ and thickness $2d/3$. The new capacitance of the capacitor is ........ $pF$.

The value of $\sqrt{12\sqrt{5} + 2\sqrt{55}}$ is

An ideal gas is subjected to a cyclic process involving four thermodynamic states. The amounts of heat $(Q)$ and work $(W)$ involved in each of these states are:
$\begin{aligned} & Q_1=6000 \text{ J}, \quad Q_2=-5500 \text{ J}, \quad Q_3=-3000 \text{ J}, \quad Q_4=3500 \text{ J} \\ & W_1=2500 \text{ J}, \quad W_2=-1000 \text{ J}, \quad W_3=-1200 \text{ J}, \quad W_4=x \text{ J} \end{aligned}$
The ratio of the net work done by the gas to the total heat absorbed by the gas is $\eta$. The values of $x$ and $\eta$ respectively are: