$A$ thin liquid film formed between a $U$-shaped wire and a light slider supports a weight of $1.5 \times 10^{-2} \ N$ (see figure). The length of the slider is $30 \ cm$ and its weight is negligible. The surface tension of the liquid film is (in $N/m$)

The diagram shows a force-extension graph for a rubber band. Consider the following statements:
$(I)$ It will be easier to compress this rubber than expand it.
$(II)$ Rubber does not return to its original length after it is stretched.
$(III)$ The rubber band will get heated if it is stretched and released.
Which of these can be deduced from the graph?

In a binomial distribution, the probability of success is $\frac{1}{4}$ and the standard deviation is $3$. Then, its mean is

If the momentum of an electron is changed by $\Delta p$,then the de-Broglie wavelength associated with it changes by $0.50\%$. The initial momentum of the electron will be

Which of the following elements forms a stable $+4$ oxidation state?

$A$ $Ge$ specimen is doped with $Al$. The concentration of acceptor atoms is $\sim 10^{21} \text{ atoms}/m^3$. Given that the intrinsic concentration of electron-hole pairs is $\sim 10^{19} /m^3$,the concentration of electrons in the specimen is: