$\lim _{x \rightarrow 0} \frac{\sqrt{1+x^2}-\sqrt{1-x+x^2}}{3^x-1}$ is equal to

$A$ wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to the current,the temperature of the wire is raised by $\Delta T$ in time $t$. $N$ number of similar cells is now connected in series with a wire of the same material and cross section but of length $2L$. The temperature of the wire is raised by the same amount $\Delta T$ in the same time $t$. The value of $N$ is:

The distance between the parallel lines given by $(x+7y)^2 + 4\sqrt{2}(x+7y) - 42 = 0$ is

The number of photo-electrons emitted per second from a metal surface increases when

Which of the following statements are correct for alkali metal compounds?
$(i)$ Superoxides are paramagnetic in nature.
$(ii)$ The basic strengths of hydroxides increase down the group.
$(iii)$ The conductivity of chlorides in their aqueous solutions decreases down the group.
$(iv)$ The basic nature of carbonates in aqueous solutions is due to cationic hydrolysis.

For intensity $I$ of a light of wavelength $5000 \mathring{A}$,the photoelectron saturation current is $0.40 \mu A$ and the stopping potential is $1.36 V$. The work function of the metal is ............. $eV$.