If $x = \log_{5}(1000)$ and $y = \log_{7}(2058)$,then:

An $X$-ray tube produces a continuous spectrum of radiation with its shortest wavelength of $45 \times 10^{-2} \text{ \AA}$. The maximum energy of a photon in the radiation in $eV$ is $(h = 6.62 \times 10^{-34} \text{ J-s}, c = 3 \times 10^8 \text{ m/s})$. (in $27,500$)

In Young's double slit experiment,the $y$-coordinates of the central maximum and the $10^{th}$ maximum are $2\, cm$ and $5\, cm$ respectively. When the $YDSE$ apparatus is immersed in a liquid of refractive index $\mu = 1.5$,what will be the new $y$-coordinates?

The angle of elevation of an object from a point $P$ on the level ground is $\alpha$. Moving $d$ metres on the ground towards the object,the angle of elevation is found to be $\beta$. Then the height (in metres) of the object is

Fossil $X$ is older than fossil $Y$ if

$4 \ g$ of an ideal gas occupies $5.6035 \ L$ of volume at $546 \ K$ and $2 \ atm$ pressure. What is its molecular weight?