$\frac{\sqrt{5/2} + \sqrt{7 - 3\sqrt{5}}}{\sqrt{7/2} + \sqrt{16 - 5\sqrt{7}}} = ?$

$A$ Van de Graaff generator has a spherical metal shell as an electrode which is at a potential $15 \times 10^6 \ V$. If the dielectric strength of the surrounding medium is $5 \times 10^7 \ V \ m^{-1}$,then the diameter of the shell is: (in $cm$)

For the electrochemical cell, $Mg ( s )\left| Mg ^{2+}( aq , 1 M ) \| Cu ^{2+}( aq , 1 M )\right| Cu ( s )$ the standard emf of the cell is $2.70 V$ at $300 K$. When the concentration of $Mg ^{2+}$ is changed to $x M$, the cell potential changes to $2.67 V$ at $300 K$. The value of $x$ is.

(given, $\frac{ F }{ R }=11500 K V ^{-1}$, where $F$ is the Faraday constant and $R$ is the gas constant, The value of $\ln (10)=2.30$ )

Which of the following is the order of maize?

$A$ car is fitted with a convex side-view mirror of focal length $20\ cm$. $A$ second car $2.8\ m$ behind the first car is overtaking the first car at a relative speed of $15\ m/s$. The speed of the image of the second car as seen in the mirror of the first one is

The approximate value of $(1.0002)^{3000}$ is