The energy that should be added to an electron to reduce its de Broglie wavelength from $1 \ nm$ to $0.5 \ nm$ is

Which one of the following compounds forms a quaternary salt on reacting with excess methyl iodide?

The cubic unit cell of a metal (molar mass $= 63.55 \ g \ mol^{-1}$) has an edge length of $362 \ pm$. Its density is $8.92 \ g \ cm^{-3}$. The type of unit cell is

The origin is translated to $(1,2)$. The point $(7,5)$ in the old system undergoes the following transformations successively.
$I$. Moves to the new point under the given translation of origin.
$II$. Translated through $2$ units along the negative direction of the new $X$-axis.
$III$. Rotated through an angle $\frac{\pi}{4}$ about the origin of the new system in the clockwise direction. The final position of the point $(7,5)$ is

Gametophyte is the dominant phase in the life cycle of

If ${a^x} = {b^y} = {(ab)^{xy}},$ then $x + y = $