The chemical reaction that involves the roasting process is

The wavelengths of electron waves in two orbits is $3: 5$. The ratio of kinetic energy of electrons will be

To which family does $Ricinus$ $communis$ belong?

$A$ body executes simple harmonic motion under the action of a force $F_1$ with a time period $(4/5) \ s$. If the force is changed to $F_2$,it executes $SHM$ with a time period $(3/5) \ s$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body,its time period (in $seconds$) is

$A$ bullet of mass $10 ~g$ is fired horizontally with a velocity $1000 ~ms^{-1}$ from a rifle situated at a height $50 ~m$ above the ground. If the bullet reaches the ground with a velocity $500 ~ms^{-1}$,the work done against air resistance in the trajectory of the bullet is : $(g=10 ~ms^{-2})$ (in $~J$)

If $y=(1+x)(1+x^2)(1+x^4) \dots (1+x^{2^n})$, then the value of $\left(\frac{dy}{dx}\right)_{x=0}$ is